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Author Topic: Can this relationship be derived between Schrodinger equation and Doppler shift?  (Read 13061 times)

Offline Colin2B

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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.
 

Offline timey

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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.
 

Offline jeffreyH

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

Offline timey

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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?
 

Offline timey

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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?
 

Offline jeffreyH

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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.
 

Offline timey

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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.
 

Offline jeffreyH

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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.
 

Offline Colin2B

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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.
 

Offline evan_au

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Quote from: timey
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.
 

Offline Colin2B

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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.
 

Offline jeffreyH

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Offline Colin2B

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Some information on the main man.

https://en.m.wikipedia.org/wiki/Christian_Doppler
Timey,
Could be worth revising Doppler effect so you are clear on how it works.
 

Offline timey

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Quote from: timey
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.
 

Offline Colin2B

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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.
 

Offline timey

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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?
 

Offline jeffreyH

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You need to learn some trigonometry.
 

Offline timey

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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.
 

Offline jeffreyH

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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.

Quote
...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.

Quote
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.

Quote
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.
 

Offline Colin2B

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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.
 

Offline timey

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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?
« Last Edit: 17/10/2016 00:33:37 by timey »
 

Offline jeffreyH

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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

Quote
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?
 

Offline Colin2B

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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.
 

Offline timey

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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?
 

Offline jeffreyH

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Now can you please explain exactly what you mean by time perturbations.
 

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