Why do you need to measure the speed of light in two directions?

[Dale]

Ohanian is making a big mistake by thinking that the one-way speed of light is really constant independent of a synchronization convention.

Agreed. The Ohanian reference is a non-scientific book and shouldn't even be referenced in this forum IMO.

 

[PAllen]

Agreed. The Ohanian reference is a non-scientific book and shouldn't even be referenced in this forum IMO.

I note that in other threads, Bcrowell referenced it as 'frustrating but useful'. He seemed to agree with the rotating Earth approach to measuring one way speed of light. I'm still pondering that, think there may be a flaw, but no conclusion yet ... can't find a problem.

 

[Dale]

But the criteria for acceptable references is not "usefulness". The Bible is also very useful, but is not an acceptable reference on this site.

 

[PAllen]

Agreed. The Ohanian reference is a non-scientific book and shouldn't even be referenced in this forum IMO.

I also have always assumed synchronization convention is needed; my difference with some is that there is real significance to the fact that a non-tautological convention agrees with a tautological convention, in all frames of reference.

I also believe the following:

1) The statement that any reasonable method of measuring one ways speed of light will give the same value, in all inertial frames (disagreeing that all are tautological) is significant (irrespective of the existence of mathematically valid interpretations where the unobservable actual one way speed of light is anisotropic).

2) To me, Occam's razor and simplicity favor interpretations where the measured value is the only value worth discussing; it is as 'real' as anything gets in physics.

 

[Dale]

I also have always assumed synchronization convention is needed; my difference with some is that there is real significance to the fact that a non-tautological convention agrees with a tautological convention, in all frames of reference.

I like the way lugita15 put it "The equivalence of Einstein synchronization and slow clock transport synchronization is an experimentally testable fact."

I also believe the following:

1) The statement that any reasonable method of measuring one ways speed of light will give the same value, in all inertial frames (disagreeing that all are tautological) is significant (irrespective of the existence of mathematically valid interpretations where the unobservable actual one way speed of light is anisotropic).

2) To me, Occam's razor and simplicity favor interpretations where the measured value is the only value worth discussing; it is as 'real' as anything gets in physics.

I think that you are clearly wrong with 1), but I agree with 2).

With respect to 1), I don't think that there are any reasonable methods of measuring the one way speed of light because I don't think that it is reasonable to assume the value you are measuring and then call it a measurement. The assumption that slowly transported clocks remain synchronized is an assumption which is equivalent to assuming the one way speed is c.

 

[PAllen]

The assumption that slowly transported clocks remain synchronized is an assumption which is equivalent to assuming the one way speed is c.

I disagree with this. This equivalence is expected only after assuming SR. If you make some, but not all, assumptions of SR (e.g if you assume only the principle of relativity and nothing about light or EM behavior), you have no such expectation. Then the Einstein synch is still tautological for measuring the one way light speed, but the clock transport is a separate convention (coupled to a separate assumption that it is valid).

Obviously also, you cannot treat comparing slow clock transport and Einstein convention experimentally, and using slow clock transport to measure one way light speed, as separate experiments. They are the same experiment.

 

[lugita15]

ghwellsjr and Dalespam, do you agree with all the points I made in post #23? If so, the disagreement in this thread may not be substantive, just a question of how you characterize this state of affairs.

This is my personal view of things. I think that points 2, 3, and 4 provide some experimental confirmation of SR. However, we have much independent confirmation of the first postulate, the Principle of Relativity going back to Galileo. So I think it's fair to say that we have experimental evidence of the second postulate, but there may be reasonable disagreement on this point.

 

[nitsuj]

Ohanian is making a big mistake by thinking that the one-way speed of light is really constant independent of a synchronization convention.

I thought that was what was being questioned here; Is the one way speed of EM c, and is it constant. And that the agreement is yes it is.

The only way to know the value of c is to make measurements. Depending on how these are done, synchronizing maybe needed. All of that seems independent of what is being measured (and what is measured in one FoR is independent of what others measure).

So I guess my question is why is it a big mistake to assume that the one way speed of c is constant?

 

[lugita15]

I thought that was what was being questioned here; Is the one way speed of EM c, and is it constant. And that the agreement is yes it is.

