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Can this relationship be derived between Schrödinger equation and Doppler shift equation?Looking at Chladni plates ,.'

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.

Quote from: timey on 04/10/2016 03:41:08Can 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 I am looking at is the Lissajous patterns having a possible connection to Doppler shift...

Quote from: timey on 13/10/2016 02:38:23When 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.

Quote from: timey on 13/10/2016 13:35:27What 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.

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.

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.

Quote from: timeyWhat 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.Quote from: timeyThe 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.Quote from: timeyThe 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.

Quote from: timey on 13/10/2016 13:24:57Here 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.Quote from: timey on 13/10/2016 13:24:57It 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.Quote from: timey on 13/10/2016 13:24:57All 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".

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.

What I want to know is how that light beam reflected at a right angle off a vibrating mirror is being phase shiftedBecause everything else described on this thread is merely concerning the reasons I wish to know this.

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°.

Ah - well I didn't actually post a link to the tuning fork version of Lissajous figures,

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?

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.

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.

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.

Quote from: timey on 15/10/2016 18:10:47Frequency 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.Quote from: timey on 15/10/2016 18:10:47 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.

You really think that posting a link to the SI definition answers the question? Or are you using sarcasm?

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.

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?

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.

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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Quote from: timeyThis 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 directionsSo 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.

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.

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.

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?

If waves periods were not being shortened, how could 2 straight lines form a circle? It would be a square wouldn't it?

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.

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.

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?

Colin - I do not understand the maths Alan provided. They mean nothing to me...