Would this experiment disprove Bohmian mechanics?

[vanhees71]

I don't comment on aether speculations in this forum.

I don't understand. Are you saying that Doppler formula for moving source differs from Doppler formula for moving observer?

Sure, you find this in any elementary textbook about sound waves. It's even derived in Wikipedia

https://en.wikipedia.org/wiki/Doppler_effect

For the important specialty of light wave, where the Doppler effect depends only on the relative velocity (of course in the correct relativistic sense!) as it must be, because for light there is no medium (or aether), at least not if you "believe" in relativity, which is so overwhelmingly confirmed by observation that I really don't see, how you want to justify an speculations of an "aether". If there is an "aether" in any sense, it's most probably not a naive one as thought in the 19th century!

For the relativistic treatment of the Doppler effect for arbitrary waves, including he special case of light in vacuo, see

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

 

[Demystifier]

If there is an "aether" in any sense, it's most probably not a naive one as thought in the 19th century!

I certainly agree on that.

 

[Demystifier]

For the relativistic treatment of the Doppler effect for arbitrary waves, including he special case of light in vacuo, see
http://www.mathpages.com/rr/s2-04/2-04.htm

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

 

[Demystifier]

I don't comment on ... speculations in this forum.

If a new theory does not produce a new prediction, then it's irrelevant for science. If a new theory does produce a new prediction, then it's a speculation that nobody takes seriously. Unless, for some sociological reasons, the theory becomes "popular".

 

[atyy]

Honestly, this is really unbelievable - if special relativity was "emergent" from Galilean classical mechanics, it would contradict the most basic claim of Galilean relativity about interactions being instantaneous which is mandatory in Galilean relativity (c.f. vol. 1 Mechanics sec. 5), there is absolutely no way special relativity can be emergent from Galilean relativity without contradicting Galilean relativity (c.f. vol 1. Mechanics sec. 5 and vol. 2 Classical Theory of Fields sec 1), there's a reason why Einstein is so famous - he fundamentally changed all of classical mechanics with special relativity, it's literally wrong to say SR is "emergent" from Galilean relativity on the most basic grounds.

Well, this is a bit farfetched since with overwhelming evidence the correct space-time description is relativistic rather than Newtonian. So the fundamental description of matter should be relativistic rather than Newtonian.

https://arxiv.org/abs/1106.4501
"The sense in which AdS/CFT duality illustrates the possibility of emergent relativity, and the special role of strong coupling, are briefly discussed."

 

[Demystifier]

https://arxiv.org/abs/1106.4501

I like the beginning:
"Every child knows that things which are further away are really just smaller. It is only grown-ups who think this an illusion. After all, a distant object looks smaller in every detail, in principle all the way down to its atomic structure. And yet, the grown-ups point out, the Bohr radius is a constant of Nature.
But perhaps it is the grown-ups who are under the illusion. Physics may indeed play out on a flat screen, with an illusion of “depth” created by shrinking or expanding mutable 2D “atoms”, conspiring to fake 3D atoms of fixed size but varying distance from us."

 

[atyy]

I don't understand what you mean concerning relativistic QFT. Of course, there are mathematical formal problems. What I'm talking about is the physical theory applied to real-world observations, and that's the Standard Model using a renormalized perturbative approach and appropriate resummations to make predictions about real-world observations that are of astonishing precision. Despite the fact that everybody in the HEP community looks for "physics beyond the standard model" as if were the holy grail, there's no established result to this effect. So standard relativistic QFT and the Standard Model are very successful theories, at least FAPP. However, there seems not to be a convincing ontological addition a la BM for non-relativistic QM that can help with the ontological quibbles some philosophers and even some physicists still have with minimally interpreted QFT.

There are ideas, for example, that lattice gauge theory can provide a non-perturbative formulation that gives rise to relativistic quantum field theory as a low energy effective theory.

https://arxiv.org/abs/hep-lat/0211036, Stefano Capitani, Lattice Perturbation Theory
"In principle all known perturbative results of continuum QED and QCD can also be reproduced using a lattice regularization instead of the more popular ones." [I think this is not strictly true, even at the physics level of rigour, because of the chiral fermion problem.]

http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf, Gerard 't Hooft, The Conceptual Basis of Quantum Field Theory
"Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

 

[vanhees71]

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

Sigh. It clearly makes the important point that for light, and only for light, in vacuo the Doppler effect depends only on the relative velocity between source and observer, while for sound it depends in addition on the (local) four-velocity of the medium. A medium always introduces a physically distinguished (local) frame of reference, namely its rest frame, while "the vacuum" doesn't provide such a disinguished frame, i.e., the vacuum is Poincare invariant.

 

[vanhees71]

There are ideas, for example, that lattice gauge theory can provide a non-perturbative formulation that gives rise to relativistic quantum field theory as a low energy effective theory.

https://arxiv.org/abs/hep-lat/0211036, Stefano Capitani, Lattice Perturbation Theory
"In principle all known perturbative results of continuum QED and QCD can also be reproduced using a lattice regularization instead of the more popular ones." [I think this is not strictly true, even at the physics level of rigour, because of the chiral fermion problem.]

http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf, Gerard 't Hooft, The Conceptual Basis of Quantum Field Theory
"Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

Well, the regularization you use is irrelevant for this debate, as long as you get a Poincare invariant continuum limit.

 

[stevendaryl]

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

The relativistic Doppler effect can be thought of as a combination of the nonrelativistic Doppler effect plus the time dilation of the moving sender. Motion through a medium doesn't normally affect the rate of clocks, so I don't see why it should have the time dilation effect.

On the other hand, you could imagine a "sound clock" with a sound echoing back and forth between two rigid walls. If the walls are in motion and are oriented perpendicular to that motion, it will experience a kind of time dilation with the speed of light replaced by the speed of sound.

 

[vanhees71]

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]

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]

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]

It was in response to your posting #150.

Well, I don't see how it related to what I said.

 

[vanhees71]

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]

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 $R = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

 

[vanhees71]

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]

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]

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.