The only way to know the value of c is to make measurements. Depending on how these are done, synchronizing maybe needed. All of that seems independent of what is being measured (and what is measured in one FoR is independent of what others measure).

So I guess my question is why is it a big mistake to assume that the one way speed of c is constant?

To be clear, the one-way speed of light is NOT indepedent of synchronization method (and I don't think Ohanian is claiming that it is). The point I've been trying to make is that even though Einstein synchronization makes Einstein's second postulate a tautology, other natural synchronization methods make it susceptible to experimental confirmation, and this is a significant fact.

 

[Dale]

So I guess my question is why is it a big mistake to assume that the one way speed of c is constant?

It is not a mistake to assume it. It is a mistake to think you can measure it independently of that assumption.

 

[Dale]

I disagree with this. This equivalence is expected only after assuming SR. If you make some, but not all, assumptions of SR (e.g if you assume only the principle of relativity and nothing about light or EM behavior), you have no such expectation. Then the Einstein synch is still tautological for measuring the one way light speed, but the clock transport is a separate convention (coupled to a separate assumption that it is valid).

Obviously also, you cannot treat comparing slow clock transport and Einstein convention experimentally, and using slow clock transport to measure one way light speed, as separate experiments. They are the same experiment.

The problem here is that there is a large class of interpretations (using your meaning above) of SR. These interpretations all share all of the same experimental predictions, including the prediction that light synchronization is experimentally equivalent to slow transport.

Depending on the one-way speed of light in each interpretation, some interpretations say that they are both equivalently correct and others say that they are both equivalently wrong, but they are equivalent in all cases. So, amongst all these possible interpretations of SR, if you assume slow clock transport is correct then you are assuming that the one-way speed of light is c.

 

[ghwellsjr]

Can we all agree on the following:
1. Relative to the Einstein synchronization, Einstein's second postulate regarding the one-way speed of light is a tautology.

Agreed, as long as we realize that some explanation is in order, specifically the construction of a frame of reference involving spacetime.

2. Relative to the slow clock transport synchronization, Einstein's second postulate is an experimentally testable fact.

No. Einstein's second postulate is not a fact, it's just a postulate that comports with reality. There are other second postulates that also comport with reality, such as the one in vogue prior to Einstein's second postulate that stated that there existed only one frame in which light propagated at c (the ether frame). There can be no experimental test that favors one of these two incompatible postulates over the other.

3. The equivalence of Einstein synchronization and slow clock transport synchronization is an experimentally testable fact.

They are not equivalent. They yield different synchronizations and the difference is an experimentally testable fact.

4. The equivalence of the two methods is also a theoretical consequence of SR.

The difference in the times on two clocks "synchronized" according to the two methods is a theoretical consequence of SR.

Beyond these four facts, I think the question of whether we can measure the one-way speed of light is largely a semantic or interpretational issue.

No, this isssue is fundamental to SR. Again, I urge you to read the wikipedia article on "One-way speed of light".

 

[lugita15]

The problem here is that there is a large class of interpretations (using your meaning above) of SR. These interpretations all share all of the same experimental predictions, including the prediction that light synchronization is experimentally equivalent to slow transport.

Depending on the one-way speed of light in each interpretation, some interpretations say that they are both equivalently correct and others say that they are both equivalently wrong, but they are equivalent in all cases. So, amongst all these possible interpretations of SR, if you assume slow clock transport is correct then you are assuming that the one-way speed of light is c.

This is precisely why we need to compare SR against theories which make different experimental predictions. In Newton's time, for instance, they would have believed in the PoR and that slow transport of clocks is a valid method of synchronization, but they would be shocked that Einstein synchronization produced the same result.

 

[PAllen]

The problem here is that there is a large class of interpretations (using your meaning above) of SR. These interpretations all share all of the same experimental predictions, including the prediction that light synchronization is experimentally equivalent to slow transport.

Depending on the one-way speed of light in each interpretation, some interpretations say that they are both equivalently correct and others say that they are both equivalently wrong, but they are equivalent in all cases. So, amongst all these possible interpretations of SR, if you assume slow clock transport is correct then you are assuming that the one-way speed of light is c.

But I am not limiting myself to interpretation of SR. There is a difference between the fact that in any conceivable theory at all, Einstein synchronization leads to one way speed = c, tautologically; versus: in the class of theories mathematically equivalent to SR, attempts to measure one way speed required to produce the same answer as the Einstein convention. Without assuming SR apriori, you can measure the one way speed of light using slow transport. You can then use the results of this treated as a measurement to be a key part of your chain of deduction leading to an SR equivalent theory.

 

[lugita15]

Agreed, as long as we realize that some explanation is in order, specifically the construction of a frame of reference involving spacetime.

I assume that you're just making the standard definition of an inertial reference frame in terms of homogeneity and isotropy of space and time.

No. Einstein's second postulate is not a fact, it's just a postulate that comports with reality.

Can't you imagine a universe in which measurements using slow clock transport did not yield the speed of light being constant?

They are not equivalent. They yield different synchronizations and the difference is an experimentally testable fact.

The definition of slow transport synchronization involves taking the limit as the speed of the transported clock goes to zero, as I specified in post #25.

The difference in the times on two clocks "synchronized" according to the two methods is a theoretical consequence of SR.

Again, you need to take the limit as the speed goes to zero.

No, this isssue is fundamental to SR.

I think it's a metatheoretical issue, not a theoretical issue. SR says the one-way speed of light is c. The question of whether this is an arbitrary feature of SR or something that has basis in physical reality is a question about SR, not a question within SR.

 

[ghwellsjr]

Ohanian is making a big mistake by thinking that the one-way speed of light is really constant independent of a synchronization convention.

I thought that was what was being questioned here; Is the one way speed of EM c, and is it constant. And that the agreement is yes it is.

The only way to know the value of c is to make measurements. Depending on how these are done, synchronizing maybe needed. All of that seems independent of what is being measured (and what is measured in one FoR is independent of what others measure).

So I guess my question is why is it a big mistake to assume that the one way speed of c is constant?

A round-trip measurement of the value of the speed of light does not require synchronization because there is only one timing device used. It is impossible to track the progress of light away from us because we don't have anything faster than the speed of light to communicate back to us where it is at any given moment in time. We really need instantaneous communication to solve this problem. Without know where it is at any moment in time (or what time it is when it arrives at any location) means we cannot measure its speed. We know that moving a clock from where we are to some distant point and back again results in a loss of time compared to a clock that remains with us. But we cannot tell whether that loss of time occurred equally during both halves of the trip or whether it occurred more in one direction and less in the other. Furthermore, as we move the clock in one direction, it needs to advance in time (just like a stationary clock) but we cannot tell if it's advancing either faster or slower than the stationary clock and we cannot tell if it is advancing at the same rate when traveling in the two directions.

Please reread the last paragraph of my post #35. I just noticed that it had a truncated ending which I just repaired.

 

[Dale]

This is precisely why we need to compare SR against theories which make different experimental predictions.

Why would we do that? Such theories have been experimentally falsified on other grounds. What they might say about the one-way speed of light is not interesting to me.

 

[ghwellsjr]

I assume that you're just making the standard definition of an inertial reference frame in terms of homogeneity and isotropy of space and time.

I meant what Einstein explained in his 1905 paper. My only point was that if he had merely stated his postulate without further explanation, no one would have any idea what he was proposing. Even with his explanation, many people don't get it. I encourage those who are still confused over this issue to read that paper again, especially the first part.

Can't you imagine a universe in which measurements using slow clock transport did not yield the speed of light being constant?

I don't have to imagine such a universe, this one already has that characteristic.

The definition of slow transport synchronization involves taking the limit as the speed of the transported clock goes to zero, as I specified in post #25.
Again, you need to take the limit as the speed goes to zero.

In the limit, as the speed goes to zero, it takes infinite time and never gets there. For any non-zero speed, no matter how small, we know how to calculate the "error" and it is never zero. But please don't get sidetracked on this minor point. I only raised it with you to refute Ohanian's charge that Einstein forgot about the slow transport of clocks. Even if you do what PAllen suggested by transporting many clocks at different speeds and extrapolating to the "correct" synchronized time, that synchronized time is just an arbitrary definition of time and from which you can derive an arbitrary definition of the one-way speed of light, but it is still nothing more than an arbitrary definition, not an independent measurement of any reality in nature.

I think it's a metatheoretical issue, not a theoretical issue. SR says the one-way speed of light is c. The question of whether this is an arbitrary feature of SR or something that has basis in physical reality is a question about SR, not a question within SR.

I could equally say: LET says the one-way speed of light is c only in a single absolute frame in which the ether is at rest. The question of whether this is an arbitrary feature of LET or something that has basis in physical reality is a question about LET, not a question within LET.

 

[Dale]

Without assuming SR apriori, you can measure the one way speed of light using slow transport.

Only if you assume that a slowly transported clock remains synchronized.

 

[DrGreg]

Mansouri & Sexl^[1] consider a "test theory" of relativity in which the transformation between two frames is postulated to be$$\begin{align} t &= a(v)\,T + \epsilon(v)\,x\\ x &= b(v)\,(X - vT) \end{align}$$where a, b and ε are unknown functions to be determined by experiment. (Note: the first equation intentionally contains x, not X.) Special relativity is a special case of this test theory for a particular choice of these three functions. Experiments to test the validity of relativity can be performed from which the values of a(v), b(v) and ε(v) can be estimated. If the experimental values match the values predicted by SR, this is a confirmation of SR.

Mansouri and Sexl point out that the function ε(v) depends on the clock sync convention chosen, whereas a(v) and b(v) are both independent of sync convention. Under these assumptions, they go on to prove a result (pp.506–508) that slow clock transport and Einstein synchronisation are equivalent if and only if a(v) takes the value predicted by SR, viz$$a(v) = \sqrt{1 - v^2/c^2}$$To avoid any misunderstanding, the term "slow clock transport" is defined to mean in the limit as the speed of clock transport tends to zero (as others have pointed out).

Thus, if you sync clocks by slow clock transport and then measure the one-way speed of light, if you get an answer of c regardless of direction, you have experimentally confirmed that a(v) takes the value predicted by SR.


Reference
[1] Mansouri, R and Sexl, R U (1977), "A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization", General Relativity and Gravitation 8 (7), pp.497–513, Bibcode: 1977GReGr...8..497M, DOI: 10.1007/BF00762634


Further reading
Test theories of special relativity, Wikipedia

 

[lugita15]

In the limit, as the speed goes to zero, it takes infinite time and never gets there.

If the speed were actually zero, of course, then the transported clock would never get there. But (using the language of my post #25) as the speed of the transported clock C goes to 0, the time it takes for C to reach B gets larger and larger, and the difference between clocks B and C once C arrives approaches a constant. If this constant is zero, then we say that clocks A and B are slow-transport synchronized.

Even if you do what PAllen suggested by transporting many clocks at different speeds and extrapolating to the "correct" synchronized time, that synchronized time is just an arbitrary definition of time and from which you can derive an arbitrary definition of the one-way speed of light, but it is still nothing more than an arbitrary definition, not an independent measurement of any reality in nature.

The definition of slow-transport synchronization is precisely what PAllen suggested: we transport clocks at different nonzero speeds, and we take the limit as the speed goes to zero. You can call this an arbitrary definition if you like, but in my mind it seems rather natural. If you had never heard of SR, you would first assume that there's no such thing as time dilation, and if you heard that moving clocks tick slowly you would assume that really slow-moving clocks don't tick that much more slowly then clocks in your rest frame.

Anyway, the key point is that even if slow clock transport is an arbitrary synchronization convention, the question of what the one-way speed of light will be measured to be relative to that convention is not a trivial matter knowable in advance (in stark contrast to Einstein synchronization). It is a significant experimental fact that relative to slow transport, the one-way speed of light is constant. (Sorry for repeating myself.)

 

[lugita15]

DrGreg, that was exactly the kind of experiment I had in mind. ghwellsjr, how would you interpret the result of M&S? I would say that since we already have such voluminous evidence of the principle of relativity, and since this experiment is evidence of SR, the natural conclusion to reach is that this kind of experiment is evidence of the second postulate. I think I would especially say this if I were living in Newton's time. But as I said, this is an question of interpretation, not physics.

 

[ghwellsjr]

DrGreg, that was exactly the kind of experiment I had in mind. ghwellsjr, how would you interpret the result of M&S? I would say that since we already have such voluminous evidence of the principle of relativity, and since this experiment is evidence of SR, the natural conclusion to reach is that this kind of experiment is evidence of the second postulate. I think I would especially say this if I were living in Newton's time. But as I said, this is an question of interpretation, not physics.

Einstein already described what would happen with the slow transport of clocks, as I have pointed out. He also described what would happen with the fast transport of clocks, I might add. The fact that all of Einstein's predictions have been verified experimentally supports the fact that SR comports with reality. But every one of these experiments that supports SR also supports LET. SR postulates that the speed of light is c in any reference frame. LET postulates that the speed of light is c only in the ether frame. There is no experiment that can decide for us which of these two opposing theories is "correct" at the expense of the other one. Identifying the reality of the one-way speed of light would do just that but it can't be done. To think that Einstein's convention of synchronizing clocks being consistent with his prediction of the timing on slowly moving clocks proves that either or both of these together results in an independent method to determine how light propagates is to miss Einstein's argument.

I can see why you defend Ohanian in his attack on Einstein in the book excerpt you referenced. Please don't make the mistake of thinking that I am offering ideas that are contrary to Einstein's. I just plead with you to read Einstein's paper or any of his other writings on the issue of one-way speed of light. He never argued that his theory was proved to be correct over LET, just that since the ether state was unmeasurable (meaning the one-way speed of light was unmeasurable) there was nothing to be gained by clinging to LET.

 

[lugita15]

Einstein already described what would happen with the slow transport of clocks, as I have pointed out. He also described what would happen with the fast transport of clocks, I might add. The fact that all of Einstein's predictions have been verified experimentally supports the fact that SR comports with reality. But every one of these experiments that supports SR also supports LET. SR postulates that the speed of light is c in any reference frame. LET postulates that the speed of light is c only in the ether frame. There is no experiment that can decide for us which of these two opposing theories is "correct" at the expense of the other one. Identifying the reality of the one-way speed of light would do just that but it can't be done. To think that Einstein's convention of synchronizing clocks being consistent with his prediction of the timing on slowly moving clocks proves that either or both of these together results in an independent method to determine how light propagates is to miss Einstein's argument.

I can see why you defend Ohanian in his attack on Einstein in the book excerpt you referenced. Please don't make the mistake of thinking that I am offering ideas that are contrary to Einstein's. I just plead with you to read Einstein's paper or any of his other writings on the issue of one-way speed of light. He never argued that his theory was proved to be correct over LET, just that since the ether state was unmeasurable (meaning the one-way speed of light was unmeasurable) there was nothing to be gained by clinging to LET.

ghwellsjr, I feel like we're talking past each other; I'm interested in theories other than LET, and you're talking about nothing but LET. Without a doubt, if someone believes in what is today known as the Lorentz Ether Theory, then absolutely no experiment can convince them to switch to SR. (That may not be true of Lorentz's historical theory, however; he believed that the electron had physical stresses which could lead to detectable electromagnetic effects.) In other words, if you believe a priori that lengths contract and time slows down for objects moving with respect to the ether, I can't convince you that the one-way speed of light is isotropic in all reference frames. But this is precisely the reason that LET is not an interesting comparison to SR. We can only find out the empirical validity of the various statements in a theory if we think along the lines DrGreg outlined.

If, however, you initially believed in Newtonian mechanics, an experiment measuring the one-way speed of light with respect to slow clock transport synchronization might be good reason to hop on to the special relativity bandwagon, in a way that the same experiment with respect to Einstein synchronization could never do.

 

[ghwellsjr]

No, I'm talking about Einstein's theory of Special Relativity and his argument in its favor. I am not saying anything differently than what he said.

Dr. Greg's post was not claiming that the one-way speed of light was measurable apart from a previously accepted timing convention or that it is intrinsic to nature.

