Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: timey on 04/10/2016 03:41:08
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Can this relationship be derived between Schrödinger equation and Doppler shift equation?
Looking at Chladni plates and the resulting node patterns versus a laser beam trained on a mirror super glued to a speaker cone, causing the dot of the laser beam to form a pattern when a tone/frequency is applied - could there be a relationship between node patterns and lissajous curves?
Let's say we have a Chladni plate of a reflective/mirrored surface, and having established node patterns at varying frequencies, would lissajous curves (?) be established at the same frequencies by pointing a laser at the surface?
And considering that the node pattern is caused at the points of least vibration of that frequency, and that the laser is depicting movement caused by the extremities of the vibration of that frequency - could it be said that the patterns created are the inverse of each other?
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could there be a relationship between [Chladni] node patterns and lissajous curves?
Chladni patterns (https://en.wikipedia.org/wiki/Ernst_Chladni#Chladni_figures) are caused by the resonance of a physical object when subjected to a drive at a single frequency. This highlights the areas of high and low amplitude vibrations in the plate.
Lissajous figures (https://en.wikipedia.org/wiki/Lissajous_curve#Examples) are created when you drive a light by two different frequencies in the X and Y axes, where those frequencies are harmonically related to each other.
They can both produce interesting patterns, but they are different patterns.
Can this relationship be derived between Schrödinger equation and Doppler shift equation?
The Chladni patterns are derived from physical resonances of a macroscopic object with varying shape, thickness and (in the case of wooden instruments) the wood grain, glue, bracing struts, lacquer and sound holes. By varying the frequency of the incoming sound, you could graph the spectral response of resonances to the incoming sound.
Doppler shift of a laser beam can be used to measure the frequency of vibration of the object from which it is reflected. By graphing this in two dimensions, you could reconstruct the Chladni pattern.
Schrödinger's equation describes the electron energy levels of an atom. By exciting the atom with difference frequencies of light, you could graph the spectral response of resonances to the incoming light.
You may try (with great difficulty) to construct an instrument that has similar resonances to the Hydrogen spectrum. If the Hydrogen spectrum had energy levels related to 1/n, this may even be compatible with the Pythagorean ideal of harmony.
However, the actual energy levels of Hydrogen are related as 1/n2, so the harmony could be described at best as "complex", but most people would just call it "noise".
See: https://en.wikipedia.org/wiki/Rydberg_formula#Rydberg_formula_for_hydrogen
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Doppler shift of a laser beam can be used to measure the frequency of vibration of the object from which it is reflected. By graphing this in two dimensions, you could reconstruct the Chladni pattern.
It is this part of what you say that is of most interest to me, but first:
With regards to the Chladni plate node patterns...
You say that Lissijous curves or figures are caused by the harmonics created by driving 2 frequencies, but that the node patterns on the plate are caused by driving only 1 frequency... Lets examine this a bit.
Here we see that there are 4 differently structured plates being used. If you hang each plate as a gong and hit it with a gong striker, each plate will have its own naturally occurring frequency. As far as I can tell, please correct me if wrong, what the bow is doing is adding another frequency to the plate that resonates with the plates natural frequency. As the video shows, by bowing at different placements of the rim of the plate, the bow can add one of a few different frequencies which resonate/harmonise with the plates natural frequency. But there are only so many frequencies that will harmonise with the plates own natural frequency. Note how the placement of thumbnail on an exterior line of the node pattern, and the placement of the bow on, or between node lines changes the pitch in steps.
Here we can see that this plate structure can only cause node patterns when subject to certain frequencies. The frequencies that can achieve node patterns on this structure are surely mathematically linked to the structures own natural frequency? Are all the frequencies that create node patterns on this structure following scale to the structures own frequency?
If so then the Chladni pattern is also created by driving 2 frequencies to harmonise/resonate, surely?
Correct me if I'm wrong but these laser patterns must be caused by Doppler shift right?
To get further understanding I watched the above. Please note the use of the timing function.*
Correct me if I am wrong, but isn't the node pattern's association with Schrödinger due to standing wave function in that a wavelength can only fit x amount of times within a confine?
https://en.m.wikipedia.org/wiki/Wave_function_collapse
Quote:
"Significantly, the combined wave function of the system and environment continue to obey theSchrödinger equation.[4]"
Unquote:
* http://physics.stackexchange.com/questions/29551/quantum-explanation-of-doppler-effect
The second answer in relation to the first is interesting in relation to SR comments and time perturbations.
As you pointed out, node patterns are created in the areas of least vibration in the plate.
The Lissijous patterns are being created by the extremities of the vibration of the mirror.
I realise, as you have pointed out, that the patterns are not the same patterns, but given that each produced a pattern associated with the same frequencies, it interested me if one would be the inverse of the other?
So... If the Lissijous pattern is being caused by the Doppler shift of the laser beam, how would one mathematically graph this in two dimensions to reconstruct the Chladni pattern?
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As far as I can tell, please correct me if wrong, what the bow is doing is adding another frequency to the plate that resonates with the plates natural frequency. As the video shows, by bowing at different placements of the rim of the plate, the bow can add one of a few different frequencies which resonate/harmonise with the plates natural frequency.
The bow doesn't add a frequency, it adds vibrational energy that allows the plate to resonate at one of its natural frequencies. Each frequency creates a different pattern caused by the standing waves. Lower order modes - those with fewer node lines - require less energy to initiate them, the simplest and lowest order being the cross/star pattern, which occurs at the lowest frequency. By bowing with differing amounts of force, ie energy, the bower can cause higher order modes to appear, you will also note that he uses his thumb nail to force a node at certain locations which produces a different mode and can bow at different points to encourage different antinodes.
What isn't clear from these videos is that the patterns are more complex than they appear at first sight. Although we see only antinodes, one antinodes might be going up while another goes down. Sometimes adjacent corners will move in opposite directions as the plate twists.
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OK - I'm following your logic, and agree that there is evidence in the video that suggests that some of the complexity of how the patterns change from one to another is lost...
But Colin, isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency? Energy has a frequency, right? Bowing with added energy, or at a placement on the edge of the plate that causes higher or lower energy, or by placing a thumbnail at a node point to alter the distribution of the added energy, these energies are all accompanied by their associated frequencies. Note that some of the bowing ie: added energy/frequency does not cause node patterning. The bowing has to be just so, or a tone/node pattern cannot be achieved.
In the second video it is shown that frequencies are being driven to the plate directly. This can also be considered to be a case of adding vibrational energy, but the machine kindly translates this added energy into its associated frequency for us. Note that the node patterns are only formed fully at specific frequencies, albeit some of the complexity as the patterns change seems to be lost.
My thoughts drifting towards thinking (subject to being wrong of course) that these specific frequencies that the patterns are fully formed at are harmonics to the plates own frequency. A frequency that is related to the plates own energy of e=mc^2.
So in light of what I've mentioned, do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
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do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
I was thinking of exciting the vibrations with a sine-wave generator, which is just 1 frequency.
If you were adding energy with a violin bow, I guess you could imagine a rectangular plate with sides in a 3:1 ratio.
If you bowed near a corner, I guess you could set up vibrations which are harmonically related in different axes, and use that to produce Lissajous figures.
Even when you are bowing a violin string, it is normal to produce several harmonics in the same string, simultaneously.
If you activated the Chladni pattern with a loudspeaker, you could feed in two different tones to excite two different resonances at the same time.
isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency?
Colin is the luthier here, but my simple understanding is that the keratin flakes of the horse-hair have a sawtooth edge, which repeatedly pulls and releases the string (or plate, in this case). This represents a fairly broadband stimulation of any resonances.
These frequent small knocks can build up into a large oscillation at the natural resonant frequency of the object.
- I assume the location, pressure, speed and direction of the bowing can accentuate or inhibit particular vibration frequencies.
- Or it can produce a chaotic screech, like most beginner violin players...
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My thoughts drifting towards thinking (subject to being wrong of course) that these specific frequencies that the patterns are fully formed at are harmonics to the plates own frequency. A frequency that is related to the plates own energy of e=mc^2.
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So in light of what I've mentioned, do you think a Chladni plate pattern is involving 2 frequencies, like the Lassijous figures do, or is it just 1 frequency?
You're in the right direction but veering off to left field.
I may have assumed understanding of what vibrational modes involve, so perhaps we need to step back a bit.
Let's take the standard vibrating string in every school textbook. Fixed at both ends if we pluck the middle we get that characteristic shape of antinode in the middle and nodes at each end. You might be excused for thinking that the centre of the string is just moving up and down, but it's more complex than that. As Evan says, all vibrations of this type involve more than one frequency, in this case when plucked at the centre the string will vibrate in all modes where there is an antinode at the centre and nodes at each end and if you draw them out you will find they are the odd harmonics of the string fundamental. In theory you should have all the odd frequencies, but as fourier analysis shows the components of a square wave are the odd harmonics up to infinity and the mechanics of the string mean that it can't support all the harmonics. If you superpose the harmonics up to about 9 you will get an envelope very similar to the one in the textbooks showing the average excursion of the points along the string – average excursion because the harmonics get out of phase so the string ends up doing some interesting contortions rather than the implied moving up and down at the centre.
Plucking at different points eg ¼ along the string, will excite a different series of harmonics.
When you look at analysing the Chladni plates you can view them as 2 dimensional open ended pipes – antinodes at the outer edge. As with strings, vibrating pipes and plates all generate multiple frequencies, but it is the mix of frequencies that give the specific patterns on the plates.
isn't stating the bowing adding an energy to the situation in as much as saying the bow is adding a frequency?
As you can see from the string example, plucking doesn't add a frequency if just allows the string to vibrate in its natural manner.
Let's look at a simple plate, a school ruler. If you hold one end on the desk and twang the end the ruler will vibrate at its natural frequency. If you bow the end of the ruler (ie plate) the rosin on the bow grips the end of the ruler and pushes it down, when the return force of the spring in the ruler overcomes the grip of the bow the ruler springs back and again will vibrate at its natural frequency.
The bow isn't adding a frequency, you could just as easily twang the edge of the Chladni plate or tap it with a stick, all would cause it to vibrate in a particular mode depending on where you hit it. However, you would have to twang it a lot of times before the sand moved to the nodes, the bow or a loudspeaker is easier.
E=mc2? No. There is mass of the plate, which affects the frequency of the modes. There is a speed which is the wave speed of sound across the plate, that is largely determined by E, Young's Modulus. But we aren't dealing here with mass energy equivalence, much more basic.
Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger equation is a very specific wave analysis not part of the analysis of string and plate vibrations.
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Colin - although your description of harmonics is highly relevant, it is something that will be obvious to anyone who has played a string instrument (Yup, I was a screechy violinist as a child Evan...(chuckle)) ...or inspected the inner workings of a piano, which I do and have.
(although I must say, in that I have worked with music, that I was literally horrified when watching the oscilloscope video at the extent of that which I didn't know and probably still don't know...)
No instrument makes a sound of itself. An instrument always requires an input of vibration to resonate with. All vibrations have an associated frequency, and all a frequency is, is the amount of vibrations per standard second.
Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger equation is a very specific wave analysis not part of the analysis of string and plate vibrations.
What you are saying here is not really correct. Please see link:
https://en.m.wikipedia.org/wiki/Ernst_Chladni
Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:
If this venture into advanced mathematics is being off left side then off left side is exactly where I want to be...
A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.
A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?
I am looking for the mathematical relationship between these patterns and am thinking that "phase shift' might be relevant?
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Colin - although your description of harmonics is highly relevant, it is something that will be obvious to anyone who has played a string instrument (Yup, I was a screechy violinist as a child Evan...(chuckle)) ...or inspected the inner workings of a piano, which I do and have.
(although I must say, in that I have worked with music, that I was literally horrified when watching the oscilloscope video at the extent of that which I didn't know and probably still don't know...)
No instrument makes a sound of itself. An instrument always requires an input of vibration to resonate with. All vibrations have an associated frequency, and all a frequency is, is the amount of vibrations per standard second.
Schrodinger? Well, the mathematical tools used in acoustic analysis eg fourier analysis, eigenvalues etc are all part of QM, but the Shrodinger equation is a very specific wave analysis not part of the analysis of string and plate vibrations.
What you are saying here is not really correct. Please see link:
https://en.m.wikipedia.org/wiki/Ernst_Chladni
Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:
If this venture into advanced mathematics is being off left side then off left side is exactly where I want to be...
A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.
A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?
I am looking for the mathematical relationship between these patterns and am thinking that "phase shift' might be relevant?
Well done.
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A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.
A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?
Lots of muddled thinking here.
Chladni figures are the inverse distribution of amplitude over a resonating body, and can in some cases resemble atomic orbitals.
Lissajous figures are the patterns produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. Where the frequencies are in a harmonic relationship such that the phases of the two curves are locked, the figure appears static. Nothing to to with resonance or orbitals, just the 2D solution of two simultaneous equations. And although not truly Lissajous, you can use a similar XY plot on an oscilloscope to investigate the phase relationship of any two periodic signals.
The Doppler shift equation is a scalar only. df/f = v/c where df is the change in observed frequency, v is the relative velocity of source and observer, and c is the velocity of sound/light/whatever. No sinusoids or spatial coordinates.
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What you are saying here is not really correct. Please see link:
https://en.m.wikipedia.org/wiki/Ernst_Chladni
Quote:
" In quantum mechanics, Chladni figures ("nodal patterns") are known to be related to the solutions of theSchrödinger equation for one-electron atoms, and the mathematics describing them was used by Erwin Schrödinger to arrive at the understanding of electron orbitals.[12]"
Unquote:
Yes, I know the history which I why I made the comment about the commonality of the maths tools. However, as I said the Shrodinger equation has a very specific application and you can't turn it round and use it to analyse Chladni patterns or reach conclusions about Doppler shift on the laser beam. As Evan pointed out:
Schrödinger's equation describes the electron energy levels of an atom. By exciting the atom with difference frequencies of light, you could graph the spectral response of resonances to the incoming light.
You may try (with great difficulty) to construct an instrument that has similar resonances to the Hydrogen spectrum. If the Hydrogen spectrum had energy levels related to 1/n, this may even be compatible with the Pythagorean ideal of harmony.
However, the actual energy levels of Hydrogen are related as 1/n2, so the harmony could be described at best as "complex", but most people would just call it "noise".
Returning to your original question:
..considering that the node pattern is caused at the points of least vibration of that frequency, and that the laser is depicting movement caused by the extremities of the vibration of that frequency - could it be said that the patterns created are the inverse of each other?
Pointing a single laser at the mirror surface won't create an inverse of the pattern as you need a way of mapping the areas of maximum displacement (as the inverse of the map of nodes), however you could use laser holography to do it.
PS We'll have to agree to disagree on whether the bow is inputting a frequency or just activating the natural resonance modes of the plate.
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A Chlani plate node pattern relates to the Schrödinger equation - and the Lissijous figures, by the nature of the mechanics that are involved in their creation, must relate to the Doppler shift equation.
A node pattern is caused at the areas of least vibration.
A Lissijous figure is caused by the areas of most vibration.
The question being: Could node patterns be the opposite, or inverse, of Lissijous figures?
Lots of muddled thinking here.
Chladni figures are the inverse distribution of amplitude over a resonating body, and can in some cases resemble atomic orbitals.
Lissajous figures are the patterns produced by the intersection of two sinusoidal curves the axes of which are at right angles to each other. Where the frequencies are in a harmonic relationship such that the phases of the two curves are locked, the figure appears static. Nothing to to with resonance or orbitals, just the 2D solution of two simultaneous equations. And although not truly Lissajous, you can use a similar XY plot on an oscilloscope to investigate the phase relationship of any two periodic signals.
The Doppler shift equation is a scalar only. df/f = v/c where df is the change in observed frequency, v is the relative velocity of source and observer, and c is the velocity of sound/light/whatever. No sinusoids or spatial coordinates.
Sorry, no muddled thinking here on my part. You just have not bothered to read the thread and therefore are unaware of the context.
Please read post 2 and observe the videos that have already outlined what you have posted, and the link to physics stack exchange and answer 2 in relation to answer 1, which will give you the context. I am thinking that phase shift is the common ground.
There are some outstanding issues that are a bit muddling though and perhaps you can indeed help.
The first being:
-is a Chladni plate being driven to resonance by 2 frequencies? ie: its own inherent frequency/tone resonating with the frequency associated with the input energy... to create harmonics of the plates natural frequency as the input frequency is increased. Or is there just 1 frequency involved in a Chladni pattern, as Colin says?
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Back to the "frequency" of a chladni plate. It doesn't have an inherent single frequency. All that is required of a vibrating plate is that there is a node(s) at the point(s) of suspension. You can then, in principle, set up any number of standing waves whose nodes correspond, by bashing it hard enough. Continuous input to a symmetrcal plate by a violin bow will select for those harmonics with antinodes at the point of contact. If you are very good at bowing, you can select just the fundamental of a circular plate, which will give you a circular pattern with a single frequency only.
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When the plate is not being vibrating, (ie: does not have an input) the structure already contains standing waves...doesn't it?
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When the plate is not being vibrating, (ie: does not have an input) the structure already contains standing waves...doesn't it?
No, there is no standing wave until the plate is vibrating at the specific resonant frequency for that standing wave(s).
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So the plate does not have an energy associated with its mass, and De Broglie matter waves are only mathematical conveniences with which to calculate quantum probabilities?
Or do you mean that there is no visible evidence of standing waves in the structure until an input frequency resonates with one or more of the inherent standing waves harmonics...
Otherwise what in the plate is the input resonating with please?
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So the plate does not have an energy associated with its mass, and De Broglie matter waves are only mathematical conveniences with which to calculate quantum probabilities?
I don't see the relevance of this. We don't need to use quantum level calculations to calculate vibrations in large scale structures. Of course the plate has an energy associated with its mass, but we are not looking to convert any of that mass to energy or vise versa, neither are we interested in its relativistic kinetic energy.
Or do you mean that there is no visible evidence of standing waves in the structure until an input frequency resonates with one or more of the inherent standing waves harmonics...
No, I mean that there are no standing waves until the plate vibrates. Standing waves are vibrations, they are the characteristic patterns of the resonances.
The input frequency does not resonate with anything, it is the plate which resonates at certain frequencies. The input frequency doesn't change its form.
Otherwise what in the plate is the input resonating with please?
I think there is a confusion of terminology here and understanding of resonance so it might help to step backwards and forget about input frequencies for a moment.
Imagine you ping the edge of the plate with a plectrum. The plectrum pushes down the edge and releases it, the speed at which the edge returns towards its undeformed position will determine the frequency at which the plate 'rings', this speed is in turn determined by the stiffness of the plate (its springyness) and its mass (inertia) and the dimensions of the plate. This is an oversimplification, but it is intended to illustrate that there is nothing inside the plate which resonates, but it is the plate itself - governed by its physical characteristics - which resonates. Also, it does not need an input frequency in order to resonate just some action to set it going.
The use of a loudspeaker as an initiator is useful because it provides a continuous stimulus and also allows us to see at which frequencies the resonances occur.
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I understand your take in the sense of analysing sound Colin, but what I'm interested in is the relationship between the Chladni patterns and the Schrödinger equations, the related analysis of wave function at quantum level, the relationship that the Lorentz transformations have in relation to Doppler shift at quantum level, the time perturbations that are used to calculate at quantum level...
And the relationship that Lissajous figures have with the electron.
Any energy added at this level is significant to frequency and therefore is relevant to standing wave function. The properties of the plate are significant because they are quite simply properties that are inherent to the plate and these properties affect the effects of any input energy. (Energy mass equivalence asside for time being)
Here we can see that Lissajous figures can also be traced out by sand dripping from a compound pendulum.
https://www.britannica.com/topic/Lissajous-figure
http://www.differencebetween.com/difference-between-simple-pendulum-and-vs-compound-pendulum/
Quote:
" What is the difference between Simple and Compound Pendulums?
• The period and, therefore, the frequency of the simple pendulum depends only on the length of the string and the gravitational acceleration. The period and the frequency of the compound pendulum depend on the length of gyration, the moment of inertia, and the mass of the pendulum, as well as the gravitational acceleration.
• The physical pendulum is the real life scenario of the simple pendulum."
Unquote:
An apparatus of frequency vibrated mirrors causing a laser beam to trace out Lissajous figures is physically equal to the actions of a compound pendulum...
Lets say the mirror was engineered to be resonant at a pure tone (the same tone as was used to create the Lissajous figure) and sand were placed on the mirror being vibrated (at same other tone that created the Lissajous figure) ...then a Chladni pattern would emerge...?
And if so, what would the mathematical relationship be?
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...it is the relationship between the Chladni patterns and the Schrödinger equations, the related analysis of wave function at quantum level, the relationship that the Lorentz transformations have in relation to Doppler shift at quantum level, the time perturbations that are used to calculate at quantum level...
And the relationship that Lissajous figures have with the electron.
Ok, I may have misunderstood what you are trying to do here. It sound like you are trying to draw some conclusions about actions at the atomic level using chladni, lissajou and Doppler, rather than trying to use shrodinger, e=mc2, etc to analyse the plates.
Here we can see that Lissajous figures can also be traced out by sand dripping from a compound pendulum.
This type of compound pendulum is in fact 2 simple pendulums linked, one oscillates as a sine wave in x direction the other in y so that their combined motion is the lissajou curve. Sorry to labour this but it is important to recognise that the curves are the result of combining 2 pure sinewaves.
An apparatus of frequency vibrated mirrors causing a laser beam to trace out Lissajous figures is physically equal to the actions of a compound pendulum...
Yes, you could cause the mirror to vibrate on 2 axes perpendicular to each other across the face of the mirror, each axis would need to vibrate with a sinewave.
Lets say the mirror was engineered to be resonant at a pure tone (the same tone as was used to create the Lissajous figure) and sand were placed on the mirror being vibrated (at same other tone that created the Lissajous figure) ...then a Chladni pattern would emerge...?
And if so, what would the mathematical relationship be?
To create a lissajou figure you need 2 sinewaves not one.
The plates do resonate at more than one frequency and it is possible to make them resonate at 2 frequencies simultaneously by feeding 2 tones into a loudspeaker.
If you take the example of the basic mode of a square plate, free at the edges (I think you used this eg somewhere) at one frequency the pattern is a cross with nodes at the centre of each face, at a second frequency the pattern is a cross with the nodes at the corners of the plate. If you force the plate to vibrate at both of these frequencies simultaneously you will get a combination of the 2 patterns i.e. 2 superimposed stars.
You could also try building a plate in the same proportion as the lissajou frequencies so that the resonating length/width is the same as the ratio of the sinewaves e.g. 2:1. In this case the rectangular plate pattern is a simple 2 nodes across the width of the plate dividing it into 3 antinodes - the ends go up and the centre goes down etc, this is the same pattern as a rectangular bar. Also this pattern doesn't change with the ratio of width to length unlike the lissajou figure.
The fact is that the lissajou curves and the chladni patterns are 2 different phenomena, giving us different information.
If you want to try applying lissajou curves to qm perhaps you ought to look for related frequencies, say, 2 harmonic oscillators to see whether they exhibit something similar to the curves.
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Yes Colin - you are on the right track, but let me more fully explain my direction...
The Chladni patterns are already connected to the Schrödinger equation. Schrödinger used the mathematics of Chladni patterns to work out the atomic orbital of the electron.
The Schrödinger equation is related to the Doppler shift equation via the Lorentz transformations, and perturbations of time are used to calculate the probability of quantum actions.
The common ground in these instances is phase shifting of either space or time.
In that Lissajous patterns can be created by reflected light being vibrating off a mirror, and this is almost synonymous to the Pound Rebka gamma ray emitter being vibrated by frequency tones creating a Doppler shift in the test signal of the experiment - Lissajous figures must have some relationship with the Doppler shift equation and therefore a connection to the gravitational shift equation.
This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.
Lissajous figures also relate to the electron via memoristor and are 'already' connected to quantum.
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Yes - you are entirely correct... I won't actually be doing this myself because I haven't got a pot to p*ss in and I'd sooner see a dinner on my plate, but yes it would be possible to create a plate that, much like xylophone notes, are engineered to resonate at a pure tone... Inputting that plate with another frequency that is known to create a Lissajous figure when combined with this pure tone, the Chladni pattern that emerges on the plate will not be the same pattern as a the Lissajous figure, but both patterns, in that they are corresponding to the use of the same frequencies, will have a mathematical relationship - and that relationship would be very interesting.
By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
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This is the wrong question anyway. How does negative kinetic energy relate general relativity to quantum mechanics?
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Perhaps, but while not detracting from Dirac's contribution, on the basis that the knee bone is connected to the thigh bone, the question could also be a lot of things, the most direct form of which being: Can quantum and the standard model be united with gravity?
I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...
Never mind or not the notion of 'how' a Chladni plate pattern is created, just 'what' the pattern is and the mathematics of the points of least vibration, I would have thought that it wouldn't be that much of a mathematical venture to analyse Lissajous patterns as to the points of least vibration on the basis that the pattern is being created from the points of most vibration?
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The coincidence of mathematical models does not necessarily indicate any fundamental connection between the phenomena they model. Tide tables look like (indeed are) multiple superpositions of sine waves and the Southampton tide in particular looks like a simple Lissajous figure as the primary Atlantic tide is modulated by the Isle of Wight, but you'd have a hell of a job predicting it from the shape of hydrogen bonds in seawater.
The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone - almost the opposite. If you apply a drive current I = a sin(ft) where a is the amplitude and f is a frequency within the linear single mode response of the cone (i.e a low frequency), the velocity of the cone at any time t is a cos (ft). If you use a phase-sensitive detector to correlate the received signal with I you can find the value of t that produces maximum signal and hence calculate the critical Doppler velocity.
The universe is made up of zillions of things (some of which we have never observed) all interacting with each other in umpteen ways (some of which we don't understand). Physics equations rarely invoke more than sine waves and x^2, so they tend to be a bit repetitive: representing the entire orchestra, choir and cathedral acoustics with one bar of dots doesn't equate Lloyd Webber with Haydn.
When you do succeed, I will of course be delighted to have that sentence quoted in your Nobel speech, but if I wanted to produce a predictive model of quantum gravity, I wouldn't start with Doppler or Chladni.
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I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...
Sorry, been very busy for other than short answers. Will respond when I get a moment.
Need to continue in new theories as your posts have moved a long way over there.
Edit - aAlan responded while I was typing, but my thoughts are similar. I'll try to go through later.
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I notice that nobody has commented to confirm or deny my observations on the difference between the physical mechanics creating these patterns...
Sorry, been very busy for other than short answers. Will respond when I get a moment.
Need to continue in new theories as your posts have moved a long way over there.
Edit - aAlan responded while I was typing, but my thoughts are similar. I'll try to go through later.
Hey Colin - no need for apology.
Actually the question "Can quantum and the standard model be united with gravity?" ...is older than I am, but New Theories is OK with me.
http://www.physicsclassroom.com/class/sound/Lesson-4/Standing-Wave-Patterns
It clearly states in this link that all objects resonate with their own natural frequency or frequencies. That it is driving these natural frequencies with an outside source that causes standing waves. That the patterns are only created within the medium at specific frequencies of vibration. And these specific frequencies are harmonics of the natural frequencies of the object.
Therefore since 1 frequency is being driven with another frequency, there 'must' be 2 frequencies involved in creating the Chladni pattern.
Is there anybody reading who can agree on this point?
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The coincidence of mathematical models does not necessarily indicate any fundamental connection between the phenomena they model. Tide tables look like (indeed are) multiple superpositions of sine waves and the Southampton tide in particular looks like a simple Lissajous figure as the primary Atlantic tide is modulated by the Isle of Wight, but you'd have a hell of a job predicting it from the shape of hydrogen bonds in seawater.
