# The Naked Scientists Forum

### Author Topic: Can this relationship be derived between Schrodinger equation and Doppler shift?  (Read 13288 times)

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #50 on: 13/10/2016 02:38:23 »
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.

#### PmbPhy

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #51 on: 13/10/2016 08:08:55 »
Can this relationship be derived between Schrödinger equation and Doppler shift equation?

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.

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #52 on: 13/10/2016 09:16:47 »
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?

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #53 on: 13/10/2016 13:24:57 »
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #54 on: 13/10/2016 13:35:27 »
Can this relationship be derived between Schrödinger equation and Doppler shift equation?

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.

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.
« Last Edit: 13/10/2016 13:39:02 by timey »

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #55 on: 13/10/2016 17:10:31 »

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.

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #56 on: 13/10/2016 17:12:42 »

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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #57 on: 13/10/2016 17:59:00 »

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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #58 on: 13/10/2016 18:01:31 »

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?

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #59 on: 13/10/2016 23:39:26 »
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".

#### PmbPhy

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #60 on: 14/10/2016 05:51:04 »
Quote from: timey
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.

Quote from: timey
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.

Quote from: timey
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.
« Last Edit: 14/10/2016 06:00:26 by PmbPhy »

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #61 on: 14/10/2016 09:15:26 »
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #62 on: 14/10/2016 12:06:21 »
Quote from: timey
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.

Quote from: timey
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.

Quote from: timey
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #63 on: 14/10/2016 12:25:05 »
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?

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #64 on: 14/10/2016 18:06:19 »
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.

#### jeffreyH

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #65 on: 14/10/2016 18:58:53 »
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #66 on: 14/10/2016 19:24:01 »
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.

Because everything else described on this thread is merely concerning the reasons I wish to know this.

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #67 on: 14/10/2016 23:10:03 »
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #68 on: 15/10/2016 00:35:17 »
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?

#### alancalverd

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #69 on: 15/10/2016 00:41:39 »
Wikipedia is succinct and correct, IIRC:

Quote
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.

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #70 on: 15/10/2016 07:07:25 »
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.
« Last Edit: 15/10/2016 09:52:11 by Colin2B »

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#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #71 on: 15/10/2016 11:33:36 »
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?

#### Colin2B

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #72 on: 15/10/2016 16:54:05 »
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.

#### timey

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #73 on: 15/10/2016 18:10:47 »
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.

#### jeffreyH

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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #74 on: 15/10/2016 22:07:56 »
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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##### Re: Can this relationship be derived between Schrodinger equation and Doppler shift?
« Reply #74 on: 15/10/2016 22:07:56 »