I Explaining Sagnac vs. SRT Violation & Reconciling Lorentz Transform

[Dale]

nevertheless, they went about testing an assumption that came from those observations over the course of hundreds of years, which by definition IS a hypothesis lol

Ok, then by that standard ALL of the listed experiments meet your criteria, and you cannot reject any of them on these grounds. That seems to me to resolve point 2. By your stated criteria and example all of those experiments are valid.

Note, I am not agreeing to your criteria. I am just pointing out that it does not support rejecting any of the listed experiments.

 

[PeterDonis]

I assume that he is correctly talking about some non-obvious generalization

He's talking about the fact that, since the GPS frame (the ECEF frame) is a rotating frame, you have to make Sagnac effect corrections when you are using light signals exchanged between different parts of the system, such as the satellites and the master ground stations that send out clock signals, to make updates.

The Ashby article in Physics Today that the OP referenced is here (but unfortunately is paywalled):

https://physicstoday.scitation.org/doi/10.1063/1.1485583

A more technical discussion is here (Section III in particular discusses the Sagnac Effect):

https://aapt.org/doorway/TGRU/articles/Ashbyarticle.pdf

A much more detailed technical discussion is in Ashby's article in the Living Reviews in Relativity series, but unfortunately I can't turn up a link at the moment.

 

[Dale]

He's talking about the fact that, since the GPS frame (the ECEF frame) is a rotating frame, you have to make Sagnac effect corrections when you are using light signals exchanged between different parts of the system

I guess that is a nomenclature thing, but I don’t like to identify the Sagnac effect with a rotating frame. The Sagnac effect is an actual observable phenomenon (phase shift of rotating ring interferometer), so it arises in inertial frames just as in rotating frames.

The anisotropy in the one way coordinate speed of light in a rotating frame is occasionally described as the Sagnac effect. Is that what he is doing?

 

[Jim Fern]

Ok, then by that standard ALL of the listed experiments meet your criteria, and you cannot reject any of them on these grounds.

Remember, it also included observations of waves and their mediums other than light, i.e. stones in a pond, wind on the grass, sound through the air, etc., that also led to the hypothesis that since light observationally behaved as a wave, then it may require the same thing...a medium. They had no reason to think otherwise. So it does always come back to observations being made first, and then being tested experimentally. I can imagine that had I lived in that time, I would be thinking the same thing based on observing the rest of nature: where's the medium for light? And I would want to find that.

 

[Dale]

Remember, it also included observations of waves and their mediums other than light, i.e. stones in a pond, wind on the grass, sound through the air, etc., that also led to the hypothesis that since light observationally behaved as a wave, then it may require the same thing...a medium. They had no reason to think otherwise. So it does always come back to observations being made first, and then being tested experimentally. I can imagine that had I lived in that time, I would be thinking the same thing based on observing the rest of nature: where's the medium for light? And I would want to find that.

Ok, so it seems like you agree that you cannot reject any of those experiments since they all had observations in the sense you are using the word.

So I guess the only open point is point 1.

 

[PeterDonis]

I don’t like to identify the Sagnac effect with a rotating frame. The Sagnac effect is an actual observable phenomenon

Yes, that was a bad choice of words; I was using "rotating frame" in the less common sense of "an actual rotating object or objects being used as a reference frame". I agree that the Sagnac effect is due to the rotation of the actual elements of the GPS system, the ground stations at fixed locations on the rotating Earth and the satellites themselves in orbit, not to picking a rotating reference frame.

 

[Sagittarius A-Star]

And how is it even possible to reconcile Sagnac's formula with the Lorentz Transform

In the following link, they use the relativistic velocity addition, which is nothing else than a Lorentz transformation of a velocity. They transform the local one-way signal speed $k$ in the rotating frame to the non-rotating, inertial frame. Rather remarkably, the $\Delta t$ of the Sagnac effect is independent of the signal velocity:
http://www.physicsinsights.org/sagnac_1.html

Then they explain, based on the difference between a one-way and a two-way signal speed and the "relativity of simultaneity", why there is no contradiction between a calculation in the inertial and in the rotating frame.

- which, the way I think I understand it, by design takes the non-relative aspect of the Sagnac formula which gave it its form for practical use - and plugs it into SRT to make it relative?

No, you understand it wrong. The Sagnac effect is a relativistic effect. In a classical, ether-theory based Sagnac formula, the $\Delta t$ of the "Sagnac effect" would depend on the signal velocity, which contradicts experiments.

 

[vanhees71]

He's talking about the fact that, since the GPS frame (the ECEF frame) is a rotating frame, you have to make Sagnac effect corrections when you are using light signals exchanged between different parts of the system, such as the satellites and the master ground stations that send out clock signals, to make updates.

The Ashby article in Physics Today that the OP referenced is here (but unfortunately is paywalled):

https://physicstoday.scitation.org/doi/10.1063/1.1485583

A more technical discussion is here (Section III in particular discusses the Sagnac Effect):

https://aapt.org/doorway/TGRU/articles/Ashbyarticle.pdf

A much more detailed technical discussion is in Ashby's article in the Living Reviews in Relativity series, but unfortunately I can't turn up a link at the moment.

Here it is (open access as all articls in LRR):

https://link.springer.com/article/10.12942/lrr-2003-1?affiliation

 

[vanhees71]

In the following link, they use the relativistic velocity addition, which is nothing else than a Lorentz transformation of a velocity. They transform the local one-way signal speed $k$ in the rotating frame to the non-rotating, inertial frame. Rather remarkably, the $\Delta t$ of the Sagnac effect is independent of the signal velocity:
http://www.physicsinsights.org/sagnac_1.html

Then they explain, based on the difference between a one-way and a two-way signal speed and the "relativity of simultaneity", why there is no contradiction between a calculation in the inertial and in the rotating frame.No, you understand it wrong. The Sagnac effect is a relativistic effect. In a classical, ether-theory based Sagnac formula, the $\Delta t$ of the "Sagnac effect" would depend on the signal velocity, which contradicts experiments.

Any $\mathcal{O}(v/c)$ effect comes out identical within SR and aether theory. The differences between the theories are famously at order $\mathcal{O}(v^2/c^2)$.

 

[Sagittarius A-Star]

Any $\mathcal{O}(v/c)$ effect comes out identical within SR and aether theory. The differences between the theories are famously at order $\mathcal{O}(v^2/c^2)$.

That's correct for light in vacuum and (with assumed Fresnel partial dragging) in fiber optics.

According to Fresnel, the $\Delta t$ would be:
$\Delta t = \frac{L}{c/n-v/n^2} - \frac{L}{c/n+v/n^2} = 2L *v / (c^2 - v^2/n^2)$

In SR, it is (in the inertial frame):
$\Delta t = 2L *v / c^2$

SR predicts the same Sagnac-$\Delta t$ also for example for de Broglie waves and for sound waves in co-rotating air.

 

[vanhees71]

Your formula for SR is given in leading order of the $v/c$ expansion. You have to apply the same approximation also for the aether-theory result
$$\Delta t=\frac{2L v}{c^2} \frac{1}{1-v^2/(n^2 c^2)}=\frac{2L v}{c^2} (1+\mathcal{O}(v^2/c^2)),$$
i.e., you get the same leading-order result in SR an Aether theory.