The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone - almost the opposite. If you apply a drive current I = a sin(ft) where a is the amplitude and f is a frequency within the linear single mode response of the cone (i.e a low frequency), the velocity of the cone at any time t is a cos (ft). If you use a phase-sensitive detector to correlate the received signal with I you can find the value of t that produces maximum signal and hence calculate the critical Doppler velocity.
The universe is made up of zillions of things (some of which we have never observed) all interacting with each other in umpteen ways (some of which we don't understand). Physics equations rarely invoke more than sine waves and x^2, so they tend to be a bit repetitive: representing the entire orchestra, choir and cathedral acoustics with one bar of dots doesn't equate Lloyd Webber with Haydn.
When you do succeed, I will of course be delighted to have that sentence quoted in your Nobel speech, but if I wanted to produce a predictive model of quantum gravity, I wouldn't start with Doppler or Chladni.
Alan - It is a text book fact that Schrödinger used the mathematics of Chladni patterns to work out the atomic orbital of the electron. It is also a text book fact that Lissajous patterns have a connection to the electron. Asking questions of coincidences in physics such as this is not irrelevant, although clearly questions asked may turn out to be irrelevant. However, without asking the questions one would not know the answers, and even questions being found to have no relevance has relevance in itself.
You said:
"The use of a sine wave drive in the Pound-Rebka experiment has nothing to do with resonance or interference in the loudspeaker cone"
Correct. Its the actions of the speaker cone vibrating the gamma ray emitter (Pound Rebka), the laser dot on mirror (Lissajous figures), that cause Doppler shift.
I'm looking at the difference in these Chladni and Lissajous patterns as being due to opposite phase shifting.
Opposite phase shifting becomes relevant to what I am saying with my theory of time and the fact that physics measures physical actions via the standard second, and my theory states the t of any mass situation as being t is equal to the phase period of its f, and any space situation as being t is equal to the phase period of the hypothetical f of the energy of the gravity field at distance from mass.
Much to my disappointment though Alan, my experience with you has led me to the understanding that if it's not already written in a text book, or is not something that yourself and Kibblewhite discussed, then it would seem to be not something that you are capable of considering without prejudice.
So Chladni patterns and Doppler shift is not where you would start in a quest to unite quantum with gravity... Just for the record, where exactly did "you" start from then?
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There is no essential connection between Lissajous and Doppler. Your connection between Lissajous and the electron would be interesting to discover. Whatever you do in science, don't confuse the mathematical model with the reality - especially if the model is continuous and the reality is quantised.
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It clearly states in this link that all objects resonate with their own natural frequency or frequencies. That it is driving these natural frequencies with an outside source that causes standing waves. That the patterns are only created within the medium at specific frequencies of vibration. And these specific frequencies are harmonics of the natural frequencies of the object.
That's the point ive been trying to make all along. It is the sum of these harmonics that causes the standing waves. You don;t need a second frequency, and the outside source doesnt need a frequency component - think blowing across the top of a bottle, yiu are only blowing not whistling or huming a frequency. You may have missed what I was saying or Im not explaining clearly enough.
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There is no essential connection between Lissajous and Doppler. Your connection between Lissajous and the electron would be interesting to discover. Whatever you do in science, don't confuse the mathematical model with the reality - especially if the model is continuous and the reality is quantised.
Light bouncing off a mirror being vibrated causes a Doppler shift in the light.
Lissajous figures are connected to the electron via memorista.
Whatever you do in science Alan don't confuse a mathematical model with reality, especially if the model is quantised and reality is continuous!
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It clearly states in this link that all objects resonate with their own natural frequency or frequencies. That it is driving these natural frequencies with an outside source that causes standing waves. That the patterns are only created within the medium at specific frequencies of vibration. And these specific frequencies are harmonics of the natural frequencies of the object.
That's the point ive been trying to make all along. It is the sum of these harmonics that causes the standing waves. You don;t need a second frequency, and the outside source doesnt need a frequency component - think blowing across the top of a bottle, yiu are only blowing not whistling or huming a frequency. You may have missed what I was saying or Im not explaining clearly enough.
No Colin - you explain yourself well and I have missed nothing...
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency. And that any energy added to an object in any fashion has an associated frequency. Some methods of adding energy such as being hit singularly with a rubber mallet will only change amplitude if more energy is given to the force of the strike, but adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.
Any change in an objects behaviour due to an energy input is an interaction between the energy of the input, and the energy or energies of the object.
Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...
How can one logically deduce otherwise?
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Assuming you mean memristor, I'd appreciate a reference to how they connect electrons to Lissajous figures. Curious devices, they seem to have disappeared from sight in the last 40 years.
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.
Alas that is not true or even generally meaningful.
And, sadly, the Lissajous figures created by reflecting light from a vibrating mirror have nothing to do with Doppler shift. It's just the path of the reflected beam when the mirror rotates about two axes.
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There may be a confusion with phonons.
https://en.m.wikipedia.org/wiki/Phonon (https://en.m.wikipedia.org/wiki/Phonon)
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Assuming you mean memristor, I'd appreciate a reference to how they connect electrons to Lissajous figures. Curious devices, they seem to have disappeared from sight in the last 40 years.
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency.
Alas that is not true or even generally meaningful.
And, sadly, the Lissajous figures created by reflecting light from a vibrating mirror have nothing to do with Doppler shift. It's just the path of the reflected beam when the mirror rotates about two axes.
https://en.wikipedia.org/wiki/Lissajous_curve
quote:
"A Lissajous curve is used in experimental tests to determine if a device may be properly categorized as a memristor."
https://en.wikipedia.org/wiki/Memristor#Experimental_tests_for_memristors
please see: experimental tests for memristor
Quote:
"Chua and his student Sung Mo Kang generalized the theory of memristors and memristive systems including a property of zero crossing in the Lissajous curve characterizing current vs. voltage behavior."
https://learn.sparkfun.com/tutorials/voltage-current-resistance-and-ohms-law
"The three basic principles for this tutorial can be explained using electrons, or more specifically, the charge they create: Voltage is the difference in charge between two points. Current is the rate at which charge is flowing. Resistance is a material's tendency to resist the flow of charge (current)"
https://prezi.com/k67jmml5iopb/applications-of-lissajous-figures/
I did not watch this as it will not play on my phone, but the write up says:
"with very difficult math approach like Hamiltonian in Quantum mechanics"
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All mass is made of atoms, which contain electrons, which have energy.
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Ah, ok...good, good! Not a Doppler shift. Lets examine that. The Pound Rebka attaches a gamma ray to a speaker cone and a Doppler shift is created in the test signal of the experiment. If we attach a laser to the speaker cone then a Doppler shift would be created in the light of the laser. So by pointing a laser at a mirror attached to a speaker cone, and pointing a laser 'straight' at it the light shining back would be Doppler shifted...
...But the Lissajous pattern is not created like this. Looking at the tuning fork version, the laser beam is pointed at a mirror set up at an angle that reflects the beam to another tuning fork with a mirror on it, that then reflects the beam onto the screen. Both tuning forks are vibrating. Both mirrors are adding a Doppler shift to the beam of laser light.
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There may be a confusion with phonons.
https://en.m.wikipedia.org/wiki/Phonon (https://en.m.wikipedia.org/wiki/Phonon)
Interesting. I'll be reading that closely.
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And try going to this web site and watch the video to see how the Chladni patterns relate to quantum mechanics. http://oyc.yale.edu/chemistry/chem-125a/lecture-9 (http://oyc.yale.edu/chemistry/chem-125a/lecture-9)
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There may be a confusion with phonons.
I agree Jeff, there is a big difference between the propagation of sound across a crystal lattice and the response of that lattice to mechanical distortion as in the Chladni plates. If we want to estimate the speed of sound in a material, we don't need to do an analysis of the atomic structure of the crystal lattice, we can use Youngs Modulus. I think there is also some confusion with phenomena like black body radiation:
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency. And that any energy added to an object in any fashion has an associated frequency.
There is no direct relationship between increasing the energy input and the resonant frequencies, in fact the resonances require less energy for a particular amplitude of vibration compared to none resonant frequencies. This is similar to the energy wells found in quantum models and that electrons find it easier to remain in certain orbitals.
adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.
In its quiescent state there are no flexing movements in the plate so no standing waves 'confined' in the plate.
Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...
How can one logically deduce otherwise?
As I explained earlier, the input frequency acts in the same way as hitting with a hammer, causing a mechanical displacement, the returning force due to stiffness and the mass of the plate determines the resonance, hence the harmonics, hence the patterns. This is all due to the flexing of the plate and there is no underlying frequency which the input signal combines with.
This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.
No, there is no gravity sinewave. Gravity acts as the returning force, in the same way as the stiffness of the plate.
By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
As Alan said, the lissajous patterns are the locus of the sum of 2 sine waves, as such they will be the resultant of nodes and antinodes of the individual waves.
If you are going to draw parallels between mechanical phenomena an atomic/quantum behaviour you need to start with a correct model of the mechanical system.
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As an aside...
memristor.... Curious devices, they seem to have disappeared from sight in the last 40 years.
Research is still continuing - the latest fads seem to be in emulating neurons, or displacing flash drives...
See: http://spectrum.ieee.org/the-human-os/semiconductors/memory/mimicking-the-synapses-of-the-brain
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There may be a confusion with phonons.
I agree Jeff, there is a big difference between the propagation of sound across a crystal lattice and the response of that lattice to mechanical distortion as in the Chladni plates. If we want to estimate the speed of sound in a material, we don't need to do an analysis of the atomic structure of the crystal lattice, we can use Youngs Modulus. I think there is also some confusion with phenomena like black body radiation:
But I am not discussing the propagation of sound - I am discussing the distribution of resonant vibration.
Phonons are the product of perturbation theory as are all quantum calculations. I'm not sure what confusion you refer to regarding the black body radiation phenomenon, but fact of the matter is that if one attempted to apply these time perturbations to the black body radiation data directly, then the quantised nature of the data would be eliminated at source.
You however seem to be missing the fact that an object has an associated energy, or energies, and that energy has an associated frequency. And that any energy added to an object in any fashion has an associated frequency.
There is no direct relationship between increasing the energy input and the resonant frequencies, in fact the resonances require less energy for a particular amplitude of vibration compared to none resonant frequencies. This is similar to the energy wells found in quantum models and that electrons find it easier to remain in certain orbitals.
adding energy that consists of an increasing frequency will cause changes in standing waves confined within the object.
In its quiescent state there are no flexing movements in the plate so no standing waves 'confined' in the plate.
The standing waves that are inherent in the plate are holding it in its non-vibrating position. Without them the plate would not be a plate.
Therefore there is the frequency or frequencies of the object, and the frequency of the input signal at play in the creation of Chladni patterns, surely...
How can one logically deduce otherwise?
As I explained earlier, the input frequency acts in the same way as hitting with a hammer, causing a mechanical displacement, the returning force due to stiffness and the mass of the plate determines the resonance, hence the harmonics, hence the patterns. This is all due to the flexing of the plate and there is no underlying frequency which the input signal combines with.
Well actually Colin, you have explained this scenario in both ways. You have told me that a plate has natural frequencies, and the input to the plate has no frequency, in that one blows rather than whistles across the top of a bottle to create a sound, or hits with a hammer,(bowing with a violin bow is actually much more complicated physics)....
And then you tell me, as we can quite clearly observe in the links provided, that Chladni patterns are forming on a plate and changing from one pattern to another as an input is being increased in its frequency.
How the different tones on steel drums are constructed and how the standing wave of this tone resonating is confined to the tone zone is interesting Colin.
This corresponds with the compound pendulums connection with Lissajous figures because gravity is one of the input sine waves of the compound pendulum.
No, there is no gravity sinewave. Gravity acts as the returning force, in the same way as the stiffness of the plate.
Gravity is one of the driving forces of the compound pendulum's representation of a Lissajous figure.
By the physical nature of how the patterns are created, the Lissajous patterns being the result of light thrown outwards into patterns from the extremities of the vibrations, and the Chladni patterns being the result of sand being pushed into the areas of least vibration, the Chladni pattern should, by all logic, be an inverse representation of the corresponding Lissajous figure.
As Alan said, the lissajous patterns are the locus of the sum of 2 sine waves, as such they will be the resultant of nodes and antinodes of the individual waves.
Precisely the connection that I am making with Chladni plates.
If you are going to draw parallels between mechanical phenomena an atomic/quantum behaviour you need to start with a correct model of the mechanical system.
My post to Alan concerning the tuning fork version of producing Lissajous patterns 'is' mechanically correct.
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Jeff - thanks for the links...
Please see first part of post to Colin above.
Please also see the 2014 link of applications of Lissajous figures in my last post to Alan, and the notion of maths approaching the Hamiltonian.
https://en.wikipedia.org/wiki/Quantum_gravity
quote:
" The Problem of Time
Main article: Problem of Time
A conceptual difficulty in combining quantum mechanics with general relativity arises from the contrasting role of time within these two frameworks. In quantum theories time acts as an independent background through which states evolve, with the Hamiltonian operator acting as the generator of infinitesmal translations of quantum states through time.[29] In contrast, general relativity treats time as a dynamical variable which interacts directly with matter and moreover requires the Hamiltonian constraint to vanish,[30] removing any possibility of employing a notion of time similar to that in quantum theory."
unquote:
Please note that Special Relativity also uses an independent time background.
Please note that the Shrodinger and Doppler shift are united in quantum via the Lorentz transformations, which phase both time and space.
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Then what is required, as I have stated in new theories, is a concept of action dilation rather than just time dilation. Then time is no longer an independent background in quantum mechanics.
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Yes, since a Lissajous figure is simply a plot of x = a sin ft against y = b sin (f't + p) where a and b are amplitudes, f and f' are frequencies, and p is a phase angle, it's quite a handy tool for looking at the behavior of nonlinear systems.
There was (maybe still is) a suggestion that memristors could form useful oscillators, in which case f = f' and the Lissajous figure can show the phase relationships around the tuned circuit. No big deal: we use L f 's for synchronising all sorts of things from atomic clocks to aircraft engines.
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Ah, ok...good, good! Not a Doppler shift. Lets examine that. The Pound Rebka attaches a gamma ray to a speaker cone and a Doppler shift is created in the test signal of the experiment. If we attach a laser to the speaker cone then a Doppler shift would be created in the light of the laser. So by pointing a laser at a mirror attached to a speaker cone, and pointing a laser 'straight' at it the light shining back would be Doppler shifted...
...But the Lissajous pattern is not created like this. Looking at the tuning fork version, the laser beam is pointed at a mirror set up at an angle that reflects the beam to another tuning fork with a mirror on it, that then reflects the beam onto the screen. Both tuning forks are vibrating. Both mirrors are adding a Doppler shift to the beam of laser light.
I see your confusion. The Lissajous figure is, as I said above, just the path of a light beam, particle or whatever that moves cyclically in the x and y directions simultaneously. To get a Doppler shift you need to move the source in the z direction, i.e. along the direction of propagation of the signal, which is what P&R did. You can do this in principle with a laser and a vibrating mirror but the Doppler shift is so small that it would be lost in the normal bandwidth of the laser. The trick with P&R was to use a Mossbauer filter which has an incredibly narrow bandwidth. I'll leave the numbers up to you, as you have the Doppler equation and at least as much experience of tuning forks as I have!
True story. My first day as a physics laboratory demonstrator brought me into contact with a student who was indeed working with (but not entirely understanding) Lissajous figures. Her experimental writeup was "different patterns were obtained by fiddling with various knobs on the oscilloscope". I gave her full marks because she had written down exactly what she did and what she saw (the essence of experimental science) whilst the other students had merely copied the method scripts that I had written and put in a few plausible numbers. A few years ago she was awarded "Physics Teacher of the Year" by the Institute of Physics.
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But I am not discussing the propagation of sound - I am discussing the distribution of resonant vibration.
Sorry, I thought for a moment you were suggesting that the standing soundwaves in the plates have discrete energies associated with their frequencies. I should have realised that you would understand why this is meaningful for v high frequencies eg light, but not for those of sound.
The standing waves that are inherent in the plate are holding it in its non-vibrating position. Without them the plate would not be a plate.
I assume that as above you are not talking about the standing sound waves in the plate, because those standing soundwaves which form the chladni patterns do not form and have no existence until the plate is stimulated to vibrate either by hammer, bow or frequency from a loudspeaker. The standing waves are the resonance we hear. The plate is still a plate without those standing waves, so I'm confused about which standing waves are holding the plate in its nonvibrating position.
Well actually Colin, you have explained this scenario in both ways. You have told me that a plate has natural frequencies, and the input to the plate has no frequency, in that one blows rather than whistles across the top of a bottle to create a sound, or hits with a hammer,(bowing with a violin bow is actually much more complicated physics)....
And then you tell me, as we can quite clearly observe in the links provided, that Chladni patterns are forming on a plate and changing from one pattern to another as an input is being increased in its frequency.
That's because, as I have explained, there are a number of different ways in which the plates may be stimulated, I agree that the bow is more complicated physics, but at the level we are discussing here it is still just another way of stimulating the different modes of resonance. But the point I have been trying to make is there is no inherent wave (standing or otherwise) which combines with another input frequency to create the patterns, the patterns are only the result of the resonance, standing soundwaves and their harmonics, which superpose onto each other.
You cannot draw a parallel between the chladni patterns and the lissajou figures and argue that they are the result of 2 frequencies. What is an interesting parallel is that the more interesting lissajous figures occur when the 2 frequencies have integer relationships. This is precisely what is happening with the chladni patterns as the harmonics are all integer multiples, the difference is that whereas lissajous is made from only 2 frequencies, chladni often have at least 6 frequencies in each vibrating length, so 12 for square/rectangle.
Gravity is one of the driving forces of the compound pendulum's representation of a Lissajous figure.
Agreed, however, gravity is not an input sinewave as you stated, the gravitational force is constant.
I'm not sure whether any further input from me will help rather than hinder your quest to link schrödinger, Doppler and lissajous, because such input would be based on sound propagation rather than quantum level. For example, we could discuss how when a violin string resonates it pushes against the bow making it slip across the strings at the resonant frequency, a similar effect occurs when blowing across a tube where the vortices which initiate the resonance are forced to follow the resonant frequency, but I can't see how such facts, fascinating as they are, can help you solve your problems at a quantum level.
Best of luck in your quest.
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That is a lovely story Colin.
(Edit: Just realised that should be 'lovely story Alan' and that the next 2 paragraphs are in answer to your post that I mistakenly thought Colin had posted)
The only part of the Pound Rebka experiment that interests me is the part where they say: When the Doppler shift of the test signal was of the correct type to be 'matched and cancelled out', the gamma ray was then able to be received by the receiver.
The only part of the Lissajous patterns that interests me is the 'outward' gyrations and inertias in relation to frequency and the fact that a change in mass or a change in gravity will affect the gyration and inertia of a Lissajous pattern being created by a compound pendulum.
Let's try a different tack. A Chladni plate pattern is caused at the points of least vibration. Now imagine that the sand was being pushed to the points of most vibration instead. Would this be a Lissajous pattern?
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(Edit: and to Colin's post)
Edit: Aww, just read your latest post. Yes blowing over a bottle top or flute is really interesting and the physics are complicated because you can change the octave of a tone by changing the shape of your mouth and the way you blow. Much the same as the wrist and pressure action of a violin bow. Might have to open a whole new thread for that one Colin. I know by experience how to facilitate these effects in both flute and violin, but could learn a lot about the why of it :)...
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Then what is required, as I have stated in new theories, is a concept of action dilation rather than just time dilation. Then time is no longer an independent background in quantum mechanics.
Well Jeff, one is free to entertain trains of thought. I'm not quite sure what you mean by dilated action. The equivalence principle denotes that each reference frame must be the physical equivalent of all other reference frames.
In stating time as variable in the quantum region at the stage of the blackbody data that produced Planck's h constant in the manner that I have suggested on your new theories thread, where... as the frequency is observed to be increasing, the length of the standard second is decreased so that the Planck data curve matches the Jean Reiliegh classical curve of the ultra violet catastrophe. Then the quantised nature of the data will become linear.
We don't need to talk in terms of quantum from that point on.
This concept does however force one into several physical cul de sacs, all of which lead to the model I describe on new theories.
But for this board:
The consequences of different reference frames running at variable rates of time gives rise to the question of simultaneity and a universally constant present.
On the basis that it would be acceptable to discuss the concept of quantum states being multiverses comprised of copies of this universe displaying the actions of what happens on the other side of Schrödinger's partitioned box, I think I can be forgiven for discussing the possibility that variable rates of time can occur simultaneously to each other, ie: side by side, and that a logical solution to maintaining the universally constant present within this construct is that our observation of reference frames of rates of time differing from our own are time frame dependent and proportional to the difference in rate of time of observation point and rate of time at point of observation.
This concept becomes interesting when considering the Bekenstien, Hawking black hole conundrum, the second law of thermodynamics and the energy conservation law.
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If we are in reference frame A and we are observing the action of a particle in reference frame B along a line element, how is that different to observing a change in relativistic mass? It is only a change in our viewpoint of the time component that makes the difference. Isn't it time that prevents a union between QM and GR?
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Well its kind of hard for me to get into the discussion of relativistic mass without straying into New Theories territory, but if you think about the implications of matching the Planck data curve to the Jean Rayliegh classical curve by decreasing the length of a standard second as frequency is increased, then you will realise that frequencies in the lower registers may require that the standard second is increased in length.
By attributing open space with a time dilation of its own that decreases the length of a second as the gravity field decreases in strength with distance from mass...
Looking at this concept of the rate of time getting slower for 'space' in relation to clocks slowing in relative motion, you will find that the necessity for relativistic mass has been rendered redundant. The universal speed limit of the speed of light is upheld as well as the equivalence principle, in that light will always travel 299 792 458 metres per second, whatever the length of that second is, the speed you travel will always be a percentage of the reference frames speed of light as per the reference frame that is being travelled through's length of second, this percentage of the speed of light you are travelling will affect your motion related slowing of time, and that the interplay of both phenomenin in relation to each other ensures that mass never achieves the speed of light of the reference frame it is travelling through, and that it is gravity potential that is the mechanical function of frequency changes for mass travelling through space.
This then forces one to look at other means of calculating what is happening with light in the gravity field, and seek an alternate perspective concerning calculating kinetic energy with respect to relative motion related slowing of time.
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Let's sum up the Lissajous stuff. Any periodic shape can be synthesised or approximated by the addition of sine waves. A Lissajous figure is the result of vector addition of two periodic functions at right angles. That's all there is to it.
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Great stuff Alan!
But could you please tell me what the maths of an inverse representation of a Lissajous figure are, what the maths for an inverse representation of a Chladni plate are, and if the inverse representation of each relates mathematically to the non inverse representation of the other?
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Let's try a different tack. A Chladni plate pattern is caused at the points of least vibration. Now imagine that the sand was being pushed to the points of most vibration instead. Would this be a Lissajous pattern?
It would still be a Chladni pattern, it wouldn't be a lissajous pattern.
Chladni patterns are just a mapping of the nodes and antinodes of a plate and it just happens that the easiest way to visualise them is by indicator gathering in the nodes, It is possible to display the antinodes pattern using a form of laser holography which shows the areas of maximum displacement as dark areas.
I can't get some maths symbols to post otherwise I would show you the maths, but lissajou patterns are the locus (movement of a point) resulting from 2 sinewaves one pushing the point in the x direction and the other in the y direction (as Alan said), whereas the wavefunction for the Chladni patterns of a rectangular plate with free edges is the product of 3 cosine functions and is stationary. Because lissajous are motions of a point and Chladni patterns are stationary it doesn't make sense to talk of one being the inverse of the other.
Interesting aside, Faraday discovered that very light material e.g. fragments of bow hair, tended to move to the antinodes drawn there by surface air currents caused by the flexing of the plate.
Edit: Aww, just read your latest post. Yes blowing over a bottle top or flute is really interesting and the physics are complicated because you can change the octave of a tone by changing the shape of your mouth and the way you blow. Much the same as the wrist and pressure action of a violin bow. Might have to open a whole new thread for that one Colin. I know by experience how to facilitate these effects in both flute and violin, but could learn a lot about the why of it :)...
Yes, overblowing has its parallel in bow technique, and it really brings out an understanding of the differences between sympathetic resonances and stimulated resonance, but as you say separate subject. Also, there is limited time and space to cover these subjects fully so it would have to be a very superficial discussion like the one we've had on Chladni where we haven't even scratched the surface.
Just as an aside before we leave this. Phonons were mentioned and these as you are aware don't play a part in chladni patterns. For others reading this, phonons propagate by longitudinal and transverse displacement of atoms in the material lattice, but because these displacements are extremely small the amplitudes of the waves are also small, in fact almost inaudible. Plate vibrations on the other hand have large displacements and can produce very loud sounds (wouldn't have string instruments otherwise - well maybe electric bass), this is because the standing waves are caused by the plates bending and twisting rather than relying on longitudinal or transverse waves through the plate.
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Colin - I will indeed open a thread to hopefully speak with you further on the physics of sound at some point in the future when I'm a bit more settled and have more time. I've always just been thrown in deep end and done everything hands on by ear, and observation. I could learn a lot about the tech, if you were willing...
But your post has made me realise that I need to explain myself a bit better...
When I am looking at Lissajous figure on a screen, what I am seeing is a representation of a 3 dimensional structure that is being displayed in 2 dimensions. ie: like a cube being represented as a square.
When I am asking for the inverse representation of a Lissajous figure, if I asked for the inverse representation of a cube, in 2 dimensions this would appear as a square divided into 4 equal squares by a horizontal line and a vertical line. In 3 dimensions one would see that a point in the middle of the square sends a line to the middle of each face of the square.
The Chladni plate patterns are also displaying in 2 dimensions... When I ask for an inverse representation of a Chladni pattern, (which I can appreciate isn't really the correct terminology), what I'm asking for is that the shape of the Chladni pattern be the innermost parts of a 3 dimensional structure, in the same way that the cube is intersected into 4 equal cubes by lines that denote its most inner points.
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Can this relationship be derived between Schrödinger equation and Doppler shift equation?
Looking at Chladni plates ,.'
I'm always amazed at how some people will automatically assume that all or most physicists must know of the very esoteric concepts that are found in science. In this case I've never heard of the term "Chladni plates" and won't bother making any attempt to study acoustics to the point I can understand your question. My main point here is that something like this should never be used to ask the kind of question you're asking. For one thing an equation like the Schrodinger equation describes a law of physics and as such must represent all phenomena. If you derive it for one situation it means nothing other than it works in that specific example. But most importantly you're asking about light and the Schrodinger equation cannot be used to describe light. The Schrodinger equation describes no relativistic particles and photons are relativistic particles and as such are properly described by quantum electrodynamics which is a relativistic theory.
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But your post has made me realise that I need to explain myself a bit better...
Thanks because I was struggling to understand what you might mean by inverse, for example you could discuss the inverse of a function f as being 1/f.
When I am looking at Lissajous figure on a screen, what I am seeing is a representation of a 3 dimensional structure that is being displayed in 2 dimensions. ie: like a cube being represented as a square.
What you are seeing is a 2d line which the mind interprets as 3d in certain circumstances e.g. If the pattern were a circle the mind might think sphere. The 3D in the lissajous is an optical illusion and has no real world existence.
When I am asking for the inverse representation of a Lissajous figure, if I asked for the inverse representation of a cube, in 2 dimensions this would appear as a square divided into 4 equal squares by a horizontal line and a vertical line. In 3 dimensions one would see that a point in the middle of the square sends a line to the middle of each face of the square.
Not sure how you get that figure, the usual 2d representation of a cube is a square and 2 joined parallelograms.
The Chladni plate patterns are also displaying in 2 dimensions...
The chladni plate is in fact 3d because of the amplitude, think contour map.
When I ask for an inverse representation of a Chladni pattern, (which I can appreciate isn't really the correct terminology), what I'm asking for is that the shape of the Chladni pattern be the innermost parts of a 3 dimensional structure, in the same way that the cube is intersected into 4 equal cubes by lines that denote its most inner points.
