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

[harrylin]

[..] This is why essentially all authors, whatever their other views on these matters, state that is a prediction or requirement of SR that slow clock transport will match Einstein light synchronization. In general, if you have a theory that says two different procedures must be equivalent, it is something you want to test.

Yes indeed. A synchronization convention (or any other convention) cannot itself be verified and therefore it isn't really part of a theory - it's just a tool to describe the predictions of a theory in a well defined way. In contrast, the predictions about the effects of clock transport (both slow and fast) are real physical predictions that can be verified.

 

[Dale]

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).

At best, you can say that you can measure the one-way speed of light wrt non-light synchronization conventions, such as slow-clock transport. But the assumption that slow clock transport gives synchronized clocks is as much an assumption as Einstein synchronization. The measurement in that case may not be tautological, but it certainly is still completely dependent on your synchronization convention.

Tautological or not, you cannot perform a measurement of the one-way speed of light independently of your synchronization convention.

 

[PAllen]

At best, you can say that you can measure the one-way speed of light wrt non-light synchronization conventions, such as slow-clock transport. But the assumption that slow clock transport gives synchronized clocks is as much an assumption as Einstein synchronization. The measurement in that case may not be tautological, but it certainly is still completely dependent on your synchronization convention.

I completely agree it is based on such a convention (and have said so in every post it was relevant). I have further noted you cannot treat:

- measuring agreement of slow transport and Einstein synchronization

- measuring one way speed of light with slow transport

as two separate experiments. They are the same experiment. You can choose either way to look at this single experiement.

 

[ghwellsjr]

I completely agree it is based on such a convention (and have said so in every post it was relevant). I have further noted you cannot treat:

- measuring agreement of slow transport and Einstein synchronization

- measuring one way speed of light with slow transport

as two separate experiments. They are the same experiment. You can choose either way to look at this single experiement.

Then do you completely agree that measuring the one way speed of light with clocks synchronized by slow transport is the same as measuring the one way speed of light with clocks synchronized by Einstein's convention?

 

[Dale]

I completely agree it is based on such a convention (and have said so in every post it was relevant). I have further noted you cannot treat:

- measuring agreement of slow transport and Einstein synchronization

- measuring one way speed of light with slow transport

as two separate experiments. They are the same experiment. You can choose either way to look at this single experiement.

OK, I think we are in agreement, or at least a close approximation thereof.

 

[PAllen]

Then do you completely agree that measuring the one way speed of light with clocks synchronized by slow transport is the same as measuring the one way speed of light with clocks synchronized by Einstein's convention?

Not quite. I agree SR and any equivalent theory/interpretation predicts they are the same. However, one is a tautology, the other is not, and if the universe worked differently than we think, could show us the error of our ways.

I agree with the statement: you cannot measure one way light speed without a synchronization or other purely conventional elements (as a result, the measurement tells you less than you might like).

I disagree with the statement that all measurements of one way light speed are tautologically true; or that it is impossible to measure one way lightspeed.

 

[ghwellsjr]

PAllen, thanks for your continued explanation. I think I'm finally getting what you are saying. Let me repeat it in my own words and you can tell me if I've got it right:

Einstein's synchronization convention is purely arbitrary and a tautology and if we had just that, then we really couldn't measure the one-way speed of light because we would be merely repeating back the time we arbitrarily set on the remote clock. In contrast, the slow transport of a clock is not arbitrary, it always yields the same time and so it allows us to experimentally determine the one-way speed of light. The fact that it is identical to Einstein's synchronization now puts the latter on a proven basis so that we can now say that Einstein's synchronization convention does indeed permit a legitimate meaurement of the one-way speed of light.

 

[PAllen]

PAllen, thanks for your continued explanation. I think I'm finally getting what you are saying. Let me repeat it in my own words and you can tell me if I've got it right:

Einstein's synchronization convention is purely arbitrary and a tautology and if we had just that, then we really couldn't measure the one-way speed of light because we would be merely repeating back the time we arbitrarily set on the remote clock. In contrast, the slow transport of a clock is not arbitrary, it always yields the same time and so it allows us to experimentally determine the one-way speed of light. The fact that it is identical to Einstein's synchronization now puts the latter on a proven basis so that we can now say that Einstein's synchronization convention does indeed permit a legitimate meaurