# Would this experiment disprove Bohmian mechanics?

• A
vanhees71
Gold Member
2019 Award
Again, I need only to point to this nice website:

https://www.mathpages.com/rr/s2-04/2-04.htm

Note that here to author works explicitly " frame of reference in which the medium of signal propagation is assumed to be at rest", when he treats the acoustic Doppler effect (sound waves) relativistically. It should be easy to derive the more general formula in an arbitrary frame of reference, where also the medium moves.

It is shown clearly that in the case for em. waves in a vacuum (optical Doppler effect), where the phase speed of the waves goes to the speed of light, the Doppler formula correctly depends only on the relative velocity of the source and the observer (which the author calls absorber) as it must be since there is no aether (within relativistic theory).

stevendaryl
Staff Emeritus
Again, I need only to point to this nice website:

https://www.mathpages.com/rr/s2-04/2-04.htm

Note that here to author works explicitly " frame of reference in which the medium of signal propagation is assumed to be at rest", when he treats the acoustic Doppler effect (sound waves) relativistically. It should be easy to derive the more general formula in an arbitrary frame of reference, where also the medium moves.

It is shown clearly that in the case for em. waves in a vacuum (optical Doppler effect), where the phase speed of the waves goes to the speed of light, the Doppler formula correctly depends only on the relative velocity of the source and the observer (which the author calls absorber) as it must be since there is no aether (within relativistic theory).
Who or what is that in response to? (It would be nice for you to give some context, such as quoting the relevant lines that you're responding to, or at least name the person you're responding to).

atyy
Well, the regularization you use is irrelevant for this debate, as long as you get a Poincare invariant continuum limit.
But we don't know how to take the lattice spacing to zero, so there is no known UV continuum limit. This is the reason that the standard model is said to be an effective theorie.

vanhees71
Gold Member
2019 Award
Who or what is that in response to? (It would be nice for you to give some context, such as quoting the relevant lines that you're responding to, or at least name the person you're responding to).
It was in response to your posting #150.

stevendaryl
Staff Emeritus
It was in response to your posting #150.
Well, I don't see how it related to what I said.

vanhees71
Gold Member
2019 Award
Well, I wanted to give you a clear derivation for the Doppler effect for sound, where of course time dilation is included as it must. Maybe I misunderstood your posting.

stevendaryl
Staff Emeritus
Well, I wanted to give you a clear derivation for the Doppler effect for sound, where of course time dilation is included as it must. Maybe I misunderstood your posting.
Well, let me make it clearer. Let's NOT assume Einstein's relativity. We assume the following:

There is a reference frame (called the "stationary frame") in which
1. A signal travels at speed ##c##, which is a constant independent of the motion of the source.
2. A clock moving at speed ##v## will run slower by a factor of ##R## relative to a clock at "rest". (##R > 1## means the moving clock is running slower)
We'll do the derivation with ##R## as an unknown parameter.

We have two observers, one at rest relative to the medium, and one moving at speed ##v## relative to the medium, away from the stationary observer. Assume that each sends a signal toward the other at the rate of once every ##T## seconds, according to his own clock. Then:
• The signals from the stationary observer are sent out every ##T## seconds.
• The signals from the stationary observer will arrive once every ##\Delta T = (\frac{c}{c-v}) T## seconds.
• Because the moving clock is moving slow by a factor of ##R##, the moving observer will measure a smaller time between signals: ##\Delta T' = (\frac{c}{c-v})T/R##
• The signals from the moving observer are sent out every ##R T## seconds.
• The signals will arrive every ##\Delta T = (1+\frac{v}{c}) RT## seconds.
Galilean Doppler shift is obtained by choosing ##R=1##, in which case, there is an asymmetry between the rate at which the signals are received by the moving observer, ##\Delta T = (\frac{c}{c-v}) T## and the rate at which signals are received by the stationary observer, ##\Delta T = (1+\frac{v}{c}) T##.

On the other hand, if you choose ##R = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##, then
• The rate at which the moving observer receives signals is ##\Delta T' = (\frac{c}{c-v})T \sqrt{1-\frac{v^2}{c^2}} = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}##
• The rate at which the stationary observer receives signals is ##\Delta T = (1+\frac{v}{c}) T \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} = \sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}##
So that's the sense in which the relativistic Doppler is a combination of the nonrelativistic Doppler plus time dilation with ##R = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}##

• Demystifier and vanhees71
vanhees71
Gold Member
2019 Award
What you nicely derive is the Doppler effect for light propagation in a vacuum and the Lorentz factor. The question, however was about the Doppler effect of sound in relativity theory, and that's nicely answered at the webpage I quoted (for the special case of the reference frame where the medium is at rest).

It also becomes clear, in which sense there's no "aether", i.e., no medium needed for light as air is a medium for sound waves.

stevendaryl
Staff Emeritus
What you nicely derive is the Doppler effect for light propagation in a vacuum and the Lorentz factor. The question, however was about the Doppler effect of sound in relativity theory, and that's nicely answered at the webpage I quoted (for the special case of the reference frame where the medium is at rest).
Okay, but the issue that I thought was under discussion was to what extent a nonrelativistic theory plus a medium can mimick relativity.

Demystifier
Gold Member
What you nicely derive is the Doppler effect for light propagation in a vacuum and the Lorentz factor. The question, however was about the Doppler effect of sound in relativity theory, and that's nicely answered at the webpage I quoted (for the special case of the reference frame where the medium is at rest).

It also becomes clear, in which sense there's no "aether", i.e., no medium needed for light as air is a medium for sound waves.
Ah, now I get your point. I agree that, to explain currently existing experiments, no medium for light is needed. But it doesn't imply that no medium is possible.

To explain it, let me first define two new words: quasi-relativity and quasi-Lorentz invariance. By those I mean a theory mathematically looking exactly like standard relativity and standard Lorentz invariance, except that the speed of light ##c## is replaced with the speed of sound ##c_s##.

Now with this language it's easy to explain why sound Doppler effect and light Doppler effect are described by different equations. In the light Doppler effect, not only the wave but also the emitter and detector obey relativistic laws. In the sound Doppler effect, only the wave obeys quasi-relativistic laws (due to the quasi-Lorentz invariant dispersion relation ##\omega=c_s|{\bf k}|##), while the detector and emitter don't.

It is conceivable that in some beyond-the-standard-model theory one has an additional term in action in which a new kind of matter interacts with light and violates Lorentz invariance. An emission and detection of light by such kind of matter could give a formula for Doppler effect that doesn't look like standard Doppler formula for light. Depending on the details of the theory, it could look more like formula for the sound Doppler effect.

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