Ok now I can see what you mean about the divided cube, but still struggling to understand how this is a 2d of a cube.
In regard to the chladni patterns I'm also having difficulty visualising what this might be or whether it makes sense.
PS I think you mean 8 cubes
Sorry, still struggling to see how these can be related in some way. Can you come at it from a different direction and explain what objective or outcome you might visualise?
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Ah yes (chuckle) 8 cubes, it was rather late...
Here I am running into terminology problems...again, but to say so, for me a 3 dimensional view of the Chladni plate pattern would incorporate the same contours to be on the bottom of the plate as well.
It matters not to me if a 3 dimensional Lissajous figure is not not a proper world view...
All I'm interested in is the mathematical difference in phase shifting between the Lissajous and the Chladni.
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Can this relationship be derived between Schrödinger equation and Doppler shift equation?
Looking at Chladni plates ,.'
I'm always amazed at how some people will automatically assume that all or most physicists must know of the very esoteric concepts that are found in science. In this case I've never heard of the term "Chladni plates" and won't bother making any attempt to study acoustics to the point I can understand your question. My main point here is that something like this should never be used to ask the kind of question you're asking. For one thing an equation like the Schrodinger equation describes a law of physics and as such must represent all phenomena. If you derive it for one situation it means nothing other than it work's in that specific example. But most importantly you're asking about light and the Schrodinger equation cannot be used to describe light. The Schrodinger equation describes no relativistic particles and photons are relativistic particles and as such are properly described by quantum electrodynamics which is a relativistic theory.
What amazes me Pete is that someone can make such sweeping statements concerning a thread that they clearly haven't read.
The Schrödinger equation is based on the maths of the Chladni plate patterns.
The Schrödinger equation is linked to the Doppler shift equation via the Lorentz transformation in quantum electrodynamics.
Therefore the link to quantum electrodynamics via the Chladni plates is ***already established*** .
What I am looking at is the Lissajous patterns having a possible connection to Doppler shift...
...and what I'm assuming is, is that someone here will be capable of telling me what the difference in phase shifting is between a Chladni pattern and a Lissajous figure, based on the fact that both are created via the nodes and antinodes of frequency.
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When I am looking at Lissajous figure on a screen, what I am seeing is a representation of a 3 dimensional structure that is being displayed in 2 dimensions. ie: like a cube being represented as a square.
Wrong. You are looking at a 2-dimensional plot of a 2D phenomenon. The oscilloscope produces a dot at (x,y) where
x = A sin at, y = B sin (bt + p) and p is the phase difference.
x and y only - no z.
If a = b and p = pi/2, you get a stationary circle. If a = n b where n is an integer, you get a stationary bowtie, cats cradle, or whatever.
The figure only appears to move in 3D if the frequencies a and b (or n b) are slightly different, but it is your mind interpreting two sine waves sliding over each other as one sine wave rotating. This becomes obvious is the frequencies are very low - say around 1 Hz - so you can follow the movement of the dot.
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What I am looking at is the Lissajous patterns having a possible connection to Doppler shift...
And here you are wasting your time because Doppler shift requires movement in the z direction, as I said earlier.
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When I am looking at Lissajous figure on a screen, what I am seeing is a representation of a 3 dimensional structure that is being displayed in 2 dimensions. ie: like a cube being represented as a square.
Wrong. You are looking at a 2-dimensional plot of a 2D phenomenon. The oscilloscope produces a dot at (x,y) where
x = A sin at, y = B sin (bt + p) and p is the phase difference.
x and y only - no z.
If a = b and p = pi/2, you get a stationary circle. If a = n b where n is an integer, you get a stationary bowtie, cats cradle, or whatever.
The figure only appears to move in 3D if the frequencies a and b (or n b) are slightly different, but it is your mind interpreting two sine waves sliding over each other as one sine wave rotating. This becomes obvious is the frequencies are very low - say around 1 Hz - so you can follow the movement of the dot.
This is all quite adequately laid out in the back to basics physics oscillator youtube video I provided in post 2.
(It is of interest that the xy function of the oscillator requires that the phase period ie: timing function, is alternatively denoted by a second frequency input. For instance if you considered for a moment that the standard second from which you are watching this dot going round from was elongated to the degree that the dot going round at that rate would again appear as a circle.)
In any case Alan, 3 dimensional or not, what I wish to know is what the mathematical phase shift difference is between a Lissajous and a Chladni.
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What I am looking at is the Lissajous patterns having a possible connection to Doppler shift...
And here you are wasting your time because Doppler shift requires movement in the z direction, as I said earlier.
You know Alan - you have an extremely dismissive manner of forwarding a conversation, but on basis you are indeed moving in the right direction:
Yes, this is true - so when light is bounced off a vibrating surface at a right angle, what type of shift 'is' occurring?
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Here I am running into terminology problems...again, but to say so, for me a 3 dimensional view of the Chladni plate pattern would incorporate the same contours to be on the bottom of the plate as well.
Terminology is very important so let's get agreement before looking at your question.
When I said "The chladni plate is in fact 3d because of the amplitude, think contour map" you might not have interpreted amplitude in the way I meant it.
Let's imagine you have an 8x4 sheet of hardboard and two 4ft trestles. Place the sheet on the trestles so that the trestles are widthways and about a 1/4 of the length from the ends (2ft). Now go to one end and press the edge down, the centre of the sheet will go up and the far end will go down, then move your edge up and the centre will go down, etc. This is a model of a rectangular plate in its 2,0 mode with the nodes at the trestles. If the dimensions of the sheet are x&y then z (perpendicular to x&y) is the amplitude of the vibration and is our 3rd dimension. Relative to the nodes up is +ve and down -ve. To think about the contours on the bottom of the sheet, when the top surface is domed the bottom is cupped, but they both move in the same direction.
Phase, when the ends go down, the centre goes up so although centre and ends are both antinodes they are antiphase whereas the ends are inphase.
It matters not to me if a 3 dimensional Lissajous figure is not not a proper world view...
OK, but I think you will agree that it is important to differentiate between objective observations and those influenced by the mis-perceptions of the brain.
All I'm interested in is the mathematical difference in phase shifting between the Lissajous and the Chladni.
Here I have a problem understanding what you mean.
So, using the terminology in the hardboard sheet example and similar examples, can you describe what you mean by "the phase shifting between lissajous and chladni".
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What amazes me Pete is that someone can make such sweeping statements concerning a thread that they clearly haven't read.
If that's the conclusion that you drew from my post then you didn't really pay close enough attention to what I wrote. I had no intention of commenting on a thread consisting of 50 or so posts. That's be an incredible waste of time. I commented only on the question that you asked in the first post.
The Schrödinger equation is based on the maths of the Chladni plate patterns.
You're extremely wrong. In fact you are now claiming as fact that which you started out asking. The Schrödinger equation cannot be formally derived. It's a postulate and as such it cannot be derived. It was informally arrived at from observations of sub atomic particles. But it is in now way based on the math of said patterns. In fact all the years of my studies in quantum mechanics, and all the textbooks I have in quantum mechanics, not one word is mentioned about such patterns.
The Schrödinger equation is linked to the Doppler shift equation via the Lorentz transformation in quantum electrodynamics.
That is absolutely incorrect. Why on Earth are you making patently false statements about the Schrödinger equation? In the first place there is no link to the Doppler equation and since it's a non-relativistic equation it's not linked to the Lorentz transformation and since it can't be used to photons it has nothing to do with quantum electrodynamics.
In any further posts that you make in which you claim otherwise then please do the proper think and provide absolute proof of your claims. What you've done in response to my post. I expect more from you. For a member with no formal physics education you're not all that bad. However by ignoring that which demonstrates that you're wrong goes quite against the scientific method. Do you know what that is? If not then I can provide the definition of it which was stated in the American Journal of Physics a while back. It was formed by a committee of physicists as I recall.
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Listen up,folks, here's an apology!
Of course you can detect Doppler shift from slow moving targets in a laser beam. It's a routine method for measuring blood flow and air pollution! Whatever was I thinking?
That said, it still has nothing to do with Lissajous, Schrodinger, Chladni, Brer Rabbit, or anyone else I can think of.
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What amazes me Pete is that someone can make such sweeping statements concerning a thread that they clearly haven't read.
If that's the conclusion that you drew from my post then you didn't really pay close enough attention to what I wrote. I had no intention of commenting on a thread consisting of 50 or so posts. That's be an incredible waste of time. I commented only on the question that you asked in the first post.
The Schrödinger equation is based on the maths of the Chladni plate patterns.
You're extremely wrong. In fact you are now claiming as fact that which you started out asking. The Schrödinger equation cannot be formally derived. It's a postulate and as such it cannot be derived. It was informally arrived at from observations of sub atomic particles. But it is in now way based on the math of said patterns. In fact all the years of my studies in quantum mechanics, and all the textbooks I have in quantum mechanics, not one word is mentioned about such patterns.
The Schrödinger equation is linked to the Doppler shift equation via the Lorentz transformation in quantum electrodynamics.
That is absolutely incorrect. Why on Earth are you making patently false statements about the Schrödinger equation? In the first place there is no link to the Doppler equation and since it's a non-relativistic equation it's not linked to the Lorentz transformation and since it can't be used to photons it has nothing to do with quantum electrodynamics.
In any further posts that you make in which you claim otherwise then please do the proper think and provide absolute proof of your claims. What you've done in response to my post. I expect more from you. For a member with no formal physics education you're not all that bad. However by ignoring that which demonstrates that you're wrong goes quite against the scientific method. Do you know what that is? If not then I can provide the definition of it which was stated in the American Journal of Physics a while back. It was formed by a committee of physicists as I recall.
Pete - There is no way in anyone's imagination that the context of a question can be included in the header title... There is a word limit you know.
Please simply google Chladni plate and Schrödinger equation. The history is clearly documented. Jeff actually posted a video on this thread from Yale that fully explains.
Please read post 2, watch the links provided, and read the question asked of physics stack exchange, and answer 2 in relation to answer 1. Here you will find the context of this thread and some quantum maths involving the Schrödinger equation in relation to Doppler shift, via Lorentz transformation.
If you still find yourself interested in commenting, then really you should indeed read the rest of the thread before you do, otherwise you will be in danger of repeating information that has already been covered...again... and that 'is' a waste of both our times.
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Here I am running into terminology problems...again, but to say so, for me a 3 dimensional view of the Chladni plate pattern would incorporate the same contours to be on the bottom of the plate as well.
Terminology is very important so let's get agreement before looking at your question.
When I said "The chladni plate is in fact 3d because of the amplitude, think contour map" you might not have interpreted amplitude in the way I meant it.
Let's imagine you have an 8x4 sheet of hardboard and two 4ft trestles. Place the sheet on the trestles so that the trestles are widthways and about a 1/4 of the length from the ends (2ft). Now go to one end and press the edge down, the centre of the sheet will go up and the far end will go down, then move your edge up and the centre will go down, etc. This is a model of a rectangular plate in its 2,0 mode with the nodes at the trestles. If the dimensions of the sheet are x&y then z (perpendicular to x&y) is the amplitude of the vibration and is our 3rd dimension. Relative to the nodes up is +ve and down -ve. To think about the contours on the bottom of the sheet, when the top surface is domed the bottom is cupped, but they both move in the same direction.
Phase, when the ends go down, the centre goes up so although centre and ends are both antinodes they are antiphase whereas the ends are inphase.
It matters not to me if a 3 dimensional Lissajous figure is not not a proper world view...
OK, but I think you will agree that it is important to differentiate between objective observations and those influenced by the mis-perceptions of the brain.
All I'm interested in is the mathematical difference in phase shifting between the Lissajous and the Chladni.
Here I have a problem understanding what you mean.
So, using the terminology in the hardboard sheet example and similar examples, can you describe what you mean by "the phase shifting between lissajous and chladni".
Sorry Colin, I thought you were saying that the Chladni pattern is a 3 d pattern. Of course the plate and its vibrations are 3 dimensional.
In your hard board and trestle analogy the patterns would form in lines along the trestle points...
...and a phase period is how much time it takes for an up and down movement to complete...
...and phase shifting is when a phase period shifts from 1 timing to another.
In some instances the Chladni patterns themselves could be considered 3 d, in that more sand gathers in some areas than others causing raised contours and shading...
...Given the impossible scenario of gravity being an equal force on both sides of the plate, (ie: an equal measure of sand, as was placed on top of the plate, placed on the underneath of the plate, doesn't fall off the plate), the pattern would be the same on the bottom of the plate as it is on the top.
A simple form of a 3 d side view of this effect, in that a side view of a cube is a square, might be viewed as a horizontal and vertical cross section of equal lines, such as the lines that would divide a square into 4 squares, but with curves shaded into the innermost corners, making a 4 pointed star-ish sort of shape. Looking at the shape as its 3 d form, it would be a 6 pointed star with inverted curves between the points. 4 points on the horizontal and 2 on the vertical. We can fit 4 circles into the curves between the points on the horizontal plane, which is the plate, and now these points are joined by the arcs of these circles. We could fit 4 circles into the curves on the vertical plane on top of the plate, and 4 more on the vertical plane underneath the plate, and if we considered the 6 pointed curved star shape that we started with and were to call this original shape an inverse representation of something, by adding the circles to finish off the innermost curves, we would have constructed the something that that the six pointed star shape is the inverse to. Clearly adding the circles to the vertical plane in the case of the plate only has meaning in respect to air displacement, its the activities on the horizontal plane of the plate that are displacing metal, but you can get the idea.
Also in watching YouTube videos of close ups of sand moving on Chladni plates, a very similar scenario to Lissajous figures that appears to be moving in 3 d occurs, and can be physically observed of movement in the sand at certain frequencies.
But the maths for Chladni plate patterns and how the distribution of resonant vibrations change when alteration to the phase period of the input signal are conducted already exist...
The maths for Lissajous figures of of various input phase periods already exist...
And although Lissajous and Chladni patterns are not the same patterns, they are both created by altering phase periods and I'd like to know what the mathematical difference is between how these patterns are being created by these phase shifts.
Looking at how the light of the laser beam is bounced of a vibrating mirror at right angles onto another vibrating mirror that bounces the light off at a right angle onto a screen - when considering that a laser beam bounced off a vibrating mirror on the z axis, (which I'm understanding is the angle that is a straight on view) a Doppler shift will occur.
But the light being reflected at a right angle will not be Doppler shifted by the vibration. Something else is occurring... And given that the next mirror that reflects the light onto the screen at the opposite right angle is vibrating at the same frequency, the exact and opposite effect is added to the beam of light again before it hits the screen.
Isn't this basically adding a right hand slanted half portion Doppler shift to a left hand slanted half portion Doppler shift?
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Pete is, strictly, correct. The Schrodinger equation is a postulate that satisfies the principal requirement of Heisenberg indeterminacy, that the electron doesn't end up in the nucleus. It just happens that some solutions of the equation look like Chladni patterns. But so do snowflakes, though I can't find a hexagonal Chladni plate image right now. And the Chladni patterns on a guitar don't look like orbitals at all.
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String theory and all of its overblown complexity arose because a relationship was seen between scattering of particles during collisions and one of Euler's functions. Beware of patterns unless backed up by observation and enabling predictions.
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Pete is, strictly, correct. The Schrodinger equation is a postulate that satisfies the principal requirement of Heisenberg indeterminacy, that the electron doesn't end up in the nucleus. It just happens that some solutions of the equation look like Chladni patterns. But so do snowflakes, though I can't find a hexagonal Chladni plate image right now. And the Chladni patterns on a guitar don't look like orbitals at all.
Yes Alan - this having been quite adequately covered in the physics stack exchange link provided in post 2, with the question "how does the Schrödinger equation relate to Doppler shift"...and answer 2 in relation to answer 1, which leads to the subsequent inclusion of perturbation theory into the threads discussion.
But anyone who'd actually read the thread would be aware of this.
Now if you would please stop talking to me as though I have the mental age of a parrot, and take on board the fact that nowhere have I said that anything 'looks like' the atomic orbit of an electron...
What I want to know is how that light beam reflected at a right angle off a vibrating mirror is being phase shifted.
Can you answer this, Alan?
Because everything else described on this thread is merely concerning the reasons I wish to know this.
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What I want to know is how that light beam reflected at a right angle off a vibrating mirror is being phase shifted
Because everything else described on this thread is merely concerning the reasons I wish to know this.
Missed the link about the tuning forks, which is what I assume you mean.
Looking at the diagram, the arms of a tuning fork are cantilevers so although we think of them going towards and away from the laser they also lean backwards and forwards each cycle, so the angle of incidence between laser and mirror changes so that if projected onto a screen you would see a straight line. If we think of first mirrror rocking in x axis, the second one rocks y axis hence lissajous curves. If the forks are started manually the phase relationship will be random, depending on when each one was tapped, with electronic stimulation you might be able to control it, not sure would need to think about that.
Although the wavelength of the laser will undergo Doppler redshift and blue shift on each cycle, you are unlikely to see the effect although sensitive instruments would detect it, but that's Alan's area of expertise.
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Ah - well I didn't actually post a link to the tuning fork version of Lissajous figures, which are prolific on youtube, and I can recommend the 10 best demonstrations with tuning forks...the wobbly forks in water is cool...
...but here is a link using oscillators and mirrors. Its in Spanish with subtitles, and gives a 'mucho claro' demonstration of the laser beam set up with the mirrors and the vertical and horizontal set up of the oscillations.
The first mirror adds a shift to the light, but the light is shining onto the mirror at an angle which reflects it onto the the second mirror at an angle that reflects it onto the screen. Clearly these minute vibrations of both mirrors are amplified by the distance from the second mirror to the screen.
A laser attached to a vibrating oscillator would suffer a Doppler shift in its light beam.
The fact that the light is arriving and leaving both the vibrating mirrors at angles changes the situation...
So what type of shift is it that is occurring in the light being reflected off these vibrating mirrors?
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Wikipedia is succinct and correct, IIRC:
Light waves change phase by 180° when they reflect from the surface of a medium with higher refractive index than that of the medium in which they are travelling.[1] A light wave travelling in air that is reflected by a glass barrier will undergo a 180° phase change, while light travelling in glass will not undergo a phase change if it is reflected by a boundary with air. For this reason, optical boundaries are normally specified as an ordered pair (air-glass, glass-air); indicating which material the light is moving out of, and in to, respectively.
"Phase" here is the phase of the electric field oscillations, not the magnetic field oscillations.[3] Also, this is referring to near-normal incidence—for p-polarized light reflecting off glass at glancing angle, beyond the Brewster angle, the phase change is 0°.
Not hugely important with moving mirrors or non-laser light because the incoming phase is changing very rapidly anyway, but significant in optical computing and interferometry.
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Ah - well I didn't actually post a link to the tuning fork version of Lissajous figures,
In your post #32 you give this link which has diagram of the setup https://prezi.com/k67jmml5iopb/applications-of-lissajous-figures/
2nd page.
Edit: thought Alan had answerd your q on shift but realised you might mean doppler rather than phase (remember there are 2 mirrors = 180x2)
Doppler at angle to moving surface need to adjust originating f by cos of angle. remeber tines of fork are going backwards and forwards and velocity varies as sine wave.
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Thanks Colin!
So I think we can ignore the phase change in the light itself, and just concentrate on these Doppler shifts being created as a sine wave in wobbles of the light beam.
Firstly though, can we now state that Lissajous figures are caused by the Doppler shift of sine waves? And that sine waves come inherent with phase periods?
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Thanks Colin!
So I think we can ignore the phase change in the light itself, and just concentrate on these Doppler shifts being created as a sine wave in wobbles of the light beam.
Sensible, with 2 mirrors, 2 phase shifts so back to square 1. But the calculation of the overall shift will be interesting as you will have to allow for the different phase relationship of the 2 tuning forks which in one position will nullify the frequency shifts.
Firstly though, can we now state that Lissajous figures are caused by the Doppler shift of sine waves?
Not in the case of the 2 tuning forks as I explained above.
Did you have any scenarios where you could use 2 sinusoidal Doppler shifts to drive the x,y axes?
And that sine waves come inherent with phase periods?
What do you mean by phase periods? It's not a term in general use.
Earlier you said
"...and a phase period is how much time it takes for an up and down movement to complete..."
If you mean up and down over a full cycle (up, down and back up to starting value), then that is just the wave period i.e. 1/f. In other words you would be saying in a different way that all waves come inherent with frequency and I don't think that is what you mean.
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Frequency is the amount of times a wave completes an up down cycle per standard second.
A phase period is the amount of time it takes to complete one up down cycle.
Phase shifting is a change occurring in the phase period, or a change in the frequency of up and down cycles per standard second.
...and all waves do come inherent with up down, or back and forth cycles.
Colin, the first mirror is adding a back and forth vibration, ie: Doppler shift, albeit at an angle, to the beam of light. Just to be clear it is not adding a Doppler shift to the frequency of the light, it is adding a Doppler shift to the passage of the light via the frequency of the vibration of the dot of the laser beam. This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the screen.
The Doppler shift of the first mirror is phase shifted by the Doppler shift of the second mirror.
It is precisely this phase shifting that I am interested in.
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Frequency is the amount of times a wave completes an up down cycle per standard second.
A phase period is the amount of time it takes to complete one up down cycle.
Phase shifting is a change occurring in the phase period, or a change in the frequency of up and down cycles per standard second.
...and all waves do come inherent with up down, or back and forth cycles.
Colin, the first mirror is adding a back and forth vibration, ie: Doppler shift, albeit at an angle, to the beam of light. Just to be clear it is not adding a Doppler shift to the frequency of the light, it is adding a Doppler shift to the passage of the light via the frequency of the vibration of the dot of the laser beam. This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the screen.
The Doppler shift of the first mirror is phase shifted by the Doppler shift of the second mirror.
It is precisely this phase shifting that I am interested in.
You keep parroting the phrase 'standard second'. Please explain its meaning.
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Frequency is the amount of times a wave completes an up down cycle per standard second.
A phase period is the amount of time it takes to complete one up down cycle.
Phase shifting is a change occurring in the phase period, or a change in the frequency of up and down cycles per standard second.
We are having problems with terminology again.
What you call phase period is just called the period T, (period of the wave, or wave period) in physics. So a change in the 'phase period' is a change of frequency.
You say that "Phase shifting is a change occurring in the phase period, or a change in the frequency". However, because phase period = period = T = 1/f = frequency change, then your definition of phase shifting is not only tautologous, it is misleading.
Phase shifting is a change in the phase relationship between 2 or more waves, or of one wave relative to a standard.
Just to be clear it is not adding a Doppler shift to the frequency of the light, it is adding a Doppler shift to the passage of the light via the frequency of the vibration of the dot of the laser beam. This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the scree.
Doppler Shift is by definition a change in the frequency of light or sound, it has a very specific cause and meaning, and we cannot apply the term to this example. Before the beam hit the first mirror there was no "frequency of the vibration of the dot of the laser beam". Even the frequencies of the tuning forks remain unchanged, and their phase relationship doesn't change.
What we see in the tuning fork example is not a Doppler shift but a deflection of the beam, first in the x direction then in the y direction, hence lissajous pattern.
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https://en.m.wikipedia.org/wiki/Second
As defined by the International System of Units, and significant in that this is the period of time against which the frequency of phase periods is measured.
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You really think that posting a link to the SI definition answers the question? Or are you using sarcasm?
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Frequency is the amount of times a wave completes an up down cycle per standard second.
A phase period is the amount of time it takes to complete one up down cycle.
Phase shifting is a change occurring in the phase period, or a change in the frequency of up and down cycles per standard second.
We are having problems with terminology again.
What you call phase period is just called the period T, (period of the wave, or wave period) in physics. So a change in the 'phase period' is a change of frequency.
You say that "Phase shifting is a change occurring in the phase period, or a change in the frequency". However, because phase period = period = T = 1/f = frequency change, then your definition of phase shifting is not only tautologous, it is misleading.
Phase shifting is a change in the phase relationship between 2 or more waves, or of one wave relative to a standard.
Just to be clear it is not adding a Doppler shift to the frequency of the light, it is adding a Doppler shift to the passage of the light via the frequency of the vibration of the dot of the laser beam. This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the scree.
Doppler Shift is by definition a change in the frequency of light or sound, it has a very specific cause and meaning, and we cannot apply the term to this example. Before the beam hit the first mirror there was no "frequency of the vibration of the dot of the laser beam". Even the frequencies of the tuning forks remain unchanged, and their phase relationship doesn't change.
What we see in the tuning fork example is not a Doppler shift but a deflection of the beam, first in the x direction then in the y direction, hence lissajous pattern.
Colin, call it a wave period instead of a phase period then. If there is a change in the wave period then there is a change in frequency of wave periods per standard second.
OK. So let's examine Doppler shift. A Doppler shift was created in the test signal of the Pound Rebka by attaching a gamma ray emitter to a speaker cone playing frequency tones. The vibrations caused a Doppler shift in the test signal.
A laser dot is trained on a mirror being vibrated at frequency tones. Light that is reflected off the mirror is being vibrated, so what type of shift is occurring if not a Doppler shift?
If only one mirror or the other mirror are vibrated, the screen shows either a horizontal, or a vertical line. It is only when both mirrors are vibrating that a Lissajous pattern occurs, and this is because the wave periods being added by the first vibrating mirror, are being vibrated again by the second vibrating mirror, and the wave period caused by the first vibration is shifted to being a different wave period by the second vibration.
The mathematics of how these wave periods are being changed by the combined vibrations is what I'm interested in... Is that so hard to understand?
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You really think that posting a link to the SI definition answers the question? Or are you using sarcasm?
Your question was:
"You keep parroting the phrase 'standard second'. Please explain its meaning.'
An SI unit is standard. A non standard second would be a dilated or contracted second.
What more do you want me to say?
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Dilated time is frame dependent and non-local in nature. The second is invariant in all inertial frames of reference and local in nature. Your addition of the word standard is misleading.
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When this conversation follows its intended direction back to the Schrödinger equation and looks at the Lorentz transformations in relation to time perturbations and Planck's h constant, the distinction between frequency of wave periods being measured against the standard second and non standard seconds will be of paramount importance.
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When this conversation follows its intended direction back to the Schrödinger equation and looks at the Lorentz transformations in relation to time perturbations and Planck's h constant, the distinction between frequency of wave periods being measured against the standard second and non standard seconds will be of paramount importance.
You are not making sense. You might be typing what you think are scientific sounding phrases but they certainly are not.
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OK. So let's examine Doppler shift. A Doppler shift was created in the test signal of the Pound Rebka by attaching a gamma ray emitter to a speaker cone playing frequency tones. The vibrations caused a Doppler shift in the test signal.
Yes, the velocity of the loudspeaker cone in one direction caused a change of frequency of the gamma rays to match the absorption window of the receiver.
Incidentally, remember there are 2 shifts, one when the cone is moving upwards and one when it moved downwards, only one matched that of the receiver.
A laser dot is trained on a mirror being vibrated at frequency tones. Light that is reflected off the mirror is being vibrated, so what type of shift is occurring if not a Doppler shift?
It is a deflection, a change of direction caused by the changing angle of incidence of the mirror. It would only be a Doppler Shift if the frequency of the laser light changed as did the gamma ray beam in Pound Rebka.
A Doppler Shift only requires movement in one direction whereas this case requires the mirror to vibrate backwards and forwards in order to create the moving spot. Also Doppler does not cause a change in the direction or angle of a beam of light.
If only one mirror or the other mirror are vibrated, the screen shows either a horizontal, or a vertical line. It is only when both mirrors are vibrating that a Lissajous pattern occurs, and this is because the wave periods being added by the first vibrating mirror, are being vibrated again by the second vibrating mirror, and the wave period caused by the first vibration is shifted to being a different wave period by the second vibration.
The wave period of the first vibration is not being shifted, it remains the same. The frequencies of the 2 tuning forks are transferred unchanged onto the screen, what is changed is their orientation to each other. This is basically another compound pendulum where the tuning forks are the pendulums and the laser spot is the sand tracing out the pattern.
The mathematics of how these wave periods are being changed by the combined vibrations is what I'm interested in... Is that so hard to understand?
Yes, because the wave periods are not being changed.
The maths of what is happening on the screen has already been described by Alan.
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This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the screen.
I think we are missing the fact that there are 3 dimensions here.
- Doppler shift occurs when there is a velocity along the path of the light. A radial velocity, measured in the (say) Z direction.
- Lissajous figures occur when there is a velocity transverse to the path of the light. A transverse velocity, measured in the and Y directions
So Doppler shift is distinct from Lissajous patterns.
Of course, if a mirror is manipulated in all 3 dimensions at once, you can impose both effects on a single beam of light.
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Of course, if a mirror is manipulated in all 3 dimensions at once, you can impose both effects on a single beam of light.
That would be fun.
With the tuning fork the tines rock, so as well as a change in angle of incidence to the mirror there will be an alternate red/blue doppler shift in the frequency of the laser. But as you say, these (doppler and lissajous) are totally independant phenomena.
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Some information on the main man.
https://en.m.wikipedia.org/wiki/Christian_Doppler (https://en.m.wikipedia.org/wiki/Christian_Doppler)
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Some information on the main man.
https://en.m.wikipedia.org/wiki/Christian_Doppler (https://en.m.wikipedia.org/wiki/Christian_Doppler)
Timey,
Could be worth revising Doppler effect so you are clear on how it works.
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This vibrated reflection of the light then hits another vibrating mirror which adds another Doppler shift, albeit at an angle, to the light reflected from this second mirror to the screen.
I think we are missing the fact that there are 3 dimensions here.
- Doppler shift occurs when there is a velocity along the path of the light. A radial velocity, measured in the (say) Z direction.
- Lissajous figures occur when there is a velocity transverse to the path of the light. A transverse velocity, measured in the and Y directions
So Doppler shift is distinct from Lissajous patterns.
Of course, if a mirror is manipulated in all 3 dimensions at once, you can impose both effects on a single beam of light.
Yes you could cause 1 mirror to be driven to both horizontal and vertical vibrations on an axis, and the laser beam would be vibrated into a Lissajous figure, but to be clear, when 2 mirrors are used there is still only 1 beam of light.
OK - so Doppler shift adds velocity to the path of the light beam in the z direction, but a light beam being reflected at an angle that is vibrating will still gain velocity and wobbles, ie: wave periods, will form. When no mirrors are vibrating the laser beam is a dot on the screen, not a line.
The back and forth vibrations of both mirrors add and subtract velocity to the path of 1 light beam. By changing the velocity of these vibrations different Lissajous figures will be displayed. But if you stop either one of the mirrors vibrating and just display the effects of one mirror being vibrated, all you will get is a horizontal or vertical line, from either the horizontally or the vertically aligned oscillator.
It is only when the velocities added at the first mirror are subject to velocities being added by the second mirror, and these added velocities partially subtract the velocities added at the first mirror, that Lissajous figures appear.
Yes it is correct to say that Doppler shifts are distinct from Lissajous figures. That they are separate phenomenon, (as Chladni patterns are a separate phenomenon from the atomic orbit of an electron), but what we can say is that Lissajous figures give us a mathematical insight (albeit complicated by the angle the light beam hits both mirrors at), into how the velocity of a wave period can be changed by the interference of the velocity of another wave period, and... this being important to the discussion, that the Lissajous figure is displaying the points of 'most' vibration left after the vibration of the second mirror has partially cancelled out some of the vibration of the first mirror.
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OK - so Doppler shift adds velocity to the path of the light beam in the z direction,
No, the velocity of the moving mirror in the z direction (parallel to the beam) changes the frequency of the light beam.
but a light beam being reflected at an angle that is vibrating will still gain velocity and wobbles, ie: wave periods, will form. When no mirrors are vibrating the laser beam is a dot on the screen, not a line.
All that is happening here is that the beam is tracing out the movement of the tuning fork arms. If you connected a pen to the end of the fork it could trace a line on a piece of paper, if you then pulled the paper along you would get a sine wave. Imagine a miniature laser connected to the arm, shining onto a screen it would trace the movement of the arm. That is all that is happening.
but what we can say is that Lissajous figures give us a mathematical insight (albeit complicated by the angle the light beam hits both mirrors at), into how the velocity of a wave period can be changed by the interference of the velocity of another wave period, and... this being important to the discussion, that the Lissajous figure is displaying the points of 'most' vibration left after the vibration of the second mirror has partially cancelled out some of the vibration of the first mirror.
No, this is the whole point of my explanation of #83 where I explain “The wave period of the first vibration is not being shifted, it remains the same. The frequencies of the 2 tuning forks are transferred unchanged onto the screen, what is changed is their orientation to each other. ”
Just to be clear, there is no interference of one velocity with the other, no 'most vibration' left, and no partial cancellation. This is just an xy plot of one frequency against another over time.
Look at the maths Alan posted.
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What I gather from your post is that you are so far unable to disconnect the notion of Doppler shift from the phenomenon of light waves and sound waves, to appreciate that velocity can be added to the wave period of any type of wave...
...and to appreciate that adding velocity to a wave period is the same physical thing as a wave period taking less time to complete.
A back an forth vibration, be that a horizontally aligned back and forth, or a vertically aligned back and forth, 'is' adding and subtracting velocity to and from the path of the beam of light...
Actually, that is not strictly speaking what is physically happening. What is really happening is that the back and forth vibrations cause the distance the light travels to be longer and shorter, and the light takes a longer or shorter amount of 'time' to travel to the screen...
This being because the wave periods 'are' longer or shorter.
Now if you look at the Spanish link I provided a few posts ago, you will see that the vibration of the first mirror is quite clearly depicted as a line of light 'on' the second mirror, as well as the screen when the second mirror is stationary. This reflection of a line is then vibrated by the second mirror at the same frequency the first mirror is vibrating at and a circle then forms on the screen...turn off the vibrations of the first mirror and you have a line again, but at right angles to the line of the first mirror.
It is the reflection of the light off the first mirror vibrating causing a line of light, that is then reflected off the second mirror vibrating that line that causes the circle. If waves periods were not being shortened, how could 2 straight lines form a circle? It would be a square wouldn't it?
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You need to learn some trigonometry.
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Be that as it may - for the sake of an interesting conversation can you please elaborate on what about what I have said makes you think so please.
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What I gather from your post is that you are so far unable to disconnect the notion of Doppler shift from the phenomenon of light waves and sound waves, to appreciate that velocity can be added to the wave period of any type of wave...
A wave is an oscillation whose wavelength may vary with time. You cannot add a velocity to it. It makes no sense to think that way.
...and to appreciate that adding velocity to a wave period is the same physical thing as a wave period taking less time to complete.
A back an forth vibration, be that a horizontally aligned back and forth, or a vertically aligned back and forth, 'is' adding and subtracting velocity to and from the path of the beam of light...
How are you going to add velocity to a photon? That would violate the laws of physics.
Actually, that is not strictly speaking what is physically happening. What is really happening is that the back and forth vibrations cause the distance the light travels to be longer and shorter, and the light takes a longer or shorter amount of 'time' to travel to the screen...
This being because the wave periods 'are' longer or shorter.
Now if you look at the Spanish link I provided a few posts ago, you will see that the vibration of the first mirror is quite clearly depicted as a line of light 'on' the second mirror, as well as the screen when the second mirror is stationary. This reflection of a line is then vibrated by the second mirror at the same frequency the first mirror is vibrating at and a circle then forms on the screen...turn off the vibrations of the first mirror and you have a line again, but at right angles to the line of the first mirror.
Here is where your deficiency in trigonometry lets you down. You make something simple sound way too complicated.
It is the reflection of the light off the first mirror vibrating causing a line of light, that is then reflected off the second mirror vibrating that line that causes the circle. If waves periods were not being shortened, how could 2 straight lines form a circle? It would be a square wouldn't it?
Alas if you only knew enough trigonometry.
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What I gather from your post is that you are so far unable to disconnect the notion of Doppler shift from the phenomenon of light waves and sound waves, to appreciate that velocity can be added to the wave period of any type of wave...
Ok, if that is what you believe there is nothing I can do to help you further. However I was only trying to help you understand what is really happening here, but you seem determined to complicate something which is very, very simple.
If waves periods were not being shortened, how could 2 straight lines form a circle? It would be a square wouldn't it?
But I will leave you with one last piece of information to answer this last question:
Wrong. You are looking at a 2-dimensional plot of a 2D phenomenon. The oscilloscope produces a dot at (x,y) where
x = A sin at, y = B sin (bt + p) and p is the phase difference.
x and y only - no z.
If a = b and p = pi/2, you get a stationary circle. If a = n b where n is an integer, you get a stationary bowtie, cats cradle, or whatever.
Maybe you didn't understand it first time round, but it explains what is happening as the laser spot is pushed in the x&y directions by mirrors on the 2 tuning forks - you are not dealing with 2 straight lines, what appears to be straight lines are the loci of sinewaves. This is far easier to understand than schodinger.
If you believe I am unable to 'disconnect' then I would rather do that and believe the true cause than believe this piece of pure fantasy:
What is really happening is that the back and forth vibrations cause the distance the light travels to be longer and shorter, and the light takes a longer or shorter amount of 'time' to travel to the screen...
This being because the wave periods 'are' longer or shorter.
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Jeff - instead of saying how its a shame how I don't know, try being informative, its much more fun.
Colin - I do not understand the maths Alan provided. They mean nothing to me...
What I can observe with my own eyes is that a mirror that is vibrating is changing position, and that a laser beam concentrated on this mirror, no matter the angle the laser is pointed from, will be reflected off a surface that is physically changing position. Am I fantasising this?
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Jeff - instead of saying how its a shame how I don't know, try being informative, its much more fun.
Colin - I do not understand the maths Alan provided. They mean nothing to me...
And therein lies your problem. The mathematics explain the way the process actually works. Not just how you think it works. Mathematics IS physics. I keep trying to tell you this but you won't listen
What I can observe with my own eyes is that a mirror that is vibrating is changing position, and that a laser beam concentrated on this mirror, no matter the angle the laser is pointed from, will be reflected off a surface that is physically changing position. Am I fantasising this?
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Colin - I do not understand the maths Alan provided. They mean nothing to me...
And yet you keep asking for the maths?
What I can observe with my own eyes is that a mirror that is vibrating is changing position, and that a laser beam concentrated on this mirror, no matter the angle the laser is pointed from, will be reflected off a surface that is physically changing position. Am I fantasising this?
The quote mentioned:
"distance the light travels to be longer and shorter, and the light takes a longer or shorter amount of 'time' to travel to the screen ....this being because the wave periods 'are' longer or shorter"
Fantasising may be unfair, but you are certainly not thinking this through properly. There are also times when your questions suggest that you have not actually read an earlier post.
One last try.
Experiment:
If you set up a laser pointer with a screen at the side of it and point it directly at a mirror so the beam is reflected back to the screen, then keeping the mirror exactly perpendicular to the laser walk it towards the laser. You should see just a stationary dot on the screen. Yet the distance between the mirror and screen is getting shorter! Also we know that head on Doppler Shift is at a maximum.
Now with mirror in same position point the laser from the side say 45 degrees with a screen or wall on the other side, now without tipping the mirror move it forward and you will see that the spot also moves forward, if you move the mirror backwards the spot moves backwards, if you moved it back & forth fast enough you would see a straight line. No significant change of distance rather angle of incidence, but note that the period of the spot moving back and forth will match that period of the mirror. No Doppler.
Back to the tuning forks.
You talk of adding a velocity to the beam/spot and that is confusing your thinking. Think rather of angular velocity. Imagine you have a 10m rod pivoted at one end, put a mark at 1 m, as you move the rod backwards and forwards around the pivot the end will move further than the mark, but the period and time to move will always be the same.
Now think mark = end of tuning fork, and end of rod = spot on screen. The lever is magnifying the motion of the mark as the distance between reflection and screen is magnifying the motion of the tuning fork, but the period remains the same.
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted. If you can't understand the geometry of that maths you might need to try drawing it out on paper.
But that is how it works, no change of period etc.
But if you can't get you mind round the maths, then schrodinger etc is going to be a nonstarter.
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I am not asking for the maths for the Lissajous figures, or the Chladni patterns. I'm asking if a relationship can be derived between the 2 sets of maths, and think that there is a connection via time perturbations.
Yes, I agree with your observation of the events of Lissajous figure creation up to here:
""So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side""
If there were 2 light beams what you are saying would be correct. However there is just one light beam, and the movement in first mirror in line to the laser beam source turns the dot into a line. If you turn off the oscillation of the first mirror and only oscillate the second mirror, then the second mirror also turns the dot into line.
The only difference between the lines produced by each mirror is that 1 mirror produces a horizontal line and the other a vertical line.
Oscillate both mirrors and the first mirror wobbles the dot into a line reflected onto the second mirror, and the second mirror wobbles that line into a circle...(or by changing the wave period of the oscillation's of each mirror, all manner of patterns)
Now Colin - a thought experiment. If we simply shine a static line of light onto the second mirror, ie: a line of light that is not being created by wobbling a dot of light, and then wobble the second mirror, will the second mirror turn this static line of light into a circle? Or any other Lissajous figures?
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Now can you please explain exactly what you mean by time perturbations.
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If there were 2 light beams what you are saying would be correct.
It works for one beam and 2 mirrors, you really arn't getting this are you. Sit down and think it through.
Now Colin - a thought experiment. If we simply shine a static line of light onto the second mirror, ie: a line of light that is not being created by wobbling a dot of light, and then wobble the second mirror, will the second mirror turn this static line of light into a circle? Or any other Lissajous figures?
Why should it?
The whole point of this is that what you see on the screen is the resultant of 2 sinewaves projected onto the screen by the 2 mirrors. If you only have one mirror and one tuning fork (i.e. one sinewave) you don't get the patterns.
I don't know if this helps but here is an example of doing the trig using graph paper, which is what I meant by drawing it out. http://www.intmath.com/trigonometric-graphs/7-lissajous-figures.php
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Colin - I've always had a nice time with you online, so tucking my sensitive soul back into top pocket, I'm going to ignore the rather hurtful tone of your recent posts.
My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen. Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.
Thank you for the link. Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.
I am interested in the maths of the physics of the wave periods creating the pattern.
It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror... In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)
Are you with me so far?
All of what I describe above are wave periods in themselves.
Can we agree on this?
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you said that a Lissajous figure is the result of 2 laser dots combining on a screen.
No he didn't! Everyone here has said in all sorts of ways that a Lissajous figure is simply the locus of a point that moves cyclically in two dimensions. The most common is the sum of two sine waves in the x and y directions. That's all there is to it.
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Yes he did...
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
...and the reality is that the first mirror in line vibrates the spot into a line, and the second mirror vibrates the line into Lissajous figures. Therefore the relationship of changing distance between the 2 vibrating mirrors has got to be the defining factor.
Now if you are telling me that the formula you provided describes not only the dimensions of the Lissajous figure itself, but also the wave periods of the changes in distance between the mirrors caused by the vibrations, and the wave period that would be apparent if you attached the laser in line to the top of a vibrating tuning fork for a measure of the distance of the back and forth, then I will agree to agree that that is all there is to Lissajous figures.
So what are you telling me?
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Yes he did...
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
...and the reality is that the first mirror in line vibrates the spot into a line, and the second mirror vibrates the line into Lissajous figures. Therefore the relationship of changing distance between the 2 vibrating mirrors has got to be the defining factor.
Now if you are telling me that the formula you provided describes not only the dimensions of the Lissajous figure itself, but also the wave periods of the changes in distance between the mirrors caused by the vibrations, and the wave period that would be apparent if you attached the laser in line to the top of a vibrating tuning fork for a measure of the distance of the back and forth, then I will agree to agree that that is all there is to Lissajous figures.
So what are you telling me?
If a trained physicist with decades of experience is telling you something it might be at least polite to pay attention.
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I've asked a question of said experienced physicist concerning the maths that were posted by that experienced physicist. A natural response from a non mathematician, and hardly impolite.
The purpose of your post being what? That you know the answer but just wish to
continue in your position of superiority and make belittling remarks?
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Please excuse my 'tone', but it is born of frustration. I've tried to explain this from a number of different angles and I've often had the feeling that you really haven't read, or at least not understood, what I have written. The impression you can give is that I really don't understand what I am talking about. So tucking my sensitive .....
Ok, example of misreading:
My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen. Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.
Look again at the quote in your reply to Alan:
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
I've emboldened the key words that show I was speaking of one spot. I've also made it clear in other posts that it is one spot.
Thank you for the link. Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.
It is the locus of the spot over time.
I'm not sure what you mean by dimensions because the figure will be larger or smaller depending on how far away the screen is. The maths shows the locus which traces out the shape. So if by dimensions you mean shape, then yes.
I am interested in the maths of the physics of the wave periods creating the pattern.
That is what the maths shown does.
a and b in the formula represent the frequency of the 2 tuning forks. As Alan explained, the relative frequency and phase of a and b determine the pattern.
It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror... In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)
Are you with me so far?
Ok up to the word albeit. Why did you write "albeit the movement of each is at right angles to the other"? The movement has to be at right angles otherwise you would just get a single line.
It's not the changing distance between the mirrors as I explained in an earlier post.
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It is not a case of me knowing the answer. We all know the answer and have been trying to impart it to you. You have chosen to be obstinate and self defeating. Instead why not pick up a book on arithmetic or algebra and start reading. You might have a pleasant surprise. Once you start becoming confident with the mathematics then you won't have these problems. To do otherwise is laziness.
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You know Jeff - I've been talking to people on this thread for a year and a half. I can remember that Colin plays guitar, is interested in outside sound recording, and has either an outsized or undersized woodpile on one side of his garage (unless he's dealt with it since last year)...
You were very ill in hospital last year, you lungs, you have worked as a water flow engineer (or something very similar), you have an intelligent wife, your dad is bigger than Theboxes dad, and your daughter displayed usual behaviour as a child...
What I remember about details of Alan would fill a couple of pages.
Is it so hard for you to remember that I conduct all my internet activity on a small phone screen (that is cracked and constantly freezing up) because my laptop is broken, that my horse and carriage business is far and beyond on the skids, I have no money and both my family and the animals are driven by a powerful need to eat, and time is the payment required to achieve that. Alternatively animal welfare will take the horses that are too old to sell or re-home, and put them to death.
I am not too lazy to learn maths, I just don't have a natural affinity with the notation and find it hard to visualise the physics of an equation unless it is broken down into words and put into context.
I think it is perfectly acceptable to ask for help, and for clarification of that help when necessary, and that skill sharing is a pleasant ideal. I have certainly always helped others to understand anything they thought that I might be able to help them with.
I also think it a display of dubious character to ridicule those who one feels are inferior to ones own self, as you clearly feel that I am to you. But please know, I am not inferior to you, I am different to you, and although I do have a high opinion of my own abilities, I don't have any less high opinion of anyone else's. I feel that we all have something to offer, and at the other end of the scale, no person can know everything. Therefore it is just as well people are different from each other, and think about things from different perspectives, because it would be a bloody well boring world if we didn't.
I'm not here to have a my cock is bigger than your cock competition. I understand and fully admit where and when my understanding is lacking, and know that I sometimes miss use terminology. But on the basis that you guys are pretty clever, right?
...I merely wish to talk in depth about physics, and the physical experiments of physics, and preferably I'd like to have FUN when I'm doing it.
Is that too much to ask?
Now what I am asking is if the formula that Alan provided describes the changes in the distance between the vibrating surfaces the light is being reflected off, or if it would be a different formula that describes this...
I'm quite sure that no-one has tried to impart this to me as of yet.
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Please excuse my 'tone', but it is born of frustration. I've tried to explain this from a number of different angles and I've often had the feeling that you really haven't read, or at least not understood, what I have written. The impression you can give is that I really don't understand what I am talking about. So tucking my sensitive .....
Ok, example of misreading:
My contention with your post was that you said that a Lissajous figure is the result of 2 laser dots combining on a screen. Its not 2 dots, its 1 dot vibrated into a line, that is then vibrated into a pattern.
Look again at the quote in your reply to Alan:
So the spot on the screen traces, albeit magnified, the motion of the end of the tuning fork.
With 2 tuning forks the motion on the screen will be a combination of one moving the spot up and down, and the other moving it side to side such that at any point in time it's xy position (coordinates) will be specified by the value derived from the formulae Alan posted.
I've emboldened the key words that show I was speaking of one spot. I've also made it clear in other posts that it is one spot.
Thank you for the link. Please excuse me if I am wrong, but the maths portrayed are describing the dimensions of the Lissajous pattern itself.
It is the locus of the spot over time.
I'm not sure what you mean by dimensions because the figure will be larger or smaller depending on how far away the screen is. The maths shows the locus which traces out the shape. So if by dimensions you mean shape, then yes.
I am interested in the maths of the physics of the wave periods creating the pattern.
That is what the maths shown does.
a and b in the formula represent the frequency of the 2 tuning forks. As Alan explained, the relative frequency and phase of a and b determine the pattern.
It is because both mirrors are vibrating back and forth that a Lissajous pattern is caused in the beam of light reflected from one vibrating mirror to another vibrating mirror... In that both mirrors are moving back and forth, albeit the movement of each is at right angles to the other, the distance between both of the mirrors is altered by this movement and constantly changing from long short, or short long - or the distance between the mirrors stays the same but the position of this distance in space is changing from one side to the other and back. (In phase, out of phase)
Are you with me so far?
Ok up to the word albeit. Why did you write "albeit the movement of each is at right angles to the other"? The movement has to be at right angles otherwise you would just get a single line.
It's not the changing distance between the mirrors as I explained in an earlier post.
Ah Colin - just saw your post, and I take on board your underlining of emphasis as pointed out, and can say I was mistaken in my interpretation...
It may look as though I am not reading through because I do not answer each point in multi quotes. It takes hours to create them on this phone screen, so much as I'd like to, I don't have time. I just pick the most relevant bits.
So if a) is one frequency, or sine wave, and b) is the other, ie: tuning fork 1 and tuning fork 2, can we now look at the phase that you refer to? What in the physical experiment represents phase?
(edit: we can come back to the angle the beam of light hits the mirrors at after)
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The distance between the tuning forks is irrelevant. What matters is the angular deflection of the beam in the x and y directions. The separation has to be small enough (or the mirrors large enough) that the beam reflected off the first mirror is always intercepted by the second mirror, but that's it.
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I realise Alan that the length of distance that the tuning forks are 'set up' apart is irrelevant, apart from the image created by the back and forth of the first mirror fitting onto the second mirror...
It is the miniscule changes in this set up distance caused by the back and forth motions of the mirrors that I'm referring to.
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That will induce a minuscule asymmetry of the Lissajous figure. So?
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So - do the maths you provided describing the geometry of a Lissajous figure also describe this asymmetry, or would describing this asymmetry of the Lissajous figure require a different set of maths?
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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!
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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!
Maybe you need to revise a little trigonometry. And no don't mention equilateral triangles.
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I think you would just add a small constant to one of the sine waves, but now I'm having difficutly even imagining the optical path!
Yes...(chuckle)... It's beyond mind boggling trying to imagine the the optical light path creating the circle, let alone more complex patterns...
The changes in the 'set up' distance between the mirrors is phase dependent...
Hit both tuning forks at same time from the left side, and we have the 'set up' distance rocking back and forth in space right to left...
Hit both tuning forks at the same time from the right side, and we have the 'set up' distance rocking back and forth in space left to right...
Hit both tuning forks at the same time, 1 to the left, 1 to the right, from the internal orientation, and the 'set up' distance changes, rocking from longer, shorter...
Hit both the tuning forks at same time, 1 to right, 1 to left, from outside orientation, and the 'set up' distance changes, rocking from shorter, longer...
...the changes in distance between the mirrors are then vastly complicated by the orientation of the movement of the mirrors being at right angles. This in effect adds another dimension of long short, short long, and rocking of distance in space from right to left, or left to right.
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So if a) is one frequency, or sine wave, and b) is the other, ie: tuning fork 1 and tuning fork 2, can we now look at the phase that you refer to? What in the physical experiment represents phase?
It is the relative phase of the 2 sinewaves.
In the double pendulum you can start them together or with any phase relationship you want.
With the tuning forks starting them with a specific phase relationship will be tricky as the common way of starting is by tapping it and, as you will never get the timing exact, the phase will be random.
However, it's not too critical, it is unlikely you will hit exactly inphase or at pi so if f1=f2 you are unlikely to get straight lines, neither are you likely to get a perfect circle, an ellipse is the most likely.
I notice you are asking Alan if the maths he described covers the change of distance between the forks. The thing to consider is that the maths describes perfect lissajous curves (produced mathematically) and any mechanical system will introduce some imperfections.
For eg I had a think about the double pendulum and reckon there are at least 3 imperfections:
- the sand comes out at a constant rate but pendulums have their max speed at the bottom of swing and minimum at the ends, so the thickness of sand will change making the line slightly wider in places.
- the sand also has inertia so at the ends of the swing I think it will overshoot slightly distorting the curves.
- the pendulum doesn't trace a path parallel to the surface, so some distortion will result.
Also, if the system uses a pen rather than sound there will be friction that affects the curves. I'm sure you can think of others.
The tuning fork/mirror system doesn't introduce much distortion, Alan is typically understating when he says minuscule as it is far less than that. I won't spoil your fun by telling you what I think it is, but to aid your calculations, the amplitude of the tuning fork can be taken as 1mm and you don't have to do all the combinations for the 2 forks, just the bounding conditions will give you the range of the effect.
When you've concluded that it is irrelevant to discussion on lissajous curves let me know.
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The phase between the sine waves is physically represented in the changes of position of the set up distance in the surrounding space, or changes in the distance of the set up distance between the mirrors...
Yes these changes in distance are minuscule, but they are the distances that the light beam travels and these miniscule differences are what is amplified by the distance between the second mirror and the display screen. If not for this amplification, what we would observe would be too miniscule to properly discern.
You are correct, this discussion is not concerning Lissajous figures, it is concerning the distribution of resonant vibrations. It's what's happening between the mirrors that interests me, not what is occurring on the screen.
Evan made a post earlier this thread explaining how a singular mirror on an axis can be driven to creating Lissajous figures. The phasing between the sine waves occurs on 1 mirror moving in 3 dimensions.
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OK let's have another go at the tuning forks. Assume the first one produces a perfect sinusoidal oscillation in the x direction. This is amplified by the distance from the center of oscillation to the final screen. The second mirror would do the same in the y direction but also alters the x amplification because it is altering the length of the optical path from the x mirror.
Of course it isn't the linear displacement that causes the beam to move, it's the angular movement, and this is a fraction of a degree for a tuning fork, so you would probably need a meter or so of optical path to get a visible display. If the amplitude of the fork vibration is 1 mm then the variation in x amplification will be +/-1/2000, almost certainly undetectable and anyway of absolutely no physical significance.
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OK - stating any amplification of effects as being due to a) the distance between the first mirror in line to the laser beam source and the second mirror, and b) the distance between the second mirror in line to the laser beam source and the screen...
We can now look at the scenario where there is just a singular mirror set up on an axis being driven by 2 sine waves, and the amplification of effect is due only to the distance between this singular mirror and the screen - where clearly these very small movements of the phasing between the sine waves in the mirror are of physical significance, because if they were not occurring, a Lissajous figure would not be reflected onto the screen...
The axis provides the mirror with 3 dimensions to move in... So - the 2 dimensional image on the screen is the result of motion occurring in 3 dimensions.
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And the third dimension is irrelevant except for a possible tiny asymmetry of the curve. Not that anyone would use an optical Lissajous to make a precise sine/sine curve anyway. It's OK for arty photographs and stadium laser shows, though it's probably easier nowadays to wiggle the laser or LED directly, but it's a bit old-hat in either case and a lot more complicated to set up than a Spirograph.
The appearance of the figure does not depend on small movements of phasing. A stationary figure will have a fixed phase difference which can vary from 0 (to give a straight line) to 90 degrees (a circle). If the phase difference is a multiple of 90 degrees + a constant, ie phase locked sine waves of different frequencies, you will get stationary multiple closed loops with a tilt. All that the z-induced phase error will do is induce a bit of jitter into your nice image.
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My interest doesn't stem from an arty point of view, nor musical...
What I am interested in is the wave period, ie: amplitude of vibration, of 1 sine wave being changed by the wave period, ie: amplitude of vibration, of the other sine wave, and that a 3rd wave period of vibration emerges as a result of this change. It is the maths of these 3 dimensions of motions that interest me. (Yes I can appreciate that jittering, or a Lissajous figure that is displaying movement is due to various degrees of 'out of phase'.
The Lissajous figure is a 2 dimensional representation of motion in 3 dimensions over time... Are there maths that describe these motions?
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The Lissajous figure is a 2 dimensional representation of motion in 3 dimensions over time... Are there maths that describe these motions?
No, because as we've said before the lissajous figures are not a 2d representation of 3D.
What I am interested in is the wave period, ie: amplitude of vibration, of 1 sine wave being changed by the wave period, ie: amplitude of vibration, of the other sine wave, and that a 3rd wave period of vibration emerges as a result of this change. It is the maths of these 3 dimensions of motions that interest me.
Just a point of terminology, wave period is not the amplitude of vibration.
What you describe doesn't happen in this tuning fork set up and doesn't need 3 dimensions. Have a look at Fourier transforms to understand mixing of waves.
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Amplitude is the height of a maximum, or half the total span.
You can alter amplitude by adding waves of the same frequency. The Lissajous figure does not do this. The x and y amplitudes are the amplitudes of the original waves.
Period is the time or distance between two successive maxima.
You can alter periods by multiplying waves of different frequencies. The Lisassajous figure does not do this although the rate of repetition of a cyclic figure does depend on the frequency difference. The x and y frequencies are the frequencies of the original waves.
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Alan - Yes, as you say "The x and y amplitudes are the amplitudes of the original waves."...
These amplitudes of those original waves are causing changes in the distance between the mirrors attached to the tuning forks creating those original waves, and this amplitude of those original waves changes in each of the mirrors at every position in time of the back and forth motions that are occurring at right angles to each other.
It is this part of the process that I wish to discuss and understand the maths of. In that a pattern is created that is a continuous line, the motions between the mirrors are repetitive... And in that the motions are repetitive, they constitute a wave form, and a wave form has a period.
Are you with me so far, 'cos if you are I'd like to expand the discussion into translating distances into time periods. If not, say where your problem is and we will address the problem/s first.
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Colin - the mechanics that cause a Lissajous figure are occurring in 3 dimensions, it is these mechanics in 3 dimensions that are of interest to me. That something that is moving in 3 dimensions creates a pattern suggests to me that there are 3 dimensions involved, but if you insist that a Lissajous figure itself is 2 dimensional, then so be it... Actually whether it is or not is incidental to the discussion itself which is about the 3 dimensional mechanics causing the patterns, ok?
As to your statement that says that the mechanics creating the patterns are not occurring in 3 dimensions, either I'm just not understanding what you mean, or you need to think it through more thouroughly. The mirror is attached to a tuning fork, the fork has a frequency it resonates at when hit, and when hit it rocks back and forth. This action tips the mirror from side to side, or up and down. These motions 'are' 3 dimensional, and it is these motions that cause the pattern, over time.
...and, I will most certainly have a look at the maths, but to be clear, are you saying that it is the Fourier transformations that are describing the 3 dimensional motions of distance change occurring between the mirrors?
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By pythagoras, the distance between two points oscillating at right angles to each other is the rest separation plus the square root of the sum of the squares of their positions which at time t are x = a sin ft and y = b sin f't.
You can't "translate distances into time periods" unless there is a known velocity, in whcih case the question is as trivial as navigating by dead reckoning. d = vt.
So you want to know the speed of each mirror at time t. Easy. a cos ft and b cos f't. The calculation of square roots is left as an exercise to the reader, but the answer must be cyclic because there's nowhere else to go!
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In this case translating distances into times wouldn't present a problem, as the light travelling these distances is doing so at constant velocity...
...but the concept of knowing the speed that the mirror is travelling at works well enough, (speed, distance, time formula) and is convenient to the discussion in that it leads to the concept of Doppler shift...
The distance the light is travelling from the first mirror to the second mirror is constantly in flux. On the forward motion the light is travelling from a surface being pushed forward towards the receiving surface. On the outward motion the light is travelling from a receding surface.
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If you are just interested in the Doppler shift from a moving mirror, why not say so? deltaf = 2v x f/c where v is the instantaneous velocity of the mirror.
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As to your statement that says that the mechanics creating the patterns are not occurring in 3 dimensions, either I'm just not understanding what you mean, or you need to think it through more thouroughly.
I can assure you I have thought it through very thoroughly. I have even worked out the best orientation of the fork/mirrors which minimises distortion and tested some ideas with mirrors and laser.
The mirror is attached to a tuning fork, the fork has a frequency it resonates at when hit, and when hit it rocks back and forth. This action tips the mirror from side to side, or up and down. These motions 'are' 3 dimensional, and it is these motions that cause the pattern, over time.
You need to separate out the motion which creates the lissajous and the motion which doesn't. I have taken to calling them lateral and longitudinal in order to keep them clear in my mind.
If the mirror is attached to the side of the fork it does, as you say, rock - like a lever pivoted at the bottom of the arm. This creates 2 movements. First, a change of angle of incidence between the beam and the mirror, this creates a changing angle of reflection or deflection causing the beam to sweep up and down - I call this the lateral movement. This sweeping, vertical movement is passed to the second mirror which vibrating at right angles to the first adds a horizontal movement. It is the combination of these 2 dimensional movements - up/down, side to side - which creates the lissajous figures. No third dimension is required - think about the double pendulum, 2 dimensions of movement.
In addition, as you say, the rocking of the arm causes a movement along the path of the beam (longitudinal) shortening and lengthening the distance between the forks. This causes, as Alan rightly said, a very small timing jitter in the beam, it also causes a very small alternating Doppler Shift in the beam.
The jitter causes a very slight variation in the dwell time as the beam traces out the lissajous (remember how the sand can pile up less when the pendulum speeds up) and if it were possible to measure it there would be a very slight variation of brightness over the curve. The Doppler, again if you could measure it, would cause slight variation to the colour of the beam at various sectors of the curve. However, both of these effects are so small that it is impossible to see them.
There is also a a very, very slight distortion of the curves due to the angle of incidence of the mirror relative to the beam not twisting in the same plane but following a slight curve, I haven't plotted this out but I think it slightly distorts the extremes of the loops, but again it is below measurable level.
As I said before, every mechanical system introduces some distortion, but this system produces very little.
It's worth noting that on the net there are diagrams showing some setups with the mirror attached to the end of a tine facing upwards with the beam shining down onto it, in this case the forward back motion is virtually eliminated and yet lissajous curves are still produced.
As you can see I have thought it through, but why do I expect you won't be convinced?
...and, I will most certainly have a look at the maths, but to be clear, are you saying that it is the Fourier transformations that are describing the 3 dimensional motions of distance change occurring between the mirrors?
No, you were asking about 2 waves being combined to create a third. If you want to look at 3 dimensional motion between the mirrors forget Fourier it won't help you.
Note- I see Alan has responded while I was typing. He understands.
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If you are just interested in the Doppler shift from a moving mirror, why not say so? deltaf = 2v x f/c where v is the instantaneous velocity of the mirror.
What interests me is that the 'speed' of a Doppler shift can be translated into a period of time via the speed distance time formula where light is the travelling phenomenon, but enough of this for the moment...
So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?
Edit: To clarify, I am not referring to a frequency change in the light... A Mossbauer effect of receiving a gamma ray conducted horizontally in a uniform gravity field will not respond differently if the gamma ray emitter is attached to a vibrating speaker cone. The photon will still be received.
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So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?
Alan agreed this back in #41 and pointed out that it doesn't affect the lissajous patterns.
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What interests me is that the 'speed' of a Doppler shift can be translated into a period of time via the speed distance time formula where light is the travelling phenomenon, but enough of this for the moment...
This sentence is meaningless.
So long as we can agree that Doppler shifts are occurring in the passage of the lights optical path?
obviously
Edit: To clarify, I am not referring to a frequency change in the light...
but that is exactly what a Doppler shift is!
A Mossbauer effect of receiving a gamma ray conducted horizontally in a uniform gravity field will not respond differently if the gamma ray emitter is attached to a vibrating speaker cone. The photon will still be received.
only at those times where v(cone) = 0 i.e. at the max and min displacement, when there's no Doppler shift. That's the whole point of the experiment.
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No, it is not meaningless Alan... The speed that the mirror moves forward with is inherent with a distance. The mirror only moves so far forward... Subtract the distance that it moves forward from the original distance, divide this distance by speed of light and you have a time value. The light didn't travel that distance, therefore the time it takes to complete the shorter distance is lesser. Subtract time value from the original time.
A backward motion will do the opposite and add time to the distance.
Yes - the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting. The frequency of the Doppler shift denotes the speed at which the expansion or contraction is occurring...
But we can see in the mechanics of the movement between the mirrors that the light does not travel the distance that is behind the moving forward mirror, nor the distance behind the moving back mirror, and neither of these forward or backward speeds can add or subtract from the velocity of the light.
Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.
The Pound Rebka is a vertical experiment... Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration. I have never come across any myself...
Provide me evidence of this and I'll be packing up my 'New Theory' on new theories as a waste of time!
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Come on, lass, this is going backwards into the mists of incomprehension that you left at least a year ago!
No, it is not meaningless Alan... The speed that the mirror moves forward with is inherent with a distance.
Please don't talk bollocks! The speed of the mirror is a cos ft. What on earth does "inherent with a distance" mean? The mirror only moves so far forward... Subtract the distance that it moves forward from the original distance, divide this distance by speed of light and you have a time value. The light didn't travel that distance, therefore the time it takes to complete the shorter distance is lesser. Subtract time value from the original time.
A backward motion will do the opposite and add time to the distance.
No! A thousand times no! It adds distance to the distance, and time to the time. If you start arbitrarily mixing dimensions you will mislead yourself and look very silly.
Yes - the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting. The frequency of the Doppler shift denotes the speed at which the expansion or contraction is occurring...
utter bollocks.
But we can see in the mechanics of the movement between the mirrors that the light does not travel the distance that is behind the moving forward mirror, nor the distance behind the moving back mirror, and neither of these forward or backward speeds can add or subtract from the velocity of the light.
as far as we know, c is constant
Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.
No. The photon has no idea of its destination. Moving the emitter adds energy, and since c is constant, this must appear as a change in frequency.
The Pound Rebka is a vertical experiment... Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration. I have never come across any myself...
Provide me evidence of this and I'll be packing up my 'New Theory' on new theories as a waste of time!
PR alone results in equal and opposite values to the gravitational shift between up and down, so horizontal = no shift.
Sorry, I can't go on responding to this drivel. I thought you had read and understood the Pound-Rebka experiment. You certainly claimed to have done so. Why have you suddenly started writing utter nonsense about it, and now Mossbauer too?
Maybe you'd prefer to delete the entire post, and I will do likewise with this one, to save embarrassment?
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Alan - you can leave the post as is... You might not comprehend the notion that if the speed of light is involved, that a distance and a time are the same thing, are interchangeable, and more to the point can be confused with each other, but someone might...
You are correct in that you thought I had read and understood the Pound Rebka. I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.
What of it? Am I not allowed to call 'anything' into question? Am I just to accept what is spoon fed to me parrot style without engaging brain?
If you have experimental data that describes the use of a speaker in a horizontal Mossbauer experiment that confirms the frequency change on the horizontal, then fair enough! As I said, my curiosity then over and done with.
Do you? 'Cos as said last post, I haven't been able to find any...
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You are correct in that you thought I had read and understood the Pound Rebka. I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.
You may think that, but it is not what you said. Alan is questioning:
the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.
which is not true.
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If you have experimental data that describes the use of a speaker in a horizontal Mossbauer experiment that confirms the frequency change on the horizontal, then fair enough! As I said, my curiosity then over and done with.
Do you? 'Cos as said last post, I haven't been able to find any...
Obviously not, because there is no frequency shift in the horizontal plane. http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossb.html describes a classic demonstration that any movement reduces the absorption.
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You are correct in that you thought I had read and understood the Pound Rebka. I have, 'extensively' and do understand that the Doppler shift is thought to add or subtract energy for a 'longer' or 'shorter' wavelength.
You may think that, but it is not what you said. Alan is questioning:
the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.
which is not true.
Before I answer your post, just want to say from one sensitive soul to another, that on my reading through of your posts that it is difficult for me to multi mlquote...so I dont, I took on board your description of a light source moving closer to the screen, and further back from the screen in relation to Doppler shift, and found your analogy of longditudal and lattititudal waves rather inspired. Thank you.
Alan is not questioning anything. He is saying bollocks, drivel, and that we sorted this out last year. No we didn't... Although I can appreciate that Alan does not read every post I make, nobody posted the data I have asked for last year either.
The frequency of light does change in a gravitational gradient. It is thought that the Doppler shift created by the velocity of the light source (star) moving away from point of observation (earth), ie: a distance expanding - or moving towards point of observation, ie: a distance contracting, changes the wave length of the light.
Where have I gone wrong?
Edit: just saw Alan's post, looking at that now.
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Alan - I just cannot get that link to load, but I gather from the short description you gave that introducing motion to the gamma ray emitter results in less absorption.
This will be the case in both the vertical experiment, where this effect would be factored in, and a horizontal replication of the vertical experiment.
In the horizontal experiment, whereas no motion is introduced to the gamma ray emitter, a rate or percentage of absorption is observed.
Replicating this horizontal experimental on the vertical, where again no motion is introduced to the gamma ray emitter, results in this rate of absorption being zero (?). It is only when the motion is introduced to the gamma ray emitter and the frequency of this motion is cancelled out, that the gamma ray is received by the Mossbauer.
To complete the experiment definitively, (in my mind anyway) one would need to replicate the vertical experiment, where motion is introduced to the gamma ray emitter on the horizontal... where by the remit of the vertical experiment, introducing the motion to the gamma ray emitter should shift the frequency of the gamma ray and the Mossbauer will not be able to receive...
If the Mossbauer does not receive, this confirms the premises of the understanding of Doppler shift in relation to distance.
If the Mossbauer still receives the gamma ray, one must then re-examine the current understanding of introducing a Doppler shift to the gamma ray on the vertical, and the fact that the Mossbauer only then receives it.
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Thank you.
Glad it helped
The frequency of light does change in a gravitational gradient. It is thought that the Doppler shift created by the velocity of the light source (star) moving away from point of observation (earth), ie: a distance expanding - or moving towards point of observation, ie: a distance contracting, changes the wave length of the light.
Where have I gone wrong?
Both of your statements are true.
Doppler is created by a moving star relative to detector.
Frequency does change in a gravitational gradient, but it changes even when source and detector are stationary relative to each other, so no Doppler in that case.
I'll let you and Alan discuss the subject as there is obviously some history I'm not aware of.
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Yes me too :)
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As to history Colin, I remember reading way back Alan saying somewhere that he only comes in 2 modes: Intellectual thug...and (scratches head), hmmm...I can't for the life of me remember the other mode...(chuckle) ...
But for anyone who might not realise, do not think that my getting gloves off and going a few rounds with Alan means that I do not respect him. It's quite the opposite actually.
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Timey: RTFM. I'm out.
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Only trouble is that the manual comes with a post script that clearly states that it is incomplete and cannot provide a full picture of the universe. Hence a bunch of frustrated physicists who are still mulling over the same unsolved problems that incite the same conversations repetitiously day in day out.
For anyone who can appreciate a conversation that deviates from the norm... that attempts to approach a problem stated in the manual by taking logical steps to unpick the physical mechanics of experiment and understand that there are symmetries that must be adhered to...
ie: That if shaking a gamma ray emitter on the vertical causes a frequency shift in the gamma ray, that shaking it in the horizontal will do the same... And because the gravitational shift will not re-shift the frequency of that shaken gamma ray on the horizontal, because the gravity field is uniform(ish) on the horizontal, that the Mossbauer on the horizontal will not be able to receive it! The gamma ray will not have the correct energy level to be received!
Am I wrong about this symmetry?
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The link Alan provided loaded for me today, so let's examine said manual.
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/mossb.html#c1
Quote:
"The Mossbauer effect involves the emission and absorption of gamma rays from the excited states of a nucleus. When an excited nucleus emits a gamma ray, it must recoil in order to conserve momentum since the gamma ray photon has momentum. But this takes energy, and the gamma photon has less energy by about 1 eV for a 100 keV photon. The sharpness of an energy state in a potential target nucleus has a natural line width on the order of 10-5 eV, so that the shift in the photon energy prevents the target nucleus from absorbing the gamma photon.
Mossbauer discovered that by placing emitting and absorbing nuclei in a crystal, you could use the crystal lattice for recoil, lessening the recoil energy loss to the point that these extremely sharp emission and absorption lines would overlap so that absorption was observed. An important result was that you now had an extremely sensitive detector for energy shifts - a motion of either source or absorber with velocities on the order of millimeters per second was enough to detune the absorption."
Unquote
So - examining this stage by stage:
Quote:
" When an excited nucleus emits a gamma ray, it must recoil in order to conserve momentum since the gamma ray photon has momentum."
Unquote
...And the gamma ray photon is not absorbed by the target nucleus...
By adding the crystal lattice this recoil motion is reduced - so we are seeing a backward motion of recoil being eliminated by the addition of the crystal lattice. Now we have overlapping line widths, and the gamma ray can be absorbed by the target nucleus.
In adding motion to the gamma ray emitter, it makes logical sense that adding a backward motion would ensure that the gamma ray will not be absorbed. Or that adding a backward motion to the target nucleus would elicit the same physical effect...
So effectively the motion added to the gamma ray emitter could be viewed as adding in the same effect that the crystal lattice took out, and the result is that we see the absorption reduced.
In the vertical experiment, when whatever it is in the gravity field cancelled out the added effect of adding in motion, absorption is observed. It is only when this added motion is matched to whatever it is in the gravity field that is cancelling out this added motion, that absorption will be observed.
The motion added has an associated distance. ie: the distance the speaker cone moves back and forth, (or mirror, where Lissajous is concerned)... This distance, in respect to the speed of light 'can' be translated into a period of time. Therefore in the vertical experiment it could be viewed that in adding a backward movement, that this is in effect adding time to the journey of the gamma ray, and that what is being matched by the gravity field is a time related matter, and not distance related. The mechanics of the motions between the mirrors of the Lissajous are suggestive that this may be the case.
A perspective that would require you to consider that a gravity field itself, ie: the space surrounding a body of mass is inherent with a gravitational time dilation factor of its own, separate from GR time dilation, and that this factor of time dilation causes time to get increasingly slower (for the empty space only) with distance from mass.
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What a load of old cobblers. If you made sense it would be worth replying to your posts.
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Sure - stick with your vastly overcomplicated quantum computations and your search for dark energy. And be as unpleasant as you like while you do it... Its hardly original behaviour.
I can fully understand why it is that so many of the people who 'have' made controversial and game changing contribution to physics and science have had such a miserable time of it in their lives.
The history books are full of exactly this kind of blatant unwillingness even to make a consideration of alternatives, a type of almost religiously slanted dogma that has historically driven many intelligently oriented minds to starvation, illness, and even suicide.
So do I take it that there is nobody here who can take a conversation beyond textbook parroting. No-one who can look at the physics of experiment asymmetrically, and no person who can observe or observe anyone else observe anything other than what is written in the text book without lapsing into rudeness, and hateful prejudice?
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If Einstein had not been looking for a steady state universe he would not have added a cosmological constant, which he then retracted in light of Hubble's redshift 'velocities'. He would have been forced to consider a contracting universe...
Now line me up and shoot me down for it as is your wont, but that is what I am considering, and it is indeed a highly logical approach!
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I am getting very tired of watching you insult the people that are trying to help you. You may find it amusing in your own passive aggressive way. I don't.
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I am getting very tired of watching you insult the people that are trying to help you. You may find it amusing in your own passive aggressive way. I don't.
And I am getting very tired of you commenting on anything apart from the topic of the thread...
I have insulted nobody. I am stating facts. Nobody here wishes to discuss anything in terms that are not already written in a text book. This is understandable, because if something is not written in a text book, then you guys have not been taught what we are talking about.
It is a fact that this seems to present a problem for all of you to some degree and manifests itself in different ways dependant upon the character of the person I'm talking to... You seem to relish any opportunity to give anyone else reading the impression that you are of the intelligence to be able to discern between sense and nonsense, and really do seem to enjoy being belittling...otherwise why would you do it?
Alan and Colin, I feel, can see that I am in possession of a degree of intelligence, but become frustrated at their lack of understanding (due partly to my having difficulty explaining myself) of the concepts I'm trying to impart.
Now 'if' you do actually wish to comment on the topic of the thread, be my guest...
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If Einstein had not been looking for a steady state universe he would not have added a cosmological constant, which he then retracted in light of Hubble's redshift 'velocities'. He would have been forced to consider a contracting universe...
Now line me up and shoot me down for it as is your wont, but that is what I am considering, and it is indeed a highly logical approach!
Clearly in a universe that is not expanding, the remit of what Hubble's red shift velocities represent must be reexamined...
And as distance and time are equal in the face of a constant speed of light, then if it's not distance expanding, then it has to be time...
Makes absolute and perfect sense to me.
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Nobody here wishes to discuss anything in terms that are not already written in a text book. This is understandable, because if something is not written in a text book, then you guys have not been taught what we are talking about.
I have been learning physics since secondary school and it is my opinion that the textbooks and teaching (sometimes by people who don't fully understand what they are teaching) only scratches the surface. But, and it really is a big but, it does give a grounding in the fundamentals of how things work, Newton F=ma, frequency, sinewaves etc, and as such gives a good toolkit for understanding the things they don't teach you. Added to this is all the experience of trying to fix things that don't work, designing experiments, and just good old trial and error.
I don't know about Alan, but I think it's the same, I had never come across the double tuning fork set up before and as far as I am aware it's workings are not described in any textbook, so you need to use the toolkit to work out how it all functions.
Is everything I say just what's in textbooks or what I've been taught? In the areas I'm interested in most of my information comes from experiments I've done, experience, talking to other researchers, and much of it isn't in any textbook. I'm convinced, from what he talks about, that the same is true for Alan.
Am I trying to belittle you or prove that you are wrong? Not my intention, nor I believe is it Alan's, but in my area of interest I have gathered information on eg Chladni, acoustics, which will conflict with the way you might think, intuitively, that it works. I had hoped that information might be helpful, but I can understand if you are skeptical.
Alan and Colin, I feel, can see that I am in possession of a degree of intelligence, but become frustrated at their lack of understanding (due partly to my having difficulty explaining myself) of the concepts I'm trying to impart.
And vise versa.
Intelligence is not really the issue. To some extent the difficulty of explaining can be down to not having worked with certain equipment, or knowledge of maths or terminology. You might not have understood the maths Alan posted, but for many of us it describes exactly what is happening. When he posted his comments about jitter I was just about to post almost exactly the same. When you spoke of phase shifts I was confused, you might think it pedantic to discuss which words to use, but without common understanding of terms, understanding of meaning becomes difficult.
Now 'if' you do actually wish to comment on the topic of the thread, be my guest...
Do I want to comment on the topic?
The topic asks “Can this relationship be derived between Schrodinger equation and Doppler shift equation? “ but doesn't specify which 'this' is being discussed. The OP only mentions Chladni, Lissajous etc.
Do I want to discuss Schrodinger and doppler? There are a lot of differences between my area of interest and QM, as we've said frequencies can have specific energies at Schrodinger's level, but not at Chladni plate level, so I'm not certain the discussion would be helpful to you or me.
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Colin - I am really appreciating this post. You will note that I did not include yourself and Alan in my tirade. You have in the past on another thread enquired of me if your input was desired or not. My answer being yes, and that your posts are appreciated.
Yes you are right, although I am well read, my use of terminology is unformalized. This being in part because I have not learnt physics in modules with exam questions in mind, but as a whole. This is where I run into problems with both you and Alan, because you are both conditioned by your education to think of things as separate issues, I'll come back to this.
My main contention is with Jeff's posts where he states that things don't make sense. Now don't get me wrong, I respect Jeff's intellect, and have made no secret of the fact that I think that he has a keen mind. This only compounds my frustration as indeed I would very much like to know what Jeff means when he drops such posts in response to mine. The fact that these posts of his are suggestive that he knows something, something that he intimates that everyone knows, everyone except me, and that everyone has already told me really annoys me, not only because it serves nothing to furthering the conversation, but also because these are the exact same responses I got from Jeff in response to my cyclic model posts on new theories - when actually it turned out that Jeff was formulating his responses based on a cyclic universe model that is not my model!
I actually read 'almost' everything posted here on the forum. My internet connection is my only luxury of late, and believe me I get my monies worth. I have a strangely oriented mind. If I had met you in person as a face rather than a name on the net, I would remember all sorts of quirky details about you, and if it became pertinent to me... (not to you mind, as my old man would attest to between gritted teeth), ...I would be able to flash back total video recall of a conversation from 10 years ago and relate it to you word for word... But unless you were a semi regular feature in my life, and even then sometimes, I would have difficulty in remembering your name. And even if you were a semi regular feature in my life, if I saw you out of context say in a supermarket aisle, I would know that I know you, but be unable to place where from. On reading about genealogy I recognise these symptoms as being synonymous with the autistic strain. And this tallies with the fact that my mapping skills are extra sensitive, in that while it doesn't entirely upset me as such when things I put somewhere are returned by other people millimeters out of place, it does severely register... and also in that I suffer of a certain sense of social awkwardness at times... In any case my point being that some of the problems I have with the remembering of terminology are not just physics related.
But back to thread business...
I mentioned earlier about viewing physics matters as separate issues from each other... I am looking at the Chladni patterns as having a connection to the Schrödinger equation. I am also looking at the mechanics creating the Lissajous figures as being connected to Doppler shift. Then I am looking at both the Chladni and the Lissajous as being connected via the distribution of resonant vibrations and 'trying' to draw parallels between the two phenomenon as they are both created due to frequency, as are Doppler shifts, and 'trying' to find a connection between the phase changes that occur. This is where the mathematical interest is for me. Not in the individual phenomenons of Chladni, Lissajous, and Doppler, but in the phenomenon that all 3 hold in common...
http://physics.stackexchange.com/questions/29551/quantum-explanation-of-doppler-effect
Then looking at the link above, and answer 2 in relation to answer 1, the Lorentz transformations, which calculate 'phase' changes in time and distance, and perturbation theory, which also calculate in a way that could be viewed as 'phase' changes, are what is connecting the Schrödinger equation with Doppler shift in quantum computations.
This is the context of the thread...
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…. although I am well read, my use of terminology is unformalized. This being in part because I have not learnt physics in modules with exam questions in mind, but as a whole. This is where I run into problems with both you and Alan, because you are both conditioned by your education to think of things as separate issues
Yes, I can see how that viewpoint highlights differences in the way we analyse information and make judgements.
In any case my point being that some of the problems I have with the remembering of terminology are not just physics related.
understood
This is where the mathematical interest is for me. Not in the individual phenomenons of Chladni, Lissajous, and Doppler, but in the phenomenon that all 3 hold in common.
I don't know how much perturbation theory you have done, but the good news is you won't need it for this. Alan has given you the maths for Lissajous in what I call the 2 lateral dimensions x&y, and in #126 and #128 he gives the maths for the longitudinal z dimension. Because both are due to the tuning forks you should be able to plot the changes in frequency and intensity onto the lissajous and it will be cyclic and in phase.
Good luck in your quest.
While I was checking which posts Alan had given the maths in I noticed this:
Adding a vibration to the gamma ray emitter of the Mossbauer simply means the light has a little less time (forward motion), or a little more time (backward motion), in which to travel to the destination.
Which although it is true is not the reason for the absorption and nonabsorbtion.
You may also remember I questioned this statement:
the frequency of light changes in a gravitational gradient and this effect is thought to be due to Doppler shift, because distance between source and receiver is expanding or contracting.
which is not true.
You say:
The Pound Rebka is a vertical experiment... Have you got any experimental data on a Mossbauer conducted on the 'horizontal' that states frequency change in the gamma ray via this vibration. I have never come across any myself...
Mossbauer spectroscopy is performed horizontally. Does this help http://ohm.bu.edu/~pbohn/REPAIR__Advanced_Lab/Mossbauer/Reference/Mossbauer%20Setups.pdf
Up to page 11 is theory but after that he goes through various mechanisms including loudspeakers.
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Unfortunately Colin that link is a pdf and I cannot download pdf's on my phone (laptop broken). I also haven't been able view the Yale link that Jeff posted earlier this thread, and the 'applications of Lissajous' link that I posted...couldn't view that either, but I'd heard of the researchers.
I haven't done any perturbation theory. I have read about it. I know that it is used to calculate the probability of position in quantum...
However, you really have arrived at the crux of the matter in saying that perturbation would not be needed to calculate the mechanics of the motions of the mirrors of the experiment in relation to the Doppler shifts these mirrors cause to the optical path of the light. And... neither perturbation, nor the Lorentz transformations would be needed to discern a relationship between the motions of the mirrors causing a Lissajous in relation to the motions of a Chladni plate causing a pattern.
I suspect that a relationship can be derived between the maths of the motions causing a Lissajous, and the maths of the Chladni patterns that correspond with the Schrödinger equation.
The implication being that by deriving a relationship between the mathematics of the motions the Lissajous, and the mathematics of the motions of the Chladni, given that the Lissajous are already connected to Doppler, that it would be possible to calculate these naturally occurring step effects of quantum without the perturbations because the indeterminacy would be fully determined. (this should correspond with what I have suggested as to Planck's h constant and the ultra violet catastrophe, which in turn is connected to the Mossbauer effect)
Now I'm not a mathematician. I only work in pictures. I can picture the mathematics as geometry, architecture and mechanics, but cannot turn these observations into notation... This would require not just a mathematician, but an advanced mathematician.
It is very much my hope that someone somewhere who is qualified for the job will pick up on what I am describing here, (and elsewhere on the forum) and give it a go.
...I will however be watching and reading an ever lengthening queue of outstanding interests, the pdf you posted, Jeff's Yale link, and the application of Lissajous link I posted, and a whole pile of outstanding interests including Humandi's light experiments on YouTube (which are pretty impossible on phone screen) as soon as I get access to a laptop, so thanks for the link!
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Chaldni patterns fit periodic equations that have antinodes at the boundaries of the plate.
Solutions to the Schrodinger equation do not have finite boundaries.
Lissajous figures are not necessarily static - in fact stasis isn't even a stable solution to the equations.
There is no connection between Lissajous (two fixed frequencies) and Doppler (one velocity-modulated frequency).
Apart from that, the conjectures are....erm....conjectures.
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Ah Alan - good to see you back!
1st paragraph - yes
2nd paragraph - yes
3rd - I don't actually view the rendition of the Lissajous figures shape or form as being relevant to the motions, or the mechanics of the motions causing the shape - other than the fact that the line of the shape remains unbroken, and this indicates that the motions creating it are repetitious.
It is however the motion that can be observed of a Lissajous figure itself, either the lines appearing to flow in a direction, or the jittering effect, that are intensely interesting and relevant.
Earlier this thread I described how the set up distance between a tuning fork experiments mirrors will either be rocking back and forth, extending and shortening the set up distance fractionally. Or that the set up distance itself will retain its original distance as it is rocked back and forth, fractionally, in space...
Clearly, due to the right angled orientation of the mirrors, there will be a combination of both types of movement in the set up distance occurring simultaneously.
Mathematically, the motion of flow appearing in the line and the jittering effect should be a lot more interesting than the shape of the figure itself.
(I will post a Youtube video later that shows Chladni plate patterns that are not static.)
4rth - OK, let me rephrase. It is the mechanics of the motion of the optical path of the light, and this paths connection to Doppler shift that I refer to as connecting Lissajous to Doppler shift. What happens to the frequency of the light is not relevant. (at this stage)
5th - Yes indeed. One could not be more conjecture-ish. But on the basis that the motions between the mirrors appear to be translating into rather complex transitions between changes of distance that the light travels, and that these transitions can either be of distance itself changing, or of a distance changing its location in space, or 'more interestingly' doing both at the same time - it could be said that these actions are pretty reminiscent of the actions of the maths that describe interaction between Schrödinger equation and Doppler shift. ie: Lorentz transformations, and perturbations...
So an interesting conjecture 'perhaps'?
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4rth - OK, let me rephrase. It is the mechanics of the motion of the optical path of the light, and this paths connection to Doppler shift that I refer to as connecting Lissajous to Doppler shift. What happens to the frequency of the light is not relevant. (at this stage)
"My honorable and learned friend's assertion that frequency shift is not relevant to Doppler is, to say the least, bollocks, m'lud."
"The Court agrees. A clear case of contempt for the Laws of Physics. Off with her head."
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When I say not relevant, I mean not relevant to the issue in hand. What is relevant to the issue in hand is the path the light beam takes.
Is there any chance at-all that you may review any parts of what I'm saying that do make sense to you. I feel that this may be a more fruitful approach, if not to an actual understanding, then at least to a more interestingly oriented conversation?
... For instance mixing the reflections of 2 mirrors causing 'the type of motion' that causes Doppler shifts to occur, causes the set up distance of the tuning fork experiment to be changed in a combination of 2 different types of motion. Motion that causes the set up distance to expand and contract, or to change its position in space.
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Is there any chance at-all that you may review any parts of what I'm saying that do make sense to you.
For me I think you should avoid trying to broad-brush connect things which do not have a strong link of relationship. I think this weakens some of your arguments and, if you do develop a workable theory, could dissuade someone from doing the maths or from taking you seriously. You need to be more specific in your observations.
For example, force is connected to acceleration by the relationship F=ma. This is a general and consistent relationship.
You say "given that the Lissajous are already connected to Doppler", however there is only one example where a mechanism producing lissajous also produces Doppler. If the mirrors are placed on the tips of the forks, no Doppler; if a laser is put in place of the sand, no Doppler; on the oscilloscope, no Doppler, on the hand drawn plot ..., etc. So you cannot claim a general connection or relationship.
You tend to do this frequently, quoting relationships that are specific to a situation rather than general.
So it would be reasonable to say that the 2 tuning fork system with mirrors on the side generates both lissajous and Doppler which have a common ....... (where ........ is whatever feature you feel you would like to examine).
If you look at influential scientific papers they are very specific about what was done, how it was done, what was tested or not, and the limits of the conclusions.
Hope that helps.
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I do not understand why you believe that placing the mirrors on the ends of the tuning forks is any different from placing them on the sides... You still have a back and forth motion, and that back and forth motion lookstill changes the distance between the mirrors. It has to because the length of the tuning fork does not fractionally increase when it goes up, or when it goes down, and if you were to trace a line of the path that the end of the tuning fork takes in space, it would be a curve, not a straight line...
This is in fact of quite considerable interest because the curve the mirror makes on the ends of the tuning fork are convex, and the curve the mirror makes on the sides of the tuning fork are concave.
It is quantum physics that forms a relationship of Doppler with the Schrödinger equation via the Lorentz transformations and perturbation theory.
All I am doing is drawing parallels between the fact of the mechanics of the Lissajous incorporating changes in distance, caused by the vibrations of the mirrors, being a combination of expanding and contracting distances, and of a distance changing its position in space...
P.S. A laser placed on end of compound pendulum would not cause a Lissajous figure. Light cannot leave itself behind. The actions causing the motions are gyration and inertia caused by the force of gravity influencing mass. (I am almost tempted to say that you make these type of mistakes frequently, but I'll stow it Colin, I have no wish to put your back up)
(My model is a fully described cyclic universe, a synopsis of which is available through my forum info. As a concept it works. Yes it needs maths. No I'm not going to be able to manage that. Someone reading who can see a mathematical interest is either there listening and being interested, or they are not. This thread is attempting to illuminate another mathematical perspective on time and distance which pertains to my model. My model is either mathematically viable, or it isn't. I'd like to know, but to know I need someone to do the maths. It's why I'm here on the forum.)
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(I am almost tempted to say that you make these type of mistakes frequently, but I'll stow it Colin, I have no wish to put your back up)
You weren't tempted to say it you actually did say it. Which is a bit of a side swipe at someone pointing out your error. Try being a bit more respectful.
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This is in fact of quite considerable interest because the curve the mirror makes on the ends of the tuning fork are convex, and the curve the mirror makes on the sides of the tuning fork are concave.
The curve on the side of the tuning fork is alternately concave and convex.
I did the calculations before making the post, and although there is a theoretical shift it is orders of magnitude smaller than that from the sides, as Alan pointed out even the mirror on the sides creates only an infinitesimal change. However, if you want to consider it significant that's OK.
It is quantum physics that forms a relationship of Doppler with the Schrödinger equation via the Lorentz transformations and perturbation theory.
When schrodinger did his work on Doppler from a particle perspective he didn't use what most people refer to as the "schrodinger equation". It's worth reading the reply given by John Rennie in the link you gave it explains the Lorentz issue quite clearly.
All I am doing is drawing parallels between the fact of the mechanics of the Lissajous incorporating changes in distance, caused by the vibrations of the mirrors, being a combination of expanding and contracting distances, and of a distance changing its position in space...
I'm aware that it seems to be significant for you, but I'm not sure why. You mention the difference due to setup distance between forks, but if you do the calculation for two 1khz forks, in order to get a pi/2 phase change you would need to move the forks 75km apart.
P.S. A laser placed on end of compound pendulum would not cause a Lissajous figure. Light cannot leave itself behind.
It wasn't a mistake. As I have said before the lissajous curves are a locus, and that is traced out whether you can see it or not. If you need to see it you could put light sensitive paper on the platform.
The actions causing the motions are gyration and inertia caused by the force of gravity influencing mass.
I'm fully aware of that, but it doesn't create a Doppler Shift. That was the point of my post which was an attempt to show how you could improve the presentation of your theory to make it more attractive to someone willing to do the physics and maths, rather than them consigning it to the Box box.
Again I get the feeling I'm not really helping. However, you have the info on Mossbaur which will resolve your distance vs doppler issue and if you post pictures of shifting Chladni patterns you have enough info in my previous posts to work out why it happens. Enjoy.
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It is quantum physics that forms a relationship of Doppler with the Schrödinger equation via the Lorentz transformations and perturbation theory.
except that Doppler is a continuum process, not quantised, and has nothing whatever to do with Schrodinger.
P.S. A laser placed on end of compound pendulum would not cause a Lissajous figure.
Oh yes it does. The Lissajous figure you see on an oscilloscope or a laser display may appear stationary but that is due to the persistence of your vision exceeding the cycle time of the figure. If the dot moves slowly, photograph it. And remember that a stationary figure is not a stable or important solution of the Lissajous equations: it just means that f(x) = n f(y).
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Alan - this is an advanced discussion, you have a degree in physics!
But for anyone reading who is studying for their GCSE's, please understand that attaching a laser beam to the end of a compound pendulum will not create a Lissajous figure in the same way that reflecting a light beam off vibrating mirrors, (or a mirror on an axis), will.
If the light beam left a mark on a piece of paper placed underneath the pendulum at each position it passed over, the positions the laser passed over would build up a picture of a Lissajous figure over time, as does the sand.
The active motions of the compound pendulum, after the initial swing input, are the gyration and inertia caused by the force of gravity in relation to the mass of the pendulum...
When the light beam is reflected off a mirror/mirriors to cause a Lissajous figure, the active motions are the vibration of the mirror/mirrors... and the motions of the mirror are the same motions that cause Doppler shift in light. However, please note that a shift in frequency of the light beam has bog all to do with the Lissajous figure itself. Please also note that the Lissajous figure created by vibrating mirrors is also built up over time, but the time it takes to build up to producing the figure on the screen is determined by the distance the light travels at the speed light between the mirrors and onto the screen.
This all being rather obvious to anyone who has studied the phenomenon, as indeed I have!
Right oh, back to advanced physics now, aye...
Can we talk about the motions between the mirrors of the tuning forks, and that they are a combination of the set up distance expanding and contracting, and the set up distance changing its position in space... please?
Yes Colin - these motions are infinitesimally fractional. Good, that's what they should be! (BTW, Your posts always further the discussion and I appreciate this)
Alan - yes, Doppler is a continuum, and quantum is not. The Lorentz transformations are alterations to distance and time, and perturbations are alterations of time. I'm showing you a means of calculating changes in distance and time, and of calculating a distance changing its position in space, and that these changes are a direct result of the mechanics that cause Doppler shift. Relate this back to the Schrödinger equation and you might find that changes in distance and space have been more fully determined.
Jeff - I am being led by example, and in that I am only following example, I'm not actually being disrespectful. I think the common language for what I'm doing is known as 'standing up for myself'...
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...sigh
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Please also note that the Lissajous figure created by vibrating mirrors is also built up over time, but the time it takes to build up to producing the figure on the screen is determined by the distance the light travels at the speed light between the mirrors and onto the screen.
Drivel. Not a good idea to base any development of a physical theory on a complete misunderstanding of simple mathematics.
By all means stand up for yourself, but I'd advise against doing so in the middle of a motorway.
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Please also note that the Lissajous figure created by vibrating mirrors is also built up over time, but the time it takes to build up to producing the figure on the screen is determined by the distance the light travels at the speed light between the mirrors and onto the screen.
Drivel. Not a good idea to base any development of a physical theory on a complete misunderstanding of simple mathematics.
By all means stand up for yourself, but I'd advise against doing so in the middle of a motorway.
What exactly is 'drivel'?
I am merely pointing out that a Lissajous figure created by sand pouring from the end of a compound pendulum is built up over time, and that the Lissajous figure, differently created by reflecting light off vibrating mirrors, is also built up over the time it takes the light to travel between the mirrors and onto the screen...
If you are saying this is not true??? Because there is no other physical means of that light arriving on the screen apart from the path between the mirrors and onto the screen, and although it gets there pretty fast, seeing as light travels at the speed of light, it still takes time to get there.
Furthermore, I am basing nothing upon any understanding or misunderstanding of simple mathematics, nor on the text you have quoted.
The Schrödinger equation calculates the atomic orbit of an electron. To calculated Doppler at quantum level the Lorentz transformations are employed as well as perturbations.
I am simply pointing out that if you look at the fractional changes that occur in the set up distance between the mirrors of the tuning fork example of the Lissajous figure - these being a combination of the set up distance contracting and dilating, and the set up distance changing its position in space - (this also applies to a mirror vibrating on an axis) that the maths involved in these repetitious motions (that cause Doppler shifts to occur) being applied in line at right angles, and the resulting fractional changes in what happens to the original distance over time, and in repetitions, could constitute a means of gaining more of a physical insight into the use of the time and distance altering Lorentz transformations, and the use of time altering perturbations when calculating between the Schrödinger equation and Doppler shift.
Do you have any comment on 'this'?
The thread 'is' headed "Can this relationship be derived between Schrödinger equation and Doppler shift?"... although admittedly it should have been worded 'mechanics' of Doppler shift'...
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The Lissajous figure is "built up" over the time it takes for the two mirrors to complete as many cycles of vibration as is required to describe the figure. If they are synchronised to the same frequency, t = 1/f, and if they are synchronised to harmonics, it is 1/f1 where f1 is the lower frequency. Difficult to say what "built up" means if they are not harmonically related as the apparent figure changes with time but you can expect the pattern to repeat after 1/(f2 - f1) seconds if the frequences are constant. Note that the speed of light does not appear in any of the equations.
Doppler shift is f' = f(c+v) /(c-v), which has nothing whatever to do with Schrodinger - c does not enter into it!
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...sigh
I don't understand why.
If you tell the people trying to help you that they don't understand simple physics and maths then it is difficult to see how they can make any meaningful contribution to further discussion. So I can fully understand why Alan hadn't replied in the interim, I also saw little point in continuing.
I however, have faith in the intelligence of GCSE (and other high school) students to discern the truth. Not only would they be able to derive the formula for the variation of distance you describe, they would also recognise that it does not create the lissajous curves - as Alan has explained. They will also recognise that a lissajous curve is the shape plotted in 2 dimensions by the interaction of 2 sine waves no matter what the mechanism used - tuning forks, or pendulums with laser attached, etc.
As I mentioned in an earlier post schrodinger never used his famous wave equation for electrons to describe the Doppler effect, it isn't necessary. He used ordinary everyday vector calculations for atoms in motion. Certainly if those atoms are moving at relativistic speeds Lorentz is necessary, but it still doesn't use the wave equation.
PS non of this is advanced physics and maths
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Alan - I am discussing the fractional changes in distance of expansion, contraction, and changing of position in space, and I am asking if these physical phenomenon can be equated with the use of the Lorentz transformations and perturbations to calculate Doppler in relation to Schrödinger. (This mathematical process was provided in the physics stack exchange link)
Colin - You have stated more than a few times in this thread that you are either not qualified or not confident regarding quantum. I have every respect for the knowledge you do have, and I have stated that you could probably teach me a lot that I should know, (but don't) in your fields of expertise.
You are right, so far we are not covering any advanced physics here, but if either you, or Alan, or anyone else started talking about what this thread is actually about, then we would be talking advanced physics. I was not suggesting that either you or Alan are on level with GCSE, but you both are rather talking to me as if I am, and I resent this.
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So again, can anyone comment on this observation that I am making of there being physical changes of distance expanding and contracting, and a changing of position in space - in relation to the physical actions of the use of Lorentz transformations, and perturbations in the maths outlined in the physics stack exchange link provided?
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As John Rennie stated the Lorentz transformations relate to quantum field theory and not to the Schrodinger equation. You have to distinguish between classical and quantum interpretations. Just randomly associating different effects is nonsense. If you had bothered to learn the physics you would know this.
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Yes Jeff - It is clearly obvious that there are classical and quantum interpretations, and as you said, the link is explanatory.
However, this does not detract from the question being asked...
Can these physical observations of distance expanding and contracting, or changing position in space be equated with the actions that the Lorentz transformations add to field theory, (be that quantum or GR), or the actions that perturbations add to quantum calculation?
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Yes Jeff - It is clearly obvious that there are classical and quantum interpretations, and as you said, the link is explanatory.
However, this does not detract from the question being asked...
Can these physical observations of distance expanding and contracting, or changing position in space be equated with the actions that the Lorentz transformations add to field theory, (be that quantum or GR), or the actions that perturbations add to quantum calculation?
What answer do you expect? The question is incomprehensible.
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Let me put it another way. Any Doppler shift is a consequence of the direction of the acceleration vector. Since this points toward the centre of the earth red shift is pointed outward and blue shift pointed inwards. Why make it more complicated than that?
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Is it incomprehensible that the Lorentz transformations are required in both GR field equations and quantum field theory?
Is it incomprehensible that the physical actions of the Lorentz transformations employ an alteration of both distance/length and time?
Is it incomprehensible that perturbations of time are used to calculate position in space?
Is it incomprehensible that an observation of directly calculable changes of position in space, and expanding/contracting distance/length may be an interesting insight into the use of these mathematical tools that are calculating exactly such actions into GR and quantum field theory, and quantum probability of position?
Edit: In reply to last post - again, not talking about frequency shift in light. Talking about distance expanding, contracting and experiencing a changing position in space.
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In an earth based frame of reference relativistic effects can be ignored since no relativistic velocities are involved.
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So, ignoring GR field theory, and just looking at quantum field theory, SR is used to give the electron a boost on its atomic orbit, and perturbations are used to determine its position.
And, again I ask - can these physical observations of a distance expanding, contracting and changing position in space be equated with the physical actions that the mathematical tools, (these being the Lorentz transformations and time perturbations), are adding into to quantum field theory?
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Colin - You have stated more than a few times in this thread that you are either not qualified or not confident regarding quantum.
That's not exactly what I said. I have studied QM and schrodinger and am confident in discussing them and working with the equations, but it is not how I choose to spend my time. In the context in this thread the question was whether I thought it would be profitable for us to discuss that area and given that we have become bogged down on the simple subject of lissajous I doubt we can have a profitable discussion on schrodinger.
You are right, so far we are not covering any advanced physics here, but if either you, or Alan, or anyone else started talking about what this thread is actually about, then we would be talking advanced physics. I was not suggesting that either you or Alan are on level with GCSE, but you both are rather talking to me as if I am, and I resent this.
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So again, can anyone comment on this observation that I am making of there being physical changes of distance expanding and contracting, and a changing of position in space
Regarding the quote in bold, can I ask who raised the subject of lissajous?
The discussion has been on lissajous and how they are produced, yes this is GCSE level, we are not talking to you as if you are at that level just pointing out that your interpretation is wrong.
However, given this comment
- in relation to the physical actions of the use of Lorentz transformations, and perturbations in the maths outlined in the physics stack exchange link provided?
I'm not convinced that lissajous is really what you should be discussing.
And, again I ask - can these physical observations of a distance expanding, contracting and changing position in space be equated with the physical actions that the mathematical tools, (these being the Lorentz transformations and time perturbations), are adding into to quantum field theory?
What observations? If you are referring to those in the lissajous set up then, as Alan and I have pointed out, your observations are incorrect.
Do you have any other observations? Is there something that you have read in a quantum related experiment that leads you to believe that something like this is occurring?
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Can you even state what my interpretation is that you have told me is wrong?
I have consistently stated that I am not discussing the Lissajous curve itself. (nor Chladni plate patterns themselves, nor Doppler shifts themselves.) Just the mechanics causing the mirrors to vibrate, and the changes in distance that the light travels between the mirrors. ie: distribution of resonant vibrations.
If you and Alan have both told me that these changes in distance that I am referring to do not occur then I have missed the fact, otherwise I would have told you that you are both mistaken...
On basis that you are just now realising that it is the orbital of the electron and the use of SR and perturbation theory in relation to these observations of changes of expansion and contraction of distance, and changing of position in space (as observed within the mechanics of the creation of a Lissajous), that I am in fact talking about - you cannot make claim to having told me a relationship between these phenomenon of changes in length of distance,and position in space, in relation to the maths of the Lorentz transformations and perturbations does not exist...
I'm happy to hear that you have studied quantum's. I have read Manjit Kumar's 'quantum' and watched Susskind's quantum lectures, as well as reading about less in depth quantum description in most of the many physics books I've read, to repetition. There's not, as Susskind says, that much to the concept, although the maths are by default complicated.
In that it has never been my intention to discuss the dimensions of a Lissajous curve itself, perhaps you may appreciate that discussing the subject I do wish to discuss may be more interestingly oriented for us all.
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If you and Alan have both told me that these changes in distance that I am referring to do not occur then I have missed the fact, otherwise I would have told you that you are both mistaken...
We have never said that the changes in distance don't occur, but we have consistently denied your statements that they influence the lissajous curves e.g.
"Please also note that the Lissajous figure created by vibrating mirrors is also built up over time, but the time it takes to build up to producing the figure on the screen is determined by the distance the light travels at the speed light between the mirrors and onto the screen."
It is misunderstandings like this that leads me to suggest that a discussion on relating these changing distances to schrodinger would be unprofitable to any of us.
it has never been my intention to discuss the dimensions of a Lissajous curve itself,
If you are not trying to suggest a link between these distances changes and lissajous curves then the discussion becomes easier.
I could give you the maths for what happens, but that won't help so I'll try to describe it.
If the forks are at the same frequency and both in phase (working together) the distance will vary as a sine wave, if phase is 180 then there will be no movement. For forks of different frequencies the maths describes exactly what happens.
I'll try and find some pictures to illustrate what happens or failing that draw and scan, I'll get back to you.
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Colin - I am not suggesting a link between the changes in the distance between the mirrors and the Lissajous curve, other than the obvious fact that these changes in distance are occurring in the tuning fork experiment causing the Lissajous curve to appear on the screen.
What I am suggesting is a vague link between the Lissajous curve and the Chladni patterns via the aspect of resonant vibrations, and that the mechanics creating these changes in distance I'm referring to are the same mechanics that cause Doppler shifts to occur...
Then I am suggesting, indeed asking if, these physical observations of fractional changes in distance expanding, contracting and changing location in space can be equated with the mechanical actions of the mathematical tools of the Lorentz transformations and perturbations currently being used to calculate the Schrödinger equation in relation to Doppler shift.
As to Lissajous figures building up over time, this really isn't important to the discussion but:
The misunderstanding is that you are not taking on board the fact that I was simply describing, (to GCSE level readers), the difference between a Lissajous figure built up over time by attaching a laser to the end of a compound pendulum that could hypothetically leave evidence of its path of gyration and inertia through space on a surface below - as would the sand pouring from the end of the compound pendulum in the documented experiment - and the fact that using a laser as such is not the same mechanics as creating a Lissajous figure via reflecting its beam along an apparatus of 2 vibrating mirrors and onto a screen.
The Lissajous figure itself on the screen is not built up over time as it would be via the compound pendulum. The beam of light now arrives on the screen as per the angles of how the reflection from the first vibrating mirror, (dot turned into a line), leaves the second mirror via the second mirror's vibrations...
It does however take the light time to travel between the mirrors and onto the screen.
As an interesting aside that could be interesting to the discussion later on - the time the light takes to travel around the apparatus of the tuning fork experiment is different when the mirrors are moving with respect to each other at each position of the motion over time.
Please Colin, realise that I have studied the matters I'm talking about. I have watched YouTube experiments of Lissajous and Chladni patterns being formed. I've read the wiki, understand the sine wave/frequency association, have studied the Schrödinger equation, quantum, the Lorentz transformations and can re-create experiments as 3 dimensional moving events in my head (with the help of a little hand waving sometimes for angle interpretation).
I am asking if these changes in distance of expansion, contraction, and changing of position in space can be equated with the actions of the Lorentz transformations and perturbations being used in the calculations laid out in the physics stack exchange link provided earlier this thread.
Do you understand now?
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The Lissajous figure itself on the screen is not built up over time as it would be via the compound pendulum.
Oh yes it is. The only difference is that the position integrator thzat turns a dot into a line is your visual cortex rather than a pile of sand.
It does however take the light time to travel between the mirrors and onto the screen.
true, but irrelevant. It takes time for the sand to fall from the pendulum, which is why the line thickness varies, unlike the apparent laser line thickness which is constant.
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SR is used to give the electron a boost on its atomic orbit, and perturbations are used to determine its position.
Please can someone put this into meaningful English?
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How the light builds up on the screen, or in the sand is irrelevant to the discussion but thanks for the more in depth description.
http://physics.stackexchange.com/questions/29551/quantum-explanation-of-doppler-effect
Please find reference to Lorentz boosts in the link above, in the answers and subsequent discussions.
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.... which is nothing whatever to do with orbiting electrons.
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...isn't an electron Doppler shifted in frequency when it departs from a Mossbauer as a photon?
...aren't electron's conducting a balancing act between gravity potential energy and kinetic energy in their atomic orbital? ...and if the atom is subject to more energy, doesn't the distance of the orbit in relation to the nucleus expand, or contract with less energy?
...the Chladni plate pattern maths are synonymous with the Schrödinger equation. This equation can describe where the electron is most likely to be situated in its atomic orbital... Could the maths of the physical changes in distance expanding, contracting, and changing position in space, (observed in the physical mechanics of the creation of Lissajous figures via the mirror vibration method), describe all the other places the electron might be found in its atomic orbital? ... potentially in relation to the hypothetical orbit/s of the components of the nucleus, with respect to a resonation with these nucleus component/s energy related frequency/ies?
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Do you read the information people post only to forget it ten seconds later. This is like groundhog day.
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...isn't an electron Doppler shifted in frequency when it departs from a Mossbauer as a photon?
...aren't electron's conducting a balancing act between gravity potential energy and kinetic energy in their atomic orbital? ...and if the atom is subject to more energy, doesn't the distance of the orbit in relation to the nucleus expand, or contract with less energy?
...the Chladni plate pattern maths are synonymous with the Schrödinger equation. This equation can describe where the electron is most likely to be situated in its atomic orbital... Could the maths of the physical changes in distance expanding, contracting, and changing position in space, (observed in the physical mechanics of the creation of Lissajous figures via the mirror vibration method), describe all the other places the electron might be found in its atomic orbital? ... potentially in relation to the hypothetical orbit/s of the components of the nucleus, with respect to a resonation with these nucleus component/s energy related frequency/ies?
There is more to science than merely placing scientific words in sentence order. They have to make sense too. What you have concocted here is a farrago of nonsense which, had it originated from anyone else, would indicate an ignorance of physics bordering on contempt. But as you are neither ignorant nor contemptuous, I guess we can put it down to the change from BST to GMT, or blame the computer. Next time, engage brain before typing!
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The impression I get from physicists who write about theoretical physics is that the physics picture is incomplete and requires either that 93℅ of the universe is unaccounted for, or that some other type of thinking is needed.
Unfortunately in the case of a lot of physicists, any type of thinking that has not been text book taught is met with contempt.
It occurs to me Alan that your bright young woman A level student who wrote down the frequencies involved in Lissajous figures might have gone on to be much more than a physics teacher had your teaching manner not incorporated such dismissive tone to exploratory discussion. I daresay any spark of innovated thought was stamped right out at source rather than discussed to a conclusion.
Hard to respond to a person that does not dissect the discussion to state where the objection is.
Schrödinger equation is based on Chkadni pattern maths. Fact.
Mossbauer experiences recoil and photon drops energy. Doppler shift. Is this the problem?
An electron does balance gravity potential energy and kinetic energy as it moves closer and further away from a nucleus on its atomic orbital. Fact.
Chladni plate patterns and Lissajous figures have a connection via the distribution of resonant vibrations. Fact.
It is thought that the nucleus components also have atomic orbitals. Fact.
In that electrons and nucleus components have energy and associated frequencies there is no reason to think that these frequencies of different component part will not be resonating with each other. Fact.
...and the rest was a question, and quite a valid one as far as I'm concerned.
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Mossbauer experiences recoil and photon drops energy. Doppler shift. Is this the problem?
Can you clarify what you are thinking here. In Mossbaur effect the atom has less recoil and photon energy is higher.
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OK, here's a dissection
...isn't an electron Doppler shifted in frequency when it departs from a Mossbauer as a photon?
This sentence is meaningless. The Mossbauer effect is concerned with the emission and absorption of photons from the nucleus, nothing to do with electrons.
...aren't electron's conducting a balancing act between gravity potential energy and kinetic energy in their atomic orbital?
No. As you know perfectly well, the electrostatic force is orders of magnitude greater than gravitation
...and if the atom is subject to more energy, doesn't the distance of the orbit in relation to the nucleus expand, or contract with less energy?
As you know that an electron can be promoted to a higher orbital by absorbing a photon, why not just say so? That way you incorporate Schrodinger, quantum mechanics and stereochemistry in fewer words and don't involve nonsense like orbits.
...the Chladni plate pattern maths are synonymous with the Schrödinger equation. This equation can describe where the electron is most likely to be situated in its atomic orbital...
The fact that sinusoidal harmonics can be added to simulate almost any shape with fixed nodes is an established mathematical principle. The problem is that atomic orbitals do not have nodes except at the nucleus. Could the maths of the physical changes in distance expanding, contracting, and changing position in space,
WTF does that mean? (observed in the physical mechanics of the creation of Lissajous figures via the mirror vibration method), describe all the other places the electron might be found in its atomic orbital?
no. The Lissajous figure is the locus of a point described by two sinusoidal oscillations in perpendicular directions. Nothing more or less. ... potentially in relation to the hypothetical orbit/s of the components of the nucleus, with respect to a resonation with these nucleus component/s energy related frequency/ies?
It is entirely possible that you could describe nuclear resonances with a synthesis of sinusoids, just as you can with a bridge or a piano, but what we measure and use to describe them is energy.
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Ok - thank you Alan. Because it is difficult to multi quote from phone screen, I'll pick up your dissections one at a time.
Because Colin also asked I'll start with the Mossbauer:
Alan, perhaps my terminology is not correct as to the emission of a gamma ray from a Mossbauer, but the Mossbauer does emit a gamma ray, and it is because of the recoil of the nucleus that the gamma ray is of a lesser energy and cannot be absorbed by the receiving Mossbauer, because it doesn't have the correct level of energy.
Place the Mossbauer in a crystal lattice and the nucleus no longer recoils as before. The gamma ray is then emitted at the correct energy level to be received by the receiver.
A recoil motion is synonymous with the action that causes Doppler shift.
We can discuss this further, or if we are all good, we can move on to next dissection.
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See how easy it is if you stick to the facts!
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Before progressing to the next dissection - if I could please refer you back to your post 185 with regards to Lorentz boosts described in the physics stack exchange link provided... for clarification?
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I have now read it five times and the words "orbit" and "electron" still do not appear anywhere on the page.
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Alan - we were in last few posts directly involved in talking about the recoil of the nucleus of a Mossbauer in relation to the Mossbauer emitting a gamma ray of reduced energy and frequency...
I said that a recoil motion is synonymous to the action that causes Doppler shift, and will now point to the gamma ray having a lower energy and frequency as being synonymous with having been Doppler shifted.
As you say, the 'link' makes no mention of an electron or an atomic orbit. The link explains how a Lorentz boost is required to calculate Doppler at quantum level.
My point being that a nucleus recoiling inside an atom will affect electron atomic orbit, and the actions of the mathematical process of calculating Doppler at quantum level must be occurring inside the atom regarding the recoil and shifting of energy and frequency of the gamma ray.
So does the Lorentz boost described in the link have anything to do with calculating the Doppler shift occurring inside the Mossbauer, or has the Lorentz boost got nothing to do with it?
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Yes. But it has nothing whatever to do with electron orbitals.
and the actions of the mathematical process of calculating Doppler at quantum level must be occurring inside the atom regarding the recoil and shifting of energy and frequency of the gamma ray.
Mind your language, young lady! There is a Doppler shift associated with any moving source or receiver. The "mathematical process" does not "occur": it is our feeble attempt to model and predict what actually happens. And every time you say "energy and frequency" you lose credibility points because everyone knows they are inextricably linked so we generally talk about one or the other, usually energy in the case of individual photons. Does it matter? Yes, to the same extent that you will get a better meal in France if you order it in recognisable French. In fact it's even more important because nobody here is trying to sell you anything, so if you don't talk proper physics you may find your brilliant insight being completely ignored by the waiters.
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So does the Lorentz boost described in the link have anything to do with calculating the Doppler shift occurring inside the Mossbauer, or has the Lorentz boost got nothing to do with it?
By Mossbauer I assume you mean Pound Rebka or Mossbauer spectrometry?
If so, using Lorentz seems overcomplicated considering the speed, why not just use Galilean transforms.
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Alan - the Mossbauer emitting a gamma ray that is not placed in a crystal lattice: Is the Mossbauer being moved externally, or is it the recoil of the nucleus that causes Doppler shift?
Colin - I'm looking at the mathematics of the changes in distance of expansion, contraction, and changing of location in space, observed between the mirror apparatus of the Lissajous tuning fork experiment, being potentially able to describe the situation.
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The recoiling nucleus absorbs some energy so the outgoing photon has marginalyl less energy than the calculated value. Nothing to do with Doppler.
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I would listen to Alan and just consider a classical Doppler shift. That way it won't get confusing.
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OK - look Akan, please forgive me, I have tried to research this. There are probably some pdf's available on line, or books, but both being out of my reach right now... - What mechanical process is causing a gamma ray to be emitted from the Mossbauer, and where in the Mossbauer is the energy of the emitted photon transfered from?
Jeff - just saw your post as posting - but a classical Doppler shift is exactly the mechsnism I'm proposing, isn't it?
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Mossbauer was a bloke, not a nucleus.
Several nuclei emit gamma photons as they transition from an intermediate high energy state. The bandwidth of that emission is very narrow so an isolated atom (e.g. in a gas) won't absorb the photon because the recoil momentum alters the emission or absorption band.
In the Mössbauer effect, a narrow resonance for nuclear gamma emission and absorption results from the momentum of recoil being delivered to a surrounding crystal lattice rather than to the emitting or absorbing nucleus alone. When this occurs, no gamma energy is lost to the kinetic energy of recoiling nuclei at either the emitting or absorbing end of a gamma transition: emission and absorption occur at the same energy, resulting in strong, resonant absorption.
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That info is written in the wiki link and is readily available all over the net, and is not referring to the questions I'm asking.
What is the root cause of the atom emitting the gamma ray? Is it an external energy input, or is it a natural decay process?
What are the mechanics of the emitting photon with regards to the electrons?
How is, ie: what are the mechanics of, the energy transfered from the emitting photon to the nucleus?
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What is the root cause of the atom emitting the gamma ray? Is it an external energy input, or is it a natural decay process?
generally, a natural decay process, as in the P-R experiment. You can initiate gamma-gamma photonuclear reactions but most externally driven primary reactions generate a broad spectrum of fission products and aren't suitable for mossbauer experimentation.
What are the mechanics of the emitting photon with regards to the electrons?
none
How is, ie: what are the mechanics of, the energy transfered from the emitting photon to the nucleus?
Conservation of momentum. Basic classical mechanics.
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Ok - I can see that I've asked wrong question: where does the momentum come from?
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Nowhere! If the nucleus is stationary then pings out a photon, it has to recoil just like a gun so that the total momentum remains at zero. Same with the Big Bang and everything in between.
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Well yeah Alan. A recoil would require a forward motion, but what is causing the forward motion of the photon pinging out of the nucleus?
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The fact that the nucleus is metastable and needs to get rid of some energy to move to a stable state. Worth studying the decay chain of Co57. Pure gamma emitters are unusual and very useful.
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I wholeheartedly agree with you. I am extremely shabbily informed as to particle physics, and am feeling a tad uncomfortable with the fact. I'll get on it.
However mechanics are mechanics, and while I get myself more informed I do feel that we can now move on to another of your dissections:
... potentially in relation to the hypothetical orbit/s of the components of the nucleus, with respect to a resonation with these nucleus component/s energy related frequency/ies?
It is entirely possible that you could describe nuclear resonances with a synthesis of sinusoids, just as you can with a bridge or a piano, but what we measure and use to describe them is energy.
If we look at the frequencies of the component parts of an atom as resonating with each other, then we could imagine that there would be a type of movement occurring within the atom that may be reminiscent of the type of motion that we see occurring in the changes of distance of expansion, contraction and changing of position in space facilitated in the lights optical path travelling between 2 mirrors vibrating at right angles...
The representation of what is occurring between those mirrors is what appears on the screen. Couldn't care a less about the shape of it right now. Just looking at it being stable, jittery, or the lines appearing to have flow in a direction within the shape.
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There's a good reason why the mossbauer effect is known as an example of resonant fluorescence, but you won't get far by using a mechanical model. In the case of the Fe57 nucleus you have a 3 dimensional array of 26 protons and 31 neutrons bound by highly nonlinear forces and swapping all sorts of virtual particles, none of which has anything to do with lights and mirrors.
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No, but it does have something to do with motion, distance, and time...
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How do you know that?
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Because the components of an atom are not stationary... If the frequencies of each resonate with the other, then this will affect the motion, and therefore the distance and the time it takes each to move in relation to the other/s.
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Because the components of an atom are not stationary... If the frequencies of each resonate with the other, then this will affect the motion, and therefore the distance and the time it takes each to move in relation to the other/s.
A knock at the door, I believe it's Mr. Heisenberg calling.
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Perhaps if Mr Heisenberg had studied the maths of changes of distance, expanding, contracting, and changing position in space between 2 mirrors vibrating at right angles, he might have managed to be a bit more fully determining.
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Perhaps if Mr Heisenberg had studied the maths of changes of distance, expanding, contracting, and changing position in space between 2 mirrors vibrating at right angles, he might have managed to be a bit more fully determining.
But it's called the Uncertainty Principle timey, supported by experiment.
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Clearly! When measuring the phenomenon directly, the apparatus of the measuring device affects the phenomenon... but this doesn't mean the calculations to describe the phenomenon need remain clouded in indeterminacy and be only determinable via calculation of probability... does it?
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but this doesn't mean the calculations to describe the phenomenon need remain clouded in indeterminacy and be only determinable via calculation of probability... does it?
I'm afraid it must remain so until we find supporting evidence to the contrary. While many speculations and hunches may eventually be accepted, until we have experimental evidence, we have to rely on the evidence we now have. Remember timey, physics presently has a well researched road map, and to revise it without proper information will only succeed in sending us down a multitude of rabbit holes.
Please understand my friend, I wish you nothing but success. And I realize that your mission here is to find help introducing reasonable math in support of your ideas. And I can assure you that members such as Alan, Jeff, Colin, and several others would gladly give you that if they could see reasonable evidence for it.
Here is the problem: All evidence points to time being reliable to our inertial frame. I may observe other frames in variance but in my personal frame, time is consistent. If it were not, we would not be able to rely on any calculation we might possibly make.
We're stuck with it timey. If we discount the regular advance of time, "in our frame", we just might as well forget counting on any physical description of reality leaving us back in the stone age. And frankly, I see no possible way of ever showing evidence of your variable time even if it truly existed.
Nevertheless, hunches are allowed and I applaud you for making one, that at least, I personally happen to be in favor of. Can you or I prove that the universe is cyclical, right now, I don't think we can. But truth is, I would also like to find the evidence and maybe, instead of a hunch, it's because a cyclical universe just simply appeals to my sensibilities more.
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Ethos - quantum is already being calculated using variable time. That is essentially what perturbations are, and use of the Lorentz transformations within quantum also variate time.
Thanks for your kind words. I think the model is tops, even if it turns out mathematically unviable. I took great care to trace each step of mechanics and make sure that nothing that we do not already observe was incorporated. In doing so, the only way to facilitate this was to view the mechanics of long standing observations in an alternative perspective.
My model does in fact suggest an experiment to prove or disprove itself... and at a cost that would be infinitesimally fractional relative to Hydron collider, LIGO, Fermilab, etc.
P.S. Did you read the Nature NIST link I posted in the Planck curve thread?
A person can climb one rung up a ladder and they will experience a different rate of time (so fractional one wouldn't ever notice), and this means that your own body, when standing up, is experiencing a different rate of time at each elevation of itself.
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Ethos - quantum is already being calculated using variable time. That is essentially what perturbations are, and use of the Lorentz transformations within quantum also variate time.
Follow me closely regarding this question timey. Every moving particle will have it's own frame of reference, and as a collection of moving particles, a human will also have our own personal frame of reference. The variable time you're referring to when you describe quantum "being calculated using variable time" is the observation we as humans witness concerning particles in motion. But these particles have their own frame and in that frame, time passes at the standard rate.
Any particle or group of particles in motion will present to our observation a dilated passage of time. But for that particle or group of particles, the passage of time will be consistent with what you describe as the "standard second".
Just because we may be in the same room where experimental observations are made of moving particles does not mean that we, both the particle and us are in the same frame of reference. Fact is, if I move my hand before my face, even though very slowly relativistic speaking, that group of particles in my hand will be in a different inertial frame.
Every particle in the universe possesses it's own individual frame of reference unless it is in lock step with another. But even that scenario may be impossible to achieve because within every atom, movement is a continuous reality.
The same principle would also apply to the gravitational effect. A body on the surface of the earth would necessarily be in a different inertial frame than one only a foot higher in elevation.
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BTW, you mentioned that you have a test that would prove or disprove your ideas. Could you briefly describe them for us, maybe we could recommend some help or alternative methods...............Ethos
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...and every reference frame has, according to Schrödinger, alternative quantum states. Quantum states are determined via perturbations, and probability of where, or when, is then determined.
I'm sorry, I don't have the time, excuse the pun, to get into a philosophical discussion about the phenomenon of time, however a standard second is not 'the' passage of time, but just an arbitrary measurement of duration that we measure everything by, that has its historical basis in being a division of the duration it takes the earth to complete one full rotation...
...A standard second is not a description of the phenomenon of time itself.
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BTW, you mentioned that you have a test that would prove or disprove your ideas. Could you briefly describe them for us, maybe we could recommend some help or alternative methods...............Ethos
Just saw your other post:
In brief... We know that a cesium atomic clock will run faster when elevated relative to another cesium atomic clock. And it is said that time runs faster at elevation.
My model says that the elevated clock is running faster due to additional gravity potential energy, and that the time in the space the elevated clock is located will be running slower than the space the lower clock is located in... But at ground level, the clock and the space it is in will be running at the more or less same rate of time.
This means that mass and its associated gravity field will increase the rate of time (contrary to accepted physics).
By placing identical cesium clocks on the ground at different locations of exactly the same elevation above sea level, so that each clock is experiencing exactly the same degree of gravity potential energy, but a significant known difference in density, my model states, (contrary to accepted physics), that the clock in the denser location will run faster.
But this thread is about the changes in distance of expansion, contraction, and changing of location in space observed between 2 mirrors vibrating at right angles, and if the maths of these changes can be equated with the use of perturbations and the Lorentz transformations in quantum, and we should stay on topic really. Forum rules, n'all...
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I'm sorry, I don't have the time, excuse the pun, to get into a philosophical discussion about the phenomenon of time,
Ouch.............................I certainly didn't aim to burden you with philosophy.
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Because the components of an atom are not stationary...
How do you know that?
You must distinguish between an oscillatory model, which has some descriptive value but is obviously nonsense, and the fact that most atoms are indefinitely stable and do not emit electromagnetic radiation.
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You must distinguish between an oscillatory model, which has some descriptive value but is obviously nonsense, and the fact that most atoms are indefinitely stable and do not emit electromagnetic radiation.
I'm with Alan on this.
Also be careful not to confuse a mathematical process e.g. perturbation theory with what you interpret as time perturbations.
Wasn't going to reply to this, but have brought it over from the other thread as it is relevant.
Colin - NIST 2010 ground level relativity tests proved that time slows for a clock in relative motion to a stationary clock at speeds as low as 36km/h
This is a good example of what I was saying
Firstly, they have a just cause for their assertion that this is due to SR.
Secondly, it is exactly as predicted by Einstein.
Thirdly, if you look at the results you can see why you would not use a Lorentz boost in the Pound Rebeka calculations.
By the way, knowing your interest in gravitational time dilation, have you seen this.
https://www.technologyreview.com/s/429238/atomic-clocks-to-measure-earths-geoid-from-the-ground/
I've only included the summary as the paper is a PDF which I know you can't access.
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Well there is the test of inverted time dilation. Results from such measurements would be interesting. Whatever the outcome timey you should just keep learning.
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Ethos - I was being literal not insulting. I have no money to feed my animals, or my family, and the internet connection runs out in about 5 days. I don't have time. OK?
Alan - I think my post from Planck curve thread answers.
Colin - Yes, I read extensively on the ideas for ground based GPS in 2010. I myself have been longing for a pair of portable clocks...as I'm sure you can imagine.
I'm glad you brought up the SR speed consideration. The clock in motion loses frequency relative to the stationary clock. How can the clock in motion lose frequency when it experiences the addition of kinetic energy?
Also confusing mathematical models with reality is a 2 way street.
Jeff - Thanks! That is a nice thing to say...
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Colin - Yes, I read extensively on the ideas for ground based GPS in 2010.
Sorry, you lost me there. GPS?
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I can't find the paper concerning, I think it might be one of the pdf's, and I can't download them at mo... but the suggestion was in 2010 that the GPS system could perhaps be run from ground based transmitters, rather than expensive satellites, on account of the findings of the ground based relativity tests... not relevant to the discussion though.
Kinetic energy increasing and clock frequency decreasing in SR relative motion scenario, any comment on that?
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Ethos - I was being literal not insulting. I have no money to feed my animals, or my family, and the internet connection runs out in about 5 days. I don't have time. OK?
No problem my friend. Please check you private messages timey, you have a message waiting for you there.
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I'm glad you brought up the SR speed consideration. The clock in motion loses frequency relative to the stationary clock. How can the clock in motion lose frequency when it experiences the addition of kinetic energy?
You need to differentiate between what happens to the clock and what happens to the light, this is just a simple case of the passage of time experienced being different in 2 frames.
Simple example. Let's say a rocket passes earth at high speed. On the rocket a torch is flashed 100 times in 10s, that's 10Hz leaving the rocket. On earth time is our clock is ticking more quickly so let's say we see those 100 flashes in 20s, that's 5Hz. The clock might experience increased KE but the light it emits is the same frequency it would have been in a stationary frame, but it then enters a different frame, different measurement.
PS I agree with Jeff, whatever you do, don't ever stop thinking.
EDIT: Sorry I missed the above question because I stopped at your comment about ground based gps. Did you manage to read the summary of the proposed measurements of local gravity/density? It should provide a test of your theory.
Also, when you can read the Mossbaur spectrometry PDF you will see it resolves the issue of horizontal Pound Rebka.
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Colin - if a clock loses frequency when it moves, then it can't be being affected by the kinetic energy it is gaining. Any increase in energy the clock experiences will increase its frequency.
The Mossbauer on the horizontal only emits a photon of lesser energy when it is not placed in the crystal lattice. When the motion of recoil is removed by the crystal lattice the photon is emitted at a higher energy.
Could kinetic energy be robbing an atom (or component/s of an atom), of its energy in a proportional subtraction?
(light itself doesn't have mass and does not have to be affected by kinetic energy, or gravity potential energy)
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This would explain why an atom, in a physical state that can be considered not to be stationary, has an energy that is less than the sum total of the energy associated to its constituent parts individually.
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Colin - if a clock loses frequency when it moves,
The clock doesn't lose frequency when it moves, in its frame the frequency is the same. Reread the example I gave.
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Yes the clock really does lose frequency. That is how it ticks slower Colin.
Read the NIST ground level relativity link. The moving clock and the stationary clock were connected by a fiber optic. This means that you can drive the moving clock at a speed in a circle around the stationary clock and record that the moving clock has a lower frequency, ie: tick rate, than the stationary clock.
There is no question about the moving clock physically having a lower frequency than the stationary clock. Yes the reference frames are different, but the physical difference between these reference frames is a proven fact.
The question then arises as to why the clock would be physically possessed of a decreased frequency when it is experiencing an increase in kinetic energy, that by the remit of current physics equations and theories will increase the frequency of the object?
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There is no question about the moving clock physically having a lower frequency than the stationary clock.
Yes there is. If you went to the moving clock and measured its frequency it will be the same as the 'stationary' clock.
Yes the reference frames are different, but the physical difference between these reference frames is a proven fact.
This is my point. The clocks are in different frames and you need to take that into account.
The question then arises as to why the clock would be physically possessed of a decreased frequency when it is experiencing an increase in kinetic energy,
As I explained in #233.
The clock is not 'possessed of a decreased frequency'. It 'thinks' it is at rest and so produces the frequency it would in the stationary frame. We, however, are measuring from a frame which considers the light after it has been emitted to be experiencing a rate of time different to ours.
that by the remit of current physics equations and theories will increase the frequency of the object?
No they don't.
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There is no question about the moving clock physically having a lower frequency than the stationary clock.
Yes there is. If you went to the moving clock and measured its frequency it will be the same as the 'stationary' clock.
I agree Colin, and my motivation in trying to explain to timey how different inertial frames only appear to an observer to be processing their time at different rates was only an attempt to clarify.
As I formerly posted, even individual particles moving at different velocities, or in varying strength of gravitational field, will also have their own personal frames of reference.
Just because the researcher is in a close proximity to the experiment does not mean that both he and the experiment are necessarily in the same frame of reference. This consideration remains important when different velocities, and or, different gravitational influences are involved.
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There is no question about the moving clock physically having a lower frequency than the stationary clock. Yes the reference frames are different, but the physical difference between these reference frames is a proven fact.
If you consider a hypothetical fixed background then you could say the above statement is true. Light could be used as a fixed background if it were not for that pesky force of gravity. Since all things are relative we are stuck with what we have. As long as you understand that observers are not all in the same frame and appear to experience varying rates of time when viewed be each other then you can't go far wrong. The important phrase is viewed by each other.
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The important phrase is viewed by each other.
Indeed..........................One thing I'd like to mention about this term we keep hearing: "the standard second"
Thought experiment:
The scenario; We Americans have established an outpost on Jupiter and have built an enormous clock facing Earth. We have as well, built an enormous clock here on Earth and it is facing Jupiter.
Mankind here on Earth will observe the clock on Jupiter running at a different rate than the one here on Earth. And likewise, those on Jupiter will notice the opposite observation that we see on Earth.
Which planet is operating by the "standard second".
The answer:.............................They both are.
In any inertial frame, whether influenced by velocity or gravitational strength, "the standard second" applies to those operating in that inertial frame.
If someone has a different definition for the "standard second", by all means, please provide it to us for our edification.
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You could define the standard second to be at infinity so that time passes more slowly everywhere else. I can't see any advantage in this.
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You could define the standard second to be at infinity so that time passes more slowly everywhere else. I can't see any advantage in this.
My point was, that the term "standard second" is misleading. Time always passes the same for those operating within their inertial frame regardless of what observers may witness while operating in another.
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Quite so Ethos :)
It's equivalent
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My point was, that the term "standard second" is misleading. Time always passes the same for those operating within their inertial frame regardless of what observers may witness while operating in another.
I agree. In the case of the Jupiter scenario it would be possible to refer back to GMT, UTC, Zulu or whichever you prefer and convert to local time accounting for gravity and motion.
As you say, standard second could refer to what you measure in your inertial frame, or as Jeff points out it could be zero gravity/freefall, but as he says there doesn't seem to be an advantage.
However, perhaps the important point is that if Timey proposes an additional time transform it ought to be identified by its own term e.g. Ramsey Transform (can you have a Ramsey boost?) and a clearly identified symbol*. At each stage it should be identified clearly what is being discussed and in which frame.
* The closest in the Greek alphabet might be iota, but it's not a clear symbol and can be confused with imaginary numbers and vectors, perhaps something from a different alphabet.
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However, perhaps the important point is that if Timey proposes an additional time transform it ought to be identified by its own term
Absolutely my friend. I suppose one could apply such a standard if they were able to determine absolute motionlessness relative to space/time. And to that I would only say: "Good luck with that one!"
My thought experiment was given precisely to illustrate the false notion that a "standard second", which all other seconds must kneel in obedience to, is not only misleading, it is not compatible with the evidence.
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Seriously - I cannot comprehend why it is that you all can read the results of the NIST 2010 ground level relativity tests and still retain that point of view.
I understand that this is observer dependancy is what you have all been taught in school, and to the man, I am sure that you are all older than I who is also not that young, and that the results of more recent experiments do not as of yet even form part of the educational curriculum.
I do think there is case for ***already emitted*** lights frequency, when observed changed in positions in a gravitational field, being viewed as observer dependant, but not the frequency that an atom emits a photon at. This is not observer dependent but a real and physical effect, and the NIST ground level relativity tests prove it.
If you are moving with the moving clock, the frequency of that clock will not be the same frequency as the stationary clock you were previously standing beside. It will be of the lower frequency that the test results state it to be. You will observe, from the frame of the moving clock, the stationary clock as being of the same frequency it was when you were standing stationary with it, this being the frequency the test results state.
Yes - you will consider your clock to be correct, whether you are with the moving clock, or with the stationary clock. Your physical make up will be affected as the clock is. This is why NASA suggests that astronauts age at a different rate in space.
How can NASA state that astronauts age in correspondence with their motion and gravity potential time affected clocks if it is not a real and physical effect?
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As far as I recall, correct me if wrong, an electron is thought to have more energy when moving than when stationary due to kinetic energy.
Again, correct me if I am wrong,light falling towards a gravity well is experiencing less gravity potential energy and more kinetic energy as it gets closer. As far as I recall, these calculations have a bearing on the lights frequency.
As far as I recall I posted a link, some time ago on another thread, that explained, correct me if wrong, how an electron also experiences less gravity potential energy and more kinetic energy as it moves closer to the nucleus, and that as it moves away the situation is reversed constituting a balancing act of energies in the electron on its inbound and outbound motions.
So if kinetic energy isn't increasing frequency, then what is it doing?
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Then again, if we want a logic to hold, the 'values' shouldn't matter for it. As long as they are in relation to each other. 'c' will still be 'c', as I see it.
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We have a tendency to seek for the holy grail, and we do it differently when we think of a universe, versus a 'frame of reference'. I think the 'grail' is hidden in local definitions, those make the 'global universe'
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It's also known as patterns.
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Timey "If you are moving with the moving clock, the frequency of that clock will not be the same frequency as the stationary clock you were previously standing beside. "
How do you prove that one?
By comparing?
and when you compare, what do you do it by? your wrist watch?
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I haven't read the NIST 2010 results.
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https://www.nist.gov/newsw-events/news/2010/09/nist-pair-aluminum-atomic-clocks-reveal-einsteins-relativity-personal-scale
http://www.nature.com/news/2010/100923/full/news.2010.487.html
More in depth PDF papers are available.
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Seriously - I cannot comprehend why it is that you all can read the results of the NIST 2010 ground level relativity tests and still retain that point of view.
I understand that this is observer dependancy is what you have all been taught in school, and to the man, I am sure that you are all older than I who is also not that young, and that the results of more recent experiments do not as of yet even form part of the educational curriculum.
I can understand how that viewpoint influences the judgement of what we are saying. However, I read the NIST papers, and previous ones, before posting and would say it is important to understand what you are reading and the terminology used.
If you are moving with the moving clock, the frequency of that clock will not be the same frequency as the stationary clock you were previously standing beside. It will be of the lower frequency that the test results state it to be. You will observe, from the frame of the moving clock, the stationary clock as being of the same frequency it was when you were standing stationary with it, this being the frequency the test results state.
Relativity is about measurements and comparisons between different frames. The atomic clocks in all these experiments are connected by a fibre optic through which the 2 clocks are compared relative to each other.
So if kinetic energy isn't increasing frequency, then what is it doing?
In the case you asked me to comment on the light is being emitted by the atom as if it is at rest. The difference in frequency is due to difference in measurement of time in different frames, as in my example, try working through counting wavecrests in the 2 frames.
Measurement of ke in different frames won't show the same result. Imagine I'm in a car stationary beside road. Car coming up behind has a ke determined by its speed relative to me, if I then accelerate to the same speed as that car its ke relative to me is 0.
I suspect we have met an impasse hear where you won't believe what we are saying.
EDIT: it would be worth considering 3 clock travelling at different relative speeds. Measurements between the different frames can result in the clocks showing different rates dependant on frame (one clock can be measured as having 2 frequencies/rates), so it is not possible to consider it to be the clock which is emitting a changed rate or frequency.
The same can be done for 2 pairs of clocks all at different heights, but arranged so 2 pairs show the same time difference, showing it is the measurement of the rate of time causing the effect. The only difference with gravitational field effects is that we can define a reference as being no gravitational influence/freefall.
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OK Colin - perhaps we have come to an impasse, and I respect your views and indeed fully understand why you have them. I am not detracting from the relativity viewpoint in the slightest by what I'm suggesting, and although please realise that I am not asking you to embrace what I am saying, on the basis that I accept your position, can I ask you to retain an open mind just with respect to furthering the discussion?
Quantum and SR relate everything to a universal present. GR states variable time and a universally variable present. (and time travel possibilities arise as a result. I really do not wish to discuss time travel here though).
Relativity states that there is no preferred reference frame, and I do not disagree, there isn't. But the reality of the current situation mathematically is that a preferred reference frame is being applied to everything by default. Anywhere that you see 'per second' in the maths, this is blatantly stating a preferred reference frame.
All of my suggestions are simply recognising the fact of this defaulted preferred reference frame, and then taking it into account.
The NIST 2010 results take relativity to a personal scale. Your feet will be experiencing a slower time than your head if you are standing up. (my model simply adds that the open space outside your head will be contrarily possessed of a slower time than the open space outside your feet).
Again, I tell you that a body cannot age differently if the time differences are not a physical actuality.
Why do the links and related NASA articles state a physical difference in aging?
So on this basis, and the fact that GR states a universally variable present, we will continue 'as if' the observations of clocks being possessed of variable times are a real and physical effect.
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Kinetic energy. All you have said there Colin is that when you are accelerated at the same rate as the other reference frame, the kinetic energy difference is 0...
But we already established this when you were standing next to the stationary clock. Neither you or the stationary clock are actually stationary, you are only stationary with respect to each other.
All you are doing in considering the moving clock relative to yourself standing with the stationary clock, is stating the reference frame of the stationary clock and your stationary self moving with the motion of the Earth through space as being 'the' preferred reference frame.
Yes - if you are moving with the clock, the difference in kinetic energy between yourself and your clock will be 0, but the difference in kinetic energy your clock and yourself experience in the moving frame relative to the stationary clock will not be 0. Both you and your clock in the moving frame will be experiencing an increased kinetic energy relative to the stationary clock... But... both you and your clock in the moving frame will be ticking with a ***decreased frequency*** relative to the stationary clock.
So - kinetic energy has a bearing on the phenomenon of the ***increase in frequency*** of light falling towards earth... Any comment?
(Just saw your edit when posting: I have never heard of clocks that are calibrated exactly identically and placed in different potentials being observed to have different rates of frequency dependent on where it is that you are looking at them from... As far as I was aware a 3rd clock would read the 2nd clock as having the same frequency as the 1st clock recorded it to have, no matter where, or what speed the 3rd clock is placed at, and that the 3rd clock will read the 1st clock as the same frequency that the 2nd clock recorded it at...
Can you provide some data on this strange notion you have stated please?)
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I think our understanding is closer than you think, but I think you are ascribing some assumptions to me that I will clear up:
The NIST 2010 results take relativity to a personal scale. Your feet will be experiencing a slower time than your head if you are standing up.
Agreed
Again, I tell you that a body cannot age differently if the time differences are not a physical actuality.
Why do the links and related NASA articles state a physical difference in aging?
The ageing is physical, but I'll deal with why below.
So on this basis, and the fact that GR states a universally variable present, we will continue 'as if' the observations of clocks being possessed of variable times are a real and physical effect.
Effect yes, possessed no, see below.
All you are doing in considering the moving clock relative to yourself standing with the stationary clock, is stating the reference frame of the stationary clock and your stationary self moving with the motion of the Earth through space as being 'the' preferred reference frame.
I do not view there being a preferred frame
So - kinetic energy has a bearing on the phenomenon of the ***increase in frequency*** of light falling towards earth... Any comment?
Agreed
As far as I was aware a 3rd clock would read the 2nd clock as having the same frequency as the 1st clock recorded it to have, no matter where, or what speed the 3rd clock is placed at, and that the 3rd clock will read the 1st clock as the same frequency that the 2nd clock recorded it at...
Can you provide some data on this strange notion you have stated please?)
Your assumption is incorrect.
Your original question was about the kinetic energy vs frequency emitted by a moving 'clock' eg atom, so I'm going to use that example.
3 spaceships having 3 clocks etc.
A considers itself at rest and B starts off in A's frame where they agree the frequency B emits. A now measures this frequency when B is moving at 0.5c relative. It is also measured by C moving relative to A at 0.25c.
As in #233, A will measure the frequency of light emitted by B as lower than measured when A & B side by side. However, C will not measure it as being so low. This being the case it is impossible to say that B is now 'possessed' of light at a specific frequency as measured by A & C, all we can say is that C considers itself to be at rest and will emit a frequency the same as it would at rest with A, and A and C measure it differently due to time dilation
Also bear in mind that if B launches a rocket at a specific KE, A and B will both measure different KEs.
So, do I think these effects are real. Yes, but what you measure depends on the frame you travel in and which you end up in.
Take B returning to a twin on A. B viewed the distance travelled as shorter due to length contraction so it took less time. On return to A if B now measures the distance travelled it appears longer, however, the journey is now part of B's history and is therefore real and permanent. But if B had returned to C's frame it would have been a different history despite having travelled the same speed and for same time.
In GR the same applies as astronauts travel different distances through timespace compared to how an earthbound person measures it.
So, I take the view of consistency that in the gravitational field the clock emits a frequency determined by it being at a state of rest ie in its own frame and we measure from a different frame and see a different passage of time hence a different frequency. However, someone else travelling at a different speed will measure another different frequency.
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The problem is you can't ignore relativity. You need the mathematics of relativity to work out the time differences. Yes time dilation causes real physical effects but you need to resort to frames of reference to make sense of things. This is the point everyone is making.
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To digress, a force acts to change the state of inertia of a system. If we associate a wavelength with the system, whether this is valid or not, and forces are absent then the constant value of the wavelength can be associated with a constant value for inertia. Therefore an applied force will change the wavelength as it changes the inertia. Force, wavelength and inertia can be directly related with this hypothetical model.
NOTE A change in inertia can be related to a change in relativistic mass. Which implies that a change in wavelength can also be related to a change in relativistic mass (for the hypothetical model).
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I am aware that the maths of relativity work, (up to a point). It is after all our best working hypothesis, but as to relativity making sense of anything, that is debatable...
If maths that are proportional to relativity maths can be achieved that give the same mathematical results for different dimensional reasons, reasons that actually could make sense of everything, without the necessity for any unobserved additions, such as dark energy, or dark matter, or the need to calculate position or direction via probability...surely the concept is worthy of consideration... and that is all I'm asking for.
This thread is concerning if the mathematics of a distance expanding, contracting, or changing position in space, as observed between 2 mirrors vibrating at right angles to each other, can be equated with the actions of the mathematical tools of the Lorentz transformations, and time/distance perturbations being used to mathematically describe Doppler shift in quantum.
Colin - the kinetic energy/SR considerations given previously tie into the nitty gritty of this question. I am saying that I suspect that it is the collective frequency of the resonation of the component parts of the atom that determines the frequency of the photon that atom emits, and as it is an atom that is emitting photons that determines the frequency, ie: tick rate, of the clock, any increase in kinetic energy will increase the frequency of the clock, which is contradictory to what we observe, but is indeed how we calculate frequency changes in light falling towards earth.
Your rocket scenarios are typical relativity thought experiments conducted without reference to gravitational shift. These considerations are hypothetical situations that are designed to explain the premise of SR and have little bearing in real life scenarios...
However - what exactly is the problem in referring back to earth's gravity and KE as a standard? Calculating everything via the standard second is already doing so...
What would be wrong with making the duration of time at sea level, earth - that is 1part in 86400 durations that make up the duration of 1 full rotation of the planet - a standard by which to measure anomalies to its own status quo?
As stands, I have read that if one tries to realistically fly rockets about in relation to each other, they will not time mesh under the premise of SR. A rocket can mathematically arrive into the future of another rockets trajectory, after the fact of the other rocket having been there etc. Of course applying a bit of magical twisting, looping or folding of the geometry of empty space will solve that one, but really? I mean people have accused me of going to lengths much less fantastical than these to save my models concepts from the scrapheap.
If a more simply derived explanation were put forth that retained a more classical geometric rendition of empty space, would you turn your nose up in favour of a twisting, looping, or folding geometry of empty space?
You said aging is physical, but you are saying that the frequency of a clock differing from a standard second is only an observation from another reference frame, not a physical reality. So - by these remit you are either saying that time has nothing to do with physical aging, or that time differing from a standard second is an illusion.
If you are agreeing that KE has a bearing on the frequency of light falling to earth, then you are also agreeing that the frequency of a moving clock relative to a stationary clock will increase. Whether the recorded frequency of a clock in relative motion is physically real, or just an illusion, one thing is for sure... the frequency of the clock in relative motion does not increase relative to the stationary clock, it decreases.
Why is the clock affected differently to light?
(Jeff - how can you possibly describe me as ignoring relativity? Was Einstein himself ignoring relativity in his quests for an absolute reference frame? )
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To digress, a force acts to change the state of inertia of a system. If we associate a wavelength with the system, whether this is valid or not, and forces are absent then the constant value of the wavelength can be associated with a constant value for inertia. Therefore an applied force will change the wavelength as it changes the inertia. Force, wavelength and inertia can be directly related with this hypothetical model.
NOTE A change in inertia can be related to a change in relativistic mass. Which implies that a change in wavelength can also be related to a change in relativistic mass (for the hypothetical model).
Ah good good Jeff - I have been waiting for you to bring up relativistic mass, because of course KE having a bearing on an 'appearance' of an increase in frequency in light falling to earth, is also directly related to an increase in relativistic mass.
So again I ask - why does a clock 'appear' to have a decreased frequency when in motion relative to a stationary clock?
(please note the relativity 'appears', for the sake of not causing unwanted comment, although quite why I would have to do this - when physics states time as a variable that can run slower or faster than a standard second, and NASA states astronauts, and NIST states tower block dwellers, as aging in keeping with their dilated or contracted clocks - is beyond me)
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This thread is concerning if the mathematics of a distance expanding, contracting, or changing position in space, as observed between 2 mirrors vibrating at right angles to each other, can be equated with the actions of the mathematical tools of the Lorentz transformations, and time/distance perturbations being used to mathematically describe Doppler shift in quantum.
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Ok, I realise that and not sure where this got diverted. However, just a few thoughts before we leave it and go back to your prime focus.
Colin - the kinetic energy/SR considerations given previously tie into the nitty gritty of this question. I am saying that I suspect that it is the collective frequency of the resonation of the component parts of the atom that determines the frequency of the photon that atom emits, and as it is an atom that is emitting photons that determines the frequency, ie: tick rate, of the clock, any increase in kinetic energy will increase the frequency of the clock, which is contradictory to what we observe, but is indeed how we calculate frequency changes in light falling towards earth.
I agree with the component parts etc, but have explained why I disagree that what we observe is contrary to current theory. However, I'm beginning to understand why you might think it is.
Your rocket scenarios are typical relativity thought experiments conducted without reference to gravitational shift. These considerations are hypothetical situations that are designed to explain the premise of SR and have little bearing in real life scenarios...
If that's what you believe then little point discussing further, however numerous experiments in accelerators suggest it is a mistake to take that position.
As stands, I have read that if one tries to realistically fly rockets about in relation to each other, they will not time mesh under the premise of SR...........
Have you tried to work through any of these yourself? I have, Pete has, and I know others who have. These scenarios are usually poorly thought through and you soon see errors of logic and maths, or you can see what is really happening without any magical twisting etc.
However - what exactly is the problem in referring back to earth's gravity and KE as a standard? Calculating everything via the standard second is already doing so...
What would be wrong with making the duration of time at sea level, earth - that is 1part in 86400 durations that make up the duration of 1 full rotation of the planet - a standard by which to measure anomalies to its own status quo?
No problem at all as long as you recognise that this is an artificial standard and there is no absolute against which you can say the 'atom is possessed of'.
You said aging is physical, but you are saying that the frequency of a clock differing from a standard second is only an observation from another reference frame, not a physical reality.
No, I'm saying it is a physical reality, but it will differ dependant on the reference frame of measured and measured. Just a note: I see you question in reply to Jeff why use term 'appears to', have you not noticed that NIST also use the terminology.
If you are agreeing that KE has a bearing on the frequency of light falling to earth, then you are also agreeing that the frequency of a moving clock relative to a stationary clock will increase.
No, the moving clock in your example was not falling through a gravitational field, just moving relative to the measurement point.
Why is the clock affected differently to light?
As above.
Just to clarify what I'm saying, then I'll leave this subject, because I think you are misunderstanding what I'm saying. Although I disagree on some items e.g. KE vs frequency of moving clock, we are really in agreement on most items. I have no problem with you looking at new theories, but here we consider current theory.
Take Pound Rebka. If you place a second absorber midway up the tower then you can vary the velocity of each 2 absorber to cancel the shift at each level and both absorbers will agree on the frequency emitted from the top of the tower.
Now put the same tower on top of a hill and the 2 absorbers will still measure the frequency at the top of the tower to be the same as the first experiment. This is because both the emitter and the absorbers have all moved up the gravity field. Yes, you can reference to a sea level standard but under SR and GR that standard is moving so cannot be viewed as an absolute. That's all I'm saying, there is no absolute and it does depend where you are in the field and whether you are moving. What is measured between 2 points depends on both the difference in gravitational potential and relative movement, this is illustrated by GPS satellites.
But yes, people in tower blocks age faster than those at sea level, our heads age faster than our feet.
So, getting back to to the tuning forks.
Not easy to describe without maths but rough idea about the changing distance.
The changing distance between the tuning forks will be a mixing of their 2 frequencies resulting in two sinewaves one of f1+f2 another of f1-f2. When the 2 frequencies are close together you get beats which you will recognise from tuning an instrument to a tuning fork.
You will also get a double effect on the laser beam in that its own frequency will be frequency modulated with both tuning fork frequencies.
The exact outcome of these waveforms will depend on the 2 frequencies and their phase.
Not sure if that helps.
EDIT: What I said about Pound Rebka measuring frequencies also applies to atomic clocks where the frequencies are compared relative to the other clock and are not an absolute frequency measurement.
And to repeat why the KE is lower for atom moving relative to measuring point - the frequency originates in a frame where the time is flowing at a different rate to the measuring frame, hence KE and frequency are measured as being lower. Either count the wavecrests against time in the 2 frames or think this way - in Pound Rebka light moves from frame where clocks tick faster to frame where tick slower and gains KE, in moving frame light moves from frame where clock ticks more slowly than frame it moves into hence loses KE.
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The accelerator will not be replicating changes in gravitational field.
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No, but I have read extensively the thoughts of prominent physicists regarding the problems that arise in relativity, and the mathematical methods that must be employed to overcome these problems.
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If the appearance of time running faster or slower in the other reference frame is a real effect, and the difference in aging between yourself and the person in the other reference frame is a real effect, then it is physically impossible that a 3rd reference frame will view the other reference frame as aging/ticking at a different rate than you will... The person in the other reference frame cannot possibly be aging at 2 different rates at the same time! This breaks the laws of physics!
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As light falls to earth, its gravity potential energy decreases and its kinetic energy increases. The frequency of the light increases.
In the clock in relative motion scenario, the gravity potential energy remains constant and the kinetic energy increases...
But the frequency of the clock does not increase, it decreases...
...again - why is the clock affected differently to light?
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Yes - it is the maths of these changes in distance that I am asking about, and if they can be equated with the actions of the mathematical use of the Lorentz transformations, and time/distance perturbations used in quantum to describe Doppler shift.
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With regards to your edit:
And to repeat why the KE is lower for atom moving relative to measuring point - the frequency originates in a frame where the time is flowing at a different rate to the measuring frame, hence KE and frequency are measured as being lower.
This is, as far as I am concerned, a truly inspired piece of logic on your part Colin. It shows how the reference frame that an object moves through is not experiencing the same rate of time the object is experiencing, and I would bet that if you worked out the value of this mathematical transaction of energy/time, that it would have the same dimensional value as adding relativistic mass.
However, this is why, under the remit of current theory, what you say is suspect, because an object that is in relative motion to another experiences an increase in relativistic mass that is accompanied by an 'increase' in kinetic energy... Correct?
Either count the wavecrests against time in the 2 frames or think this way - in Pound Rebka light moves from frame where clocks tick faster to frame where tick slower and gains KE, in moving frame light moves from frame where clock ticks more slowly than frame it moves into hence loses KE."
How can light, when moving into a frame that is ticking more 'slowly', gain KE? 299 792 458 m/slower second would incorporate a decrease in KE...
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If the appearance of time running faster or slower in the other reference frame is a real effect, and the difference in aging between yourself and the person in the other reference frame is a real effect, then it is physically impossible that a 3rd reference frame will view the other reference frame as aging/ticking at a different rate than you will... The person in the other reference frame cannot possibly be aging at 2 different rates at the same time! This breaks the laws of physics!
That's relativity. The person on the top of everest will be viewed as ageing at a different rate by a person at sea level and by a person in a moving satellite and by a person travelling in a jet aircraft at the height of everest, etc.
As I said that is my last post on this, I don't intend to go on repeating myself. I'm sure you have tried calculating the frequency as I suggested and obviously get different results, so we will have to agree to disagree.
Happy to discuss the distance changes when you find something to apply it to. You will be looking for evidence of sum/difference frequencies or a compound frequency modulation in the output from an atom or other system.
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Lol Colin - Did you forget? I don't do maths, if I did I wouldn't be publicly posting my ideas before equating them... I've got about as much chance of working out the maths of those changes in distance of expansion, contraction, and changing of position in space, over time, as I have of learning how to play Beethoven's violin concerto D minor from sheet music. I could at a push learn this piece by ear, and although its been some 36 years since I played a violin, I could render some type of rendition that would be at least a notational resemblance just from memory, although I suspect my out of practice bow work, and fumbled finger timing would mean my singing it to you instead might be marginally more pleasant to the ear.
I can physically see that the maths of these changes could correspond with the actions of maths in current use - maths with actions that actually have no known corresponding physical cause, but effect the correct results in the interests of achieving coherent maths...
This is what I am asking about, and I am suggesting applying a direct comparison between the maths of these changes of distance expanding, contracting, and changing position in space, with the use of the Lorentz transformations and time/distance perturbations to calculate Doppler shift in quantum.
(Colin - you may not wish to be involved in what comes below, and its not specifically aimed at you, so no pressure, ok?)
So - relativity breaks the laws of physics, but people cannot break the rules of mathematics...
If light falling towards earth has a decreasing gravity potential energy, an increasing kinetic energy, and an increasing frequency... why does a clock in relative motion on the horizontal, despite retaining a constant gravity potential energy, and experiencing an increase in kinetic energy, appear to have a decreased frequency relative to the stationary clock?
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With the horizontal clock I've given an examples of how to work out the frequency, hence energy. No point repeating.
This is what I am asking about, and I am suggesting applying a direct comparison between the maths of these changes of distance expanding, contracting, and changing position in space, with the use of the Lorentz transformations and time/distance perturbations to calculate Doppler shift in quantum.
(Colin - you may not wish to be involved in what comes below, and its not specifically aimed at you, so no pressure, ok?)
Yes, I'm about to become much busier, I have 2 articles in preparation, I've been asked to check the maths on a QM paper, and I'm preparing experiments for my research project, plus living!
Based on the skill set and background of the type of person you would need, I think you are unlikely to get someone interested in the maths based on that brief and the discussion in this thread, you would do better with a more specific objective. For example Planck was trying to solve a specific knowledge gap in blackbody radiation.
You could try opening up a discussion in NT where you would have greater freedom to explore non standard ideas.
If I think of anything relevant I'll let you know.
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Theoretical physics (the domain of mathematicians) is worthless without observational data to back up its conclusions. Experimental physicists have always been the real pioneers. For without their data the theories would not have been formulated. You have to ask yourself what observations prompted you to come to the conclusions you have reached.
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Colin - I pointed out to you why your explanation of the decrease in frequency recorded of a clock in relative motion does not correspond with the mathematical inclusion of KE in the calculation of light increasing in frequency as it falls to earth...
However I have now given the subject its own thread.
Glad to hear you are keeping busy, good luck with your project.
Jeff - As above... And really, I do highly recommend reading "The Trouble with Physics"... It explains the quite considerable outstanding non correspondences observed of the current (as of when it was written) physics status...
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So - relativity breaks the laws of physics,
No. Relativity IS the laws of physics. It just happens that for most engineering purposes. newtonian physics is adequate, but it doesn't work for particle accelerators (I've just spent an afternoon at CERN, so I know everything!), GPS, astronomy, or very precise measurements of frequency, where you need the full relativistic equations to predict what actually happens.
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As light falls to earth, its gravity potential energy decreases and its kinetic energy increases. The frequency of the light increases.
In the clock in relative motion scenario, the gravity potential energy remains constant and the kinetic energy increases...
But the frequency of the clock does not increase, it decreases...
...again - why is the clock affected differently to light?
It isn't. The difference is between an accelerating frame of reference and an inertial frame. The clever bit of general relativity is recognising that a gravitational field is equivalent to an accelerating frame of reference. Displacement through a gravitational potential alters the energy of a particle, travelling at constant speed doesn't. In face these are simple Newtonian statements.
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As light falls to earth, its gravity potential energy decreases and its kinetic energy increases. The frequency of the light increases.
In the clock in relative motion scenario, the gravity potential energy remains constant and the kinetic energy increases...
But the frequency of the clock does not increase, it decreases...
...again - why is the clock affected differently to light?
It isn't. The difference is between an accelerating frame of reference and an inertial frame. The clever bit of general relativity is recognising that a gravitational field is equivalent to an accelerating frame of reference. Displacement through a gravitational potential alters the energy of a particle, travelling at constant speed doesn't. In face these are simple Newtonian statements.
Ah Alan - you have returned! Good, I've missed you... despite the 'no it isn't's', and I could even perhaps stomach a few 'drivels', and 'b*llocks'...(maybe, (chuckle))
I've actually given the subject its own thread here:
http://www.thenakedscientists.com/forum/index.php?topic=68917.0
...and your comments are welcome, but please do read through first to understand the context. (Warning: you will find your favourite Pound Rebka experiment in mention again)
This thread is concerning if the mathematics of the changes in distance of expansion, contraction, and changing of position in space, observed between 2 mirrors vibrating at right angles, can be equated with the actions of the Lorentz transformations and Perturbation theory within the mathematics equating Doppler shift in quantum.
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So - relativity breaks the laws of physics,
No. Relativity IS the laws of physics. It just happens that for most engineering purposes. newtonian physics is adequate, but it doesn't work for particle accelerators (I've just spent an afternoon at CERN, so I know everything!), GPS, astronomy, or very precise measurements of frequency, where you need the full relativistic equations to predict what actually happens.
And again Alan, again and again and again - the laws of physics, as relativity currently interprets them, require that 93% of the universe remain unaccounted for... which leaves a lot of room for discussion on my planet, how's about yours?
Been to CERN? You lucky devil, I watched the movie...
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It is important to remember that the "laws" of physics are not rigid prescriptions, but useful descriptions which evolve with time as we discover more about how the universe works. Since we now know that c is constant, it is foolish to presume that classical mechanics is the best description of the universe: relativistic mechanics fits the experimental data much better.
Gravitation however remains a bit of a mystery. My bet is that there isn't any dark matter or dark energy, just a hell of a lot of misunderstanding about how gravity works, and like relativity, the next level of understanding will be astonishing/revolutionary/controversial in prospect, and bloody obvious in retrospect.
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Colin - I pointed out to you why your explanation of the decrease in frequency recorded of a clock in relative motion does not correspond with the mathematical inclusion of KE in the calculation of light increasing in frequency as it falls to earth...
No you haven't. See my post in the other thread.