Explaining Sagnac vs. SRT Violation & Reconciling Lorentz Transform

[Jim Fern]

Can someone please explain how a Sagnac ring laser gyro or fiber-optic gyro seems to violate SRT, since the second postulate of SRT holds that the speed of light does not vary in vacuum regardless of the position or motion of any observer (in this case, receivers)? And how is it even possible to reconcile Sagnac's formula with the Lorentz Transform - 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? Does this question make any sense? Thanks.

 

[A.T.]

Can someone please explain how a Sagnac ring laser gyro or fiber-optic gyro seems to violate SRT, since the second postulate of SRT holds that the speed of light does not vary in vacuum regardless of the position or motion of any observer (in this case, receivers)?

The second postulate of SRT holds regardless of inertial motion. A gyro measures rotation, which is not inertial.

 

[Jim Fern]

I've really been trying to understand this stuff, but if that is the case, then why is it that the Global Positioning System cannot function properly without adjustments based upon Sagnac’s experimental results? It would seem that whenever the need arises for inertial navigation (such as an absolute frame from which to measure all other coordinates), the Sagnac formula is always included in that. Is the Sagnac effect NOT a universal principle for all electromagnetic counter-propagations, as well as neutron beams, de Broglie waves and the like - basically any waves that travel in opposite directions, such as in two-way communication between satellites?

Something else of confusion is that Sagnac's interferometer experiment was conducted without any consideration of rotation. What caught my eye specifically in regards to this confusion was Ruyong Wang's experiments. According to his notes, he said that "A rotating frame of reference is usually used in explanations but….the travel-time difference of two counter-propagating light beams in moving fiber is proportional to both the total length and the speed of the fiber regardless of whether the motion is circular or uniform"...which of course leads me back to the question about the fiber-optic gyro...and THEN back to the ring laser gyro since the form of motion doesn't seem to matter LOL. How is SRT resolved in this? Thanks.

 

[Nugatory]

then why is it that the Global Positioning System cannot function properly without adjustments based upon Sagnac’s experimental results?

The frame in which the surface of the Earth is at rest (an oversimplification of the GPS coordinate system that doesn’t matter here) is not inertial, so any attempt to synchronize clocks by exchanging radio signals requires Sagnac corrections.

Often the Sagnac effect is most easily understood from a frame that is inertial. Here we can imagine a ring of satellites in geostationary orbit in the plane of the earth’s equator. Now consider two adjacent satellites exchanging radio signals, using the inertial frame of an observer floating in space far above the North Pole and seeing all the satellites moving in their 24-hour orbits: the distance traveled by the east-directed signal is longer than the distance traveled by the west-directed signal so of course the travel times are different. If we instead choose to use GPS coordinates in which the satellites and the surface of the Earth are at rest we’ll need a Sagnac correction to allow for the difference in travel times.

 

[Nugatory]

Ruyong Wang's experiments. According to his notes,...

Link? Please, always cite your sources.

How is SRT resolved in this?

A fiber-optic cable is not a vacuum; light propagates at a constant speed relative to the cable, not relative to all inertial observers. You’ll get the right results if you analyze the problem using an inertial frame in which the cable is moving.

 

[Jim Fern]

Sorry, here it is: “Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber,” Ruyong Wang, et al., Physics Letters A 312 (2003), pp. 1, 4

The fiber was indeed moving. :)

 

[vanhees71]

There is nothing surprising or contradicting relativity in this paper. Wikipedia gives a nice derivation of the Sagnac effect within (special) relativity:

https://en.wikipedia.org/wiki/Sagnac_effect#Relativistic_derivation_of_Sagnac_formula

 

[Dale]

Can someone please explain how a Sagnac ring laser gyro or fiber-optic gyro seems to violate SRT

The Sagnac effect is a prediction of SR. How could a prediction of SR possibly be considered as a violation of SR?

If you read any source that claims the Sagnac effect violates SR then you immediately know that you are reading a source that doesn’t understand SR.

the second postulate of SRT holds that the speed of light does not vary in vacuum regardless of the position or motion of any observer (in this case, receivers)?

