Explaining Sagnac vs. SRT Violation & Reconciling Lorentz Transform

[robphy]

To me, the “scientific method” is more of a guide and a way of thinking (how our understanding could have been developed if we had the proper tools and insights at the time of the observation… if only history was as orderly)…. not a step by step recipe….and certainly not the only way to understand the universe
…at least in my experience as a scientist.

 

[Jim Fern]

Hmm. Key takeaways.

Institutions of learning: "Keep to the code."
@robphy: "The code is more what you call 'guidelines' than actual rules."

 

[Dale]

Institutions of learning: "Keep to the code."
@robphy: "The code is more what you call 'guidelines' than actual rules."

If by “institutions of learning” you mean “middle school” then yes that is right.

 

[PeterDonis]

It was based on their observations of the sun and other celestial bodies in relation to the earth.

Huh? Those observations had nothing whatever to do with the ether hypothesis.

They were testing a hypothesis (step 2) based on those observations,

Nonsense. Those observations give no indication whatever of the presence of an ether.

such as the wave behavior of light

Observations of the relative motions of the sun and planets tells you nothing about the wave behavior of light.

and the notion of the Earth going round the sun

Precise observations of the positions of the sun and planets in the sky did indeed enable the heliocentric hypothesis to out-compete the geocentric hypothesis. But this had nothing to do with the ether hypothesis.

 

[Jim Fern]

Hmm, I don’t see it. There aren’t any round trip signals in GPS that would be the equivalent of a ring interferometer (no rings and no interferometry). So I think that he must be making a generalization. I will take your and his word for it that the generalization is valid, but it isn’t a clear application.

I hated quoting Wikipedia since it takes fun out of research, but I'm going to bed, so here it is:
A ring laser gyroscope (RLG) consists of a ring laser having two independent counter-propagating resonant modes over the same path; the difference in the frequencies is used to detect rotation. It operates on the principle of the Sagnac effect which shifts the nulls of the internal standing wave pattern in response to angular rotation. Interference between the counter-propagating beams, observed externally, results in motion of the standing wave pattern, and thus indicates rotation.
https://en.wikipedia.org/wiki/Ring_laser_gyroscope

The two independent counter-propagating resonant modes ARE the light beams. The difference in the frequencies is the "fringe distance" in interferometry. The "shifting of the nulls" is arbitrarily carried out by the Lorentz Transform, but isn't required to program the Sagnac adjustments, and is done so only to "indicate" a preferred frame of rotation. The reason that the LT isn't required is that the Sagnac formula works just fine for inertial forces (i.e., centrifugal, coriolis, euler) in a Machian system, since it preceded the LT. Fun little factoid.

Good night.

 

[PeterDonis]

They are indeed employed in the GPS. It depends on them.

The fact that the frame of reference the GPS uses (roughly, the ECEF--Earth Centered Earth Fixed--frame) is a rotating frame, and that the Sagnac effect appears in a rotating frame, does not mean that ring laser gyroscopes are used by the GPS system. They're not.

 

[Jim Fern]

Nonsense. Those observations give no indication whatever of the presence of an ether.

Of course not. But 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.

The M-M hypothesis went something like this: if the Earth moves around the sun at 67,000 mph, and this movement is conducted through a medium that fills all of space through which light propagates (known as "luminiferous ether"), then a light beam discharged into the forward-westward direction of the Earth's supposed motion would have its speed impeded to a degree that is proportional to the speed of the earth.

 

[Jim Fern]

The fact that the frame of reference the GPS uses (roughly, the ECEF--Earth Centered Earth Fixed--frame) is a rotating frame, and that the Sagnac effect appears in a rotating frame, does not mean that ring laser gyroscopes are used by the GPS system. They're not.

If you say so chief. But here it is again: "Contemporary applications of the Ring Laser Gyroscope (RLG) include an embedded GPS capability to further enhance accuracy of RLG Inertial Navigation Systems (INS)s on military aircraft, commercial airliners, ships and spacecraft . These hybrid INS/GPS units have replaced their mechanical counterparts in most applications." Ibid.

 

[robphy]

Hmm. Key takeaways.

Institutions of learning: "Keep to the code."
@robphy: "The code is more what you call 'guidelines' than actual rules."

A few times, I've seen the "scientific method" mentioned in the first chapter of
the intro physics textbook... I have always ignored it and never make reference to it.
It seems like a good way of thinking... but certainly not the only way...
and certainly not the primary way I see advances in our understanding of physics.

(At times, it does seem like some of the pseudo-history in textbooks makes it seem
like the method was followed for various topics... so it helps tell a story about science.)

Instead, my treatment of such "chapter 1"s
is to briefly give my view of what physics is and what the big ideas appear to be.seems like a related thought...