The one-way speed of light is isotropic in all reference frames because of the way that a reference frame is defined according to Einstein's postulate, definitions and conventions. Apart from some type of postulate, definitions and conventions, it is impossible to discuss the meaning of time and therefore the meaning of speed.

 

[lugita15]

No, I'm talking about Einstein's theory of Special Relativity and his argument in its favor. I am not saying anything differently than what he said.

Dr. Greg's post was not claiming that the one-way speed of light was measurable apart from a previously accepted timing convention or that it is intrinsic to nature.

The one-way speed of light is isotropic in all reference frames because of the way that a reference frame is defined according to Einstein's postulate, definitions and conventions. Apart from some type of postulate, definitions and conventions, it is impossible to discuss the meaning of time and therefore the meaning of speed.

I didn't say DrGreg claimed anything like that. His post was about how measuring the one-way speed of light with respect to slow transport synchronization constitutes experimental confirmation of SR. I (and I think Ohanian as well) agree wholeheartedly that you need a synchronization convention to measure the one-way speed of light. But which convention you choose affects whether certain experiments you perform are predictable in advance or provide useful and significant results.

I go back to what I said in post #23. These are the only relevant facts on this issue, all the rest is just interpretation; my preferred view is that if you have evidence of Postulates 1 and 2 combined, and you also have separate evidence of Postulate 1 alone, that suggests that you have some experimental reason to believe Postulate 2.

As I said, I think we're talking past each other.

 

[lugita15]

FYI, there's another way you can think about slow transport of clocks, which I think I may have gotten from Lieber's excellent book "The Einstein Theory of Relativity". Instead of transporting a clock from point A all the way to point B, you instead fill the line segment from A to B with lots of stationary clocks laid end to end. Each clock is just synchronized with its neighbors, so there's absolutely no motion required or distant signal exchanges. If you do this, then intuitively the first clock and the last clock should be in sync. According to Lieber, this gives you the same synchronization method as slow transport. I don't know how accurate her statement is, but if it's true it gives a lot of intuition to the slow transport method.

 

[PAllen]

FYI, there's another way you can think about slow transport of clocks, which I think I may have gotten from Lieber's excellent book "The Einstein Theory of Relativity". Instead of transporting a clock from point A all the way to point B, you instead fill the line segment from A to B with lots of stationary clocks laid end to end. Each clock is just synchronized with its neighbors, so there's absolutely no motion required or distant signal exchanges. If you do this, then intuitively the first clock and the last clock should be in sync. According to Lieber, this gives you the same synchronization method as slow transport. I don't know how accurate her statement is, but if it's true it gives a lot of intuition to the slow transport method.

I would think that amounts to piecewise Einstein convention, and is thus equivalent to clock transport only given other assumptions or experimental verification. The analog for slow clock transport would be a chain of people, and you hand the clock from person to person, as slow as you want.

Of course, I haven't seen their full discussion. I do remember this book from ages ago (think I took it out of the library once), but never owned it.

 

[ghwellsjr]

FYI, there's another way you can think about slow transport of clocks, which I think I may have gotten from Lieber's excellent book "The Einstein Theory of Relativity". Instead of transporting a clock from point A all the way to point B, you instead fill the line segment from A to B with lots of stationary clocks laid end to end. Each clock is just synchronized with its neighbors, so there's absolutely no motion required or distant signal exchanges. If you do this, then intuitively the first clock and the last clock should be in sync. According to Lieber, this gives you the same synchronization method as slow transport. I don't know how accurate her statement is, but if it's true it gives a lot of intuition to the slow transport method.

If there's no motion involved and if each pair of clocks is synchronized with its neighbor according to Einstein's convention, then, as Einstein pointed out in his 1905 paper, all clocks will be synchronized with each other. It's not the same as slow transport unless you actually slowly transport each clock.

 

[lugita15]

If there's no motion involved and if each pair of clocks is synchronized with its neighbor according to Einstein's convention, then, as Einstein pointed out in his 1905 paper, all clocks will be synchronized with each other. It's not the same as slow transport unless you actually slowly transport each clock.