The second postulate states that the speed of light is c in any inertial frame.

if that is the case, then why is it that the Global Positioning System cannot function properly without adjustments based upon Sagnac’s experimental results

How would the Sagnac effect be relevant in GPS? There are no ring interferometers in the GPS.

 

[Dale]

Sorry, here it is: “Modified Sagnac experiment for measuring travel-time difference between counter-propagating light beams in a uniformly moving fiber,” Ruyong Wang, et al., Physics Letters A 312 (2003), pp. 1, 4

The fiber was indeed moving. :)

I just read that paper. The authors did not claim any contradiction with relativity anywhere in the paper.

I also did not spot any implied-but-not-claimed contradictions.

According to his notes, he said that "A rotating frame of reference is usually used in explanations but….the travel-time difference of two counter-propagating light beams in moving fiber is proportional to both the total length and the speed of the fiber regardless of whether the motion is circular or uniform"

Specifically, the author does not claim that as a violation of SR. Can you show mathematically what you think is contradicting SR there?

 

[Jim Fern]

I beg your indulgence for this line of reasoning, but the math seems circular to me. How can I objectively use math that is based on what appears to be a supposition? The original intents of interferometry seem to be considered a mark of blasphemy against modern views, and thus I can only view the math as biased...unless I have observational evidence to support it, which is what I am searching for. I am not a physicist, but I am a student of science, and an avid researcher who knows how to read. I know intermediate level physics, enough to plug and chug LOL, and so I know enough to say that the requirement of observations that prove out the Lorentz Transform in matters such as the Sagnac Effect and SRT seems...pretty important. Where are they...the observations? In modern interferometry, such as LIGO, the LT is already applied, which seems to be by nature a presupposition that is, rather pointedly, unmentionable in this forum. This seems to be the crux of what I am trying to learn. This is the source of my confusion, and I can't seem to get past it.

 

[Ibix]

I beg your indulgence for this line of reasoning, but the math seems circular to me.

What maths seems circular? The Sagnac effect simply depends on the fact that if the distance around half-plus-a-little-bit of a circle is not equal to half-minus-a-little-bit. Apart from the obvious gag I don't see what you think is circular.

Where are they...the observations?

Observations supporting what? The Lorentz transforms? See all of electromagnetism.

 

[Jim Fern]

I'm not sure why you think there is a gag here as I simply want to learn and understand, but circular in that the LT seems to mathematically resolve electromagnetism for SRT, but the observations required to support SRT do not appear to be present. Indeed they may be there, but everywhere I look, I see how to "observe with SRT," but never how to "observe SRT" itself. I thought that the Sagnac effect would be a good thing to look into since it involves current tech we use every day. What am I missing? Please bear in mind that I am researching this for myself and my own scientific curiosity, but in order to do so, it seems that I have to skate a thin line in regards to what I am specifically allowed to mention here, and so it is possible that I will not have these questions answered fully. But every little bit helps. I'll keep digging though. Thanks. :)

 

[weirdoguy]

Indeed they may be there, but everywhere I look, I see how to "observe with SRT," but never how to "observe SRT" itself.

Maybe try this link:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[Ibix]

I'm not sure why you think there is a gag here

Fiber optic Sagnac interferometers are frequently circular. My point was that you don't seem to lay out the maths you say is circular, so it's a bit hard to work out where you've gone wrong. Can you lay out the mathematical argument with which you have a problem? Saying something that's incorrect isn't against forum rules, if that's what's bothering you. We'd all be banned. Stating something wrong and refusing to listen to assisstance would be a problem.

As @weirdoguy notes, there is an extensive FAQ on experimental support for SR, split into types of tests of different aspects. This Insight article on early evidence around the speed of light (more detailed but nowhere near as general) may also be of interest.

 

[Jim Fern]

@weirdoguy Yes, I've looked at that, and I am previously already familiar with the majority of the "tests." But I'm not looking for tests alone. I'm looking for an observation that SETS UP the experimental requirements for a test. Relative frames of reference are, at least to what I have found in my research, a philosophical convention that is presupposed, which "feels" like working backwards through the scientific method, beginning with the conclusion that everything is relative, resulting in presuppositions such as Lorentz transforms. In the historical context of experimentation, it would appear that SRT and transform equations were invented and applied AFTER the experiments had already been conducted, often times years afterward. I'm looking for an experiment that follows those suppositions, thus making them true hypotheses, rather than preceding them which by definition renders them as axiomatic. Thanks.

 

[Ibix]

In the historical context of experimentation, it would appear that SRT and transform equations were invented and applied AFTER the experiments had already been conducted, often times years afterward. I'm looking for an experiment that follows those suppositions, thus making them true hypotheses, rather than preceding them which by definition renders them as axiomatic.

I'm confused. The earliest paper I see referenced there at a quick glance is 1728 and the latest 2005. Some are set up before Einstein's 1905 publication, some after. One or other set seems to match what you are after...

 

[PeterDonis]

everywhere I look, I see how to "observe with SRT," but never how to "observe SRT" itself.

What, to you, would count as "observing SRT itself"? What specific experiment would you like to see, that you haven't been able to find?

 

[Jim Fern]

You're confused? I've been confused the whole time LOL, and I find it most difficult to find a straight answer. The classic example - the most widely known - is the M-M experiment of 1881, which preceded both Relativity and the Lorentz Transform, which came about, especially the LT, as a reactive response to the null results. I'm looking for the reverse of that - any experiment where neither relativity nor transforms were assumed after the fact; an actual observation that led to those ideas before it was experimented upon. Any experiment will suffice, so long as it is the direct result of empirical observations pointing directly to relativity and the LT, rather than a response to a previously conducted experiment. Thanks.

 

[PeterDonis]

I'm looking for the reverse of that - any experiment where neither relativity nor transforms were assumed after the fact; an actual observation that led to those ideas before it was experimented upon.

This is obviously impossible since we already know about relativity and the Lorentz transforms, so no possible experiment we could run now could lead to those ideas. You can't put the toothpaste back in the tube.

Instead of making everyone else guess what kind of experiment would satisfy you, can you propose a specific experiment that would?

 

[PeterDonis]

Any experiment will suffice, so long as it is the direct result of empirical observations pointing directly to relativity and the LT, rather than a response to a previously conducted experiment.

This makes no sense to me. First you want "empirical observations pointing directly to relativity and the LT" before the experiment you say you are looking for is done (the experiment "is the direct result of empirical observations"). But then you say you don't want an experiment that is "a response to a previously conducted experiment". How else is anyone supposed to make the "empirical observations" you say you want to be made before the experiment you are looking for?

I find it most difficult to find a straight answer.

I think you need to consider the possibility that this is because you have not really thought through your questions.

 

[Jim Fern]

Doesn't the scientific method require that observations precede experiment? Otherwise, how would one know how to set up the experiment in the first place? In this desired scenario, relativity and LT would be hypotheses to be experimented with based on observations that led to those hypotheses. An experiment is setup to test an observation in order to prove or disprove a hypothesis based on those observations. Is this not so?

 

[PeterDonis]

Doesn't the scientific method require that observations precede experiment?

Nope. The scientific method allows hypotheses that are tested by experiment to come from anywhere at all. There is no requirement that they come from previous observations.

Otherwise, how would one know how to set up the experiment in the first place?

The hypothesis you are testing tells you that. For example, Michelson and Morley were testing the hypothesis that light that appears to propagate in a vacuum is actually propagating in a medium called "ether". That hypothesis told them how to test it: by looking for interference fringes between light beams that had traveled the same distance but in different directions on a moving platform (the Earth).

Note that there were no previous observations that suggested the "ether" hypothesis; it was purely based on theoretical considerations (basically, how electromagnetism would have to work to be consistent with Newtonian mechanics).

An experiment is setup to test an observation in order to prove or disprove a hypothesis based on those observations

See my corrections above.

 

[Ibix]

Doesn't the scientific method require that observations precede experiment?

The idealised process is that experiment or natural observation produces something weird. Eventually someone produces an improved theory that explains preceding experimental data and makes new predictions. Then we test those predictions. Reality is usually messier but built on that skeleton.

You may wish to look up test theories (I think they're discussed in the SR FAQ linked earlier). They are general theories that include parameters that let you change smoothly from (e.g.) Newton to relativity. Then you make predictions with different values of those parameters and see that the best predictions come when you set the parameters to relativity.

Nope. The scientific method allows hypotheses that are tested by experiment to come from anywhere at all.

It amuses me that "the moon is made of green cheese" is a valid hypothesis, although comprehensively falsified.

 

[etotheipi]

It amuses me that "the moon is made of green cheese" is a valid hypothesis, although comprehensively falsified.

Yes, quite laughable. All the latest research by NASA points towards it being a Stilton.

 

[Dale]

I beg your indulgence for this line of reasoning, but the math seems circular to me. How can I objectively use math that is based on what appears to be a supposition?

All math is based on suppositions called axioms. That is an irrelevant objection. The question isn’t whether or not math is based on axioms, it is whether or not it is self consistent and whether or not it is consistent with observations.

I can only view the math as biased...unless I have observational evidence to support it, which is what I am searching for.

I agree, that is the final arbiter of the correctness of the math. Here is my favorite resource regarding the experimental support of special relativity: https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

Since this is what you are searching for, I would recommend that you read this summary in its entirety. That will give you a basic overview of the existing evidence. Section 9.2 specifically discusses the Sagnac effect which behaves as predicted by SR.

I know enough to say that the requirement of observations that prove out the Lorentz Transform in matters such as the Sagnac Effect and SRT seems...pretty important. Where are they...the observations?

Absolutely! They are essential. See the link above. The body of evidence is overwhelming. Any alternative must explain all of these observations, as SR does.

In modern interferometry, such as LIGO, the LT is already applied, which seems to be by nature a presupposition that is, rather pointedly, unmentionable in this forum. This seems to be the crux of what I am trying to learn. This is the source of my confusion, and I can't seem to get past it.

Of course it is a presupposition. That is well known. In science your foundational assumptions are called postulates and in math they are called axioms.

There is no system of science or math that is without assumptions. So objecting to the mere fact of the existence of assumptions is irrelevant. The only question is whether or not the assumptions lead to predictions that are consistent with the experimental evidence. See above for that

I'm looking for an experiment that follows those suppositions, thus making them true hypotheses, rather than preceding them which by definition renders them as axiomatic.

That would be all listed experiments conducted after 1905. Many of the experiments from the first decade or two after 1905 were specifically from scientists hoping to disprove relativity, as are many of the more recent high precision tests of Lorentz invariance.

I'm looking for the reverse of that - any experiment where neither relativity nor transforms were assumed after the fact; an actual observation that led to those ideas before it was experimented upon.

Hmm, it seems like you may not be aware of the test theories for special relativity.

When you test a theory you cannot assume the theory. So instead you assume a test theory which contains parameters that can be adjusted to obtain the theory of interest and one or more competing theories. Then you use the test theory to design an experiment to measure one or more of the adjustable parameters. If the measured parameter (within the limits of experimental error) matches the parameter for the theory of interest then the theory is validated, otherwise it is falsified. Test theories are very important for good experiments.

Doesn't the scientific method require that observations precede experiment?

No. The observations are the result of the experiment. How could they possibly precede the experiment?

An experiment is setup to test an observation in order to prove or disprove a hypothesis based on those observations. Is this not so?

No. An experiment is setup to produce an observation to prove or disprove a hypothesis.

 

[Jim Fern]

The first step in the Scientific Method is to make objective observations. These observations are based on specific events that have already happened and can be verified by others as true or false. Step 2. Form a hypothesis. Step 3. Make a prediction. Step 4. Perform an experiment. Step 5. Analyze the results. Step 6. Draw a conclusion. Step 7. Report you results.

We all had to learn this in middle school. How does step 5 become step 1?

 

[PeterDonis]

The first step in the Scientific Method is to make objective observations.

Please give a reference for this claim.

We all had to learn this in middle school.

I learned no such thing as Step 1 in middle school.

 

[PeterDonis]

How does step 5 become step 1?

You are creating this problem entirely for yourself by putting Step 1 in front to begin with, instead of at Step 5 where it belongs.

 

[Jim Fern]

Just look up the scientific method anywhere you see fit. Observations come first. Always have.

 

[PeterDonis]

The first step in the Scientific Method is to make objective observations.

As I pointed out in post #22, the example you brought up, the Michelson-Morley experiment, contradicts this claim. There were no "objective observations" of the ether that M-M hypothesized and constructed their experiment expecting it to confirm the presence of; the hypothesis was entirely driven by theory.

 

[Jim Fern]

It was based on their observations of the sun and other celestial bodies in relation to the earth...of course there were observations. They were testing a hypothesis (step 2) based on those observations, such as the wave behavior of light the and the notion of the Earth going round the sun. They wanted to test the ether, what was believed to be the medium of light propagation.

 

[Jim Fern]

How would the Sagnac effect be relevant in GPS? There are no ring interferometers in the GPS.

A ring laser gyroscope IS an interferometer, since it employs interference of counter-propagating beams of light. Also according to GPS Engineer Neil Ashby:

​

One of the most confusing relativistic effects – the Sagnac effect – appears in rotating reference frames. The Sagnac effect is the basis of ring-laser gyroscopes now commonly used in aircraft navigation. In the GPS, the Sagnac effect can produce discrepancies amounting to hundreds of nanoseconds...The Sagnac effect is particularly important when GPS signals are used to compare times of primary reference cesium clocks at national standards laboratories far from each other….A Sagnac correction is needed to account for the diurnal motion of each receiver during signal propagation. In fact, one can use the GPS to observe the Sagnac effect.…this creates some subtle conceptual problems that must be carefully sorted out…For example, the principle of the constancy of c [speed of light] cannot be applied in a rotating reference frame, where the paths of light rays are not straight.

- Neil Ashby, “Relativity and the Global Positioning System,” Physics Today, May 2002, pp. 5;6

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

 

[Vanadium 50]

Observations come first. Always have.

1. Hertzian waves.
2. X-ray diffraction.
3. Quantization of electron charge.
4. Discovery of the neutron.
5. Discovery of the positron.
6. Prediction and later discovery of pions.
7. The Lamb shift.
8. Prediction and later discovery of parity violation.
9. Discovery of the J/ψ.
10. Discovery of the W and Z.

All discoveries that have come after prediction. All got the Nobel prize. And I only got to 1984.

 

[Dale]

The first step in the Scientific Method is to make objective observations. These observations are based on specific events that have already happened and can be verified by others as true or false. Step 2. Form a hypothesis. Step 3. Make a prediction. Step 4. Perform an experiment. Step 5. Analyze the results. Step 6. Draw a conclusion. Step 7. Report you results.

We all had to learn this in middle school. How does step 5 become step 1?

Perhaps that is how middle-school students do science fair projects, but the way that professional scientists do science is much more iterative. The basics are to have a theory and compare the predictions of that theory to experimental results. It can be done in that rigorous middle-school way, but anything that compares theoretical predictions to actual experimental observations is legitimate science. Real life science just isn’t as clean and organized as middle school.

Personally, it seems to me that you are trying to reject a huge body of legitimate evidence simply because it doesn’t fit neatly into your middle school paradigm. That is not scientifically legitimate. All of the evidence cited above is valid evidence.

 

[Dale]

A ring laser gyroscope IS an interferometer, since it employs interference of counter-propagating beams of light.

Yes, obviously. That isn’t in dispute. I just don’t see any clear ring interferometers in the GPS.

Neil Ashby, “Relativity and the Global Positioning System,” Physics Today, May 2002, pp. 5;6

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

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.