 

[Jim Fern]

I really just found an opportunity to quote Pirates of the Caribbean...and I took it! ;)

 

[PeterDonis]

they went about testing an assumption that came from those observations

No, they did not. See below.

The M-M hypothesis went something like this: if the Earth moves around the sun at 67,000 mph, and this movement is conducted through a medium that fills all of space through which light propagates (known as "luminiferous ether"), then a light beam discharged into the forward-westward direction of the Earth's supposed motion would have its speed impeded to a degree that is proportional to the speed of the earth.

No, that's not what the M-M hypothesis went something like.

First, the Earth "moving around the Sun" was not the important part. The important part was that, as seen from any inertial frame (using the Newtonian definition of an inertial frame), the direction of the Earth's motion had to change over the course of a year. That's why M-M extended their experiment over six months or so. A single run, or set of runs, at just one time of year would not have been sufficient. They expected the interference fringes visible in their instrument to change over the course of the six months: that was their prediction.

Why did they make that particular prediction? Because they understood that the ether hypothesis that they were testing made no prediction about which Newtonian inertial frame was the ether rest frame. They could not assume that it was the frame in which the Sun was at rest and in which the Earth is "moving around the Sun". It was perfectly possible that the frame in which the Earth was at rest at the start of the experiment would be the ether rest frame, in which case their hypothesis would predict a null result at that time of year; but wait a few months and the Earth's direction of motion would have changed relative to that frame, so their hypothesis would predict a non-null result.

Second, all of the above stuff about the motion of the Earth was not part of the hypothesis being tested by M-M. They were not trying to test the Earth's motion relative to the Sun; that was taken as an already established fact. They were trying to test the Earth's motion relative to the ether, and there were no observations up to that time that suggested even the presence of an ether, let alone which frame was the ether rest frame. As I have already said, the ether hypothesis they were testing was purely theory-driven.

 

[Dale]

I hated quoting Wikipedia since it takes fun out of research, but I'm going to bed, so here it is

I am not sure why you quoted that. Neither ring laser interferometers/gyroscopes nor the Sagnac effect are at all under dispute in this thread.

As far as I can tell there are only two points of dispute in this thread:

1) You have claimed without any substantiation that Wang’s experiment contradicts SR. A claim not made by Wang in his paper.

2) You have rejected a large body of evidence because it did not fit your idea of the proper order of science.

I wonder if you intend to address either of those actual topics of disagreement or will you continue to pretend that we disagree on topics where we agree?

 

[PeterDonis]

here it is again: "Contemporary applications of the Ring Laser Gyroscope (RLG) include an embedded GPS capability to further enhance accuracy of RLG Inertial Navigation Systems (INS)s on military aircraft, commercial airliners, ships and spacecraft . These hybrid INS/GPS units have replaced their mechanical counterparts in most applications."

These systems use Ring Laser Gyroscopes for inertial navigation--just as the name says. Inertial navigation systems estimate their current position by using ring laser gyroscopes to continuously measure acceleration, then integrating twice to get position. But such integrations are always subject to some error, which grows over time; so every so often the system has to use some external source to correct its estimate of position, so it has a new starting point for integration.

The systems described in what you quote use GPS signals as the external source to correct the inertial navigation system's estimates of position, which makes them more accurate because they don't have to navigate inertially for a long time between external checks of their position--they get a GPS-updated position every few seconds. The GPS signals these units use do not involve ring laser gyroscopes at all, nor does any part of the GPS system.

If you say so chief.

You need to lose the attitude. You do not know anywhere near as much about the things you are talking about as you think you do.

 

[Dale]

If you say so chief. But here it is again: "Contemporary applications of the Ring Laser Gyroscope (RLG) include an embedded GPS capability to further enhance accuracy of RLG Inertial Navigation Systems (INS)s on military aircraft, commercial airliners, ships and spacecraft . These hybrid INS/GPS units have replaced their mechanical counterparts in most applications." Ibid.

You seem to misunderstand that. That says that modern laser ring gyroscopes use GPS, not that GPS is a big laser ring gyroscope.

In any case, you quoted a good source earlier that claimed that the Sagnac effect is indeed involved in GPS. I assume that he is correctly talking about some non-obvious generalization, and I am not inclined to dispute it without reading his paper. So the Sagnac effect in the GPS is not a point of dispute on my part.

 

[PeterDonis]

That says that modern laser ring gyroscopes use GPS

No, it doesn't even say that. It says that modern inertial navigation systems that use ring laser gyroscopes as accelerometers, also use GPS signals as an external update to their position. The ring laser gyroscopes are just accelerometers; they aren't involved at all in GPS. See my post #48.

 

[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.