Yes, I see now that it's just begging the question, because you need to know what method to use to synchronize the neighboring clocks. So ignore what I said.

 

[ghwellsjr]

I didn't say DrGreg claimed anything like that. His post was about how measuring the one-way speed of light with respect to slow transport synchronization constitutes experimental confirmation of SR. I (and I think Ohanian as well) agree wholeheartedly that you need a synchronization convention to measure the one-way speed of light. But which convention you choose affects whether certain experiments you perform are predictable in advance or provide useful and significant results.

I go back to what I said in post #23. These are the only relevant facts on this issue, all the rest is just interpretation; my preferred view is that if you have evidence of Postulates 1 and 2 combined, and you also have separate evidence of Postulate 1 alone, that suggests that you have some experimental reason to believe Postulate 2.

As I said, I think we're talking past each other.

OK, for the purpose of getting past the issue of whether synchronization by the slow transport of clocks is identical to Einstein's convention, I will stipulate on this thread that they are identical. I think this is largely the reason we have been talking past each other. So, please, no more trying to convince me on this issue.

Dr. Greg's post was not about "how measuring the one-way speed of light with respect to slow transport synchronization constitutes experimental confirmation of SR". It was, as he said in bold, about how "slow clock transport and Einstein synchronisation are equivalent", about which I have now stipulated. Furthermore, if you look at the wikipedia link at the bottom of his post, you will read these comments:

On the other hand, in special relativity both the one- and two-way speed of light is isotropic, and because only the two-way speed is accessible to experimental tests, Robertson's theory gives different experimental predictions as special relativity.

The value of e(v) depends only on the choice of clock synchronisation and cannot be determined by experiment.

...only the two-way speed is accessible to experimental tests...

However, it is possible to make such an ether/test-theory (independent of the chosen synchronization) experimentally equivalent to special relativity, by giving the effects of time dilation and length contraction the exact relativistic value. So Mansouri and Sexl spoke about the "remarkable result that a theory maintaining absolute simultaneity is equivalent to special relativity." They also noticed the similarity between this test theory and Lorentz ether theory of Hendrik Lorentz, Joseph Larmor and Henri Poincaré. Though Mansouri, Sexl, and the overwhelming majority of physicists, prefer special relativity over such an ether theory, because the latter "destroys the internal symmetry of a physical theory".

You have repeated again what you have said many times on this thread that the slow transport of clocks is experimental evidence for Einstein's second postulate. Now that I have stipulated that it is an identical synchronization method to Einstein's convention, I'd like you to focus on why neither one can be experimentally tested. I have already explained why in posts #35 and #52 which I quote here:

But the real issue is, does a moving clock lose exactly the same amount of time when you move it from point A to point B as it does when you move it back from point B to point A? If you analyze it according to SR in a frame where A and B are stationary, then the answer is yes (because it is defined to be such). But if you transform to a different frame which is moving in the direction from A to B, the answer is no. This is because there is a different time dilation as the clock is moving in the two different directions. There is of course a fixed amount of time dilation while the clock is stationary at A or B but when it moves from A to B the time dilation increases and when it moves back from B to A the time dilation decreases. The net difference in time compared to a clock that remained at A is the same no matter what frame is used but that difference is made up of two unequal times corresponding to the trips in each direction. This difference is frame dependent.

A round-trip measurement of the value of the speed of light does not require synchronization because there is only one timing device used. It is impossible to track the progress of light away from us because we don't have anything faster than the speed of light to communicate back to us where it is at any given moment in time. We really need instantaneous communication to solve this problem. Without know where it is at any moment in time (or what time it is when it arrives at any location) means we cannot measure its speed. We know that moving a clock from where we are to some distant point and back again results in a loss of time compared to a clock that remains with us. But we cannot tell whether that loss of time occurred equally during both halves of the trip or whether it occurred more in one direction and less in the other. Furthermore, as we move the clock in one direction, it needs to advance in time (just like a stationary clock) but we cannot tell if it's advancing either faster or slower than the stationary clock and we cannot tell if it is advancing at the same rate when traveling in the two directions.

Please study these two posts and see if you understand what I am saying here. If you don't understand, please ask what the problem is so that I can add further clarification.

 

[harrylin]

Indeed, measuring the speed of light in two directions is just a purer way of measuring, as no assumption (or definition) needs to be made about the synchronization of a second clock.

And just a little remark:

[..] At the time Einstein wrote his 1905 paper, that universe did not include SR but it did include LET. His paper was written in that context. If you don't distinguish between SR and LET, then you're missing the whole point of the second postulate which is what distinguishes SR from LET. [..]

I agree with Pallen on this. In fact, Einstein did not make such a distinction; the "LET" concept was invented later for the purpose of making such a distinction. He even denied to have known of Lorentz's 1904 paper and he also wrote a summary paper based on these two papers (what we now call "SR").

 

[Dale]

Mansouri & Sexl^[1] consider a "test theory" of relativity in which the transformation between two frames is postulated to be$$\begin{align} t &= a(v)\,T + \epsilon(v)\,x\\ x &= b(v)\,(X - vT) \end{align}$$where a, b and ε are unknown functions to be determined by experiment. (Note: the first equation intentionally contains x, not X.) Special relativity is a special case of this test theory for a particular choice of these three functions. Experiments to test the validity of relativity can be performed from which the values of a(v), b(v) and ε(v) can be estimated. If the experimental values match the values predicted by SR, this is a confirmation of SR.

Mansouri and Sexl point out that the function ε(v) depends on the clock sync convention chosen, whereas a(v) and b(v) are both independent of sync convention. Under these assumptions, they go on to prove a result (pp.506–508) that slow clock transport and Einstein synchronisation are equivalent if and only if a(v) takes the value predicted by SR, viz$$a(v) = \sqrt{1 - v^2/c^2}$$To avoid any misunderstanding, the term "slow clock transport" is defined to mean in the limit as the speed of clock transport tends to zero (as others have pointed out).

Thus, if you sync clocks by slow clock transport and then measure the one-way speed of light, if you get an answer of c regardless of direction, you have experimentally confirmed that a(v) takes the value predicted by SR.

That is not in dispute. And, if I am not mistaken, I believe that Doppler experiments fix the value of b as $\sqrt{\frac{c+v}{c-v}}$, but experiments do not fix the value of ε.

In the Mansouri and Sexl test theory the one way speed of light depends on a, b, and ε. Since a and b are fixed by experiment that leaves ε available as a free parameter to define a class of theories which are compatible with experiment.

If I did my math right the one way speed of light is given by $c\frac{1-v\epsilon[v]}{1-c\epsilon[v]}$. Thus, there is a class of theories which is compatible with experiment and in which the one way speed of light is not c. These theories are distinguished by different values of ε which, as you mentioned, is determined by the synchronization convention of the theory.

 

[PAllen]

I will summarize my point of view as follows (I am sure no consensus will be reached on this thread):

Both of the following are true statements, as of best current knowledge:

1) It is possible to perform non-tautological measurements of the one way speed of light (using slow clock transport; methods proposed in the papers in my post #32; a rotation method described (but not invented) by Ohanian).

2) No experiment can rule out logically valid interpretations of physical laws in which there is an unobservable absolute rest frame, and/or an unobservable anisotropic one way speed of light. (Isotropic two way speed of light, on the other hand, is a well established fact).

There are several defensible ways to respond to this state of affairs. One is to emphasize (2), and say no more than that the one way speed of light is unknowable. This is strongly justified by the philosophy of "don't say more than you can know". Another is to emphasize (1) and focus on measurable one way c as the useful element of physical interpretation. In which case, one states that measurable one way c is isotropic and constant in all frames. You may call this philosophy "avoid unobservable quantities in physical interpretations".

It is also worth noting the indisputable fact that if there were ever a measurement of anisotropic one way c in any inertial frame, SR would be refuted.

 

[lugita15]

I like everything PAllen said, especially the following:

It is also worth noting the indisputable fact that if there were ever a measurement of anisotropic one way c in any inertial frame, SR would be refuted.

To put it another way, the equivalence of Einstein synchronization and certain other methods, including slow clock transport, is a falsifiable prediction of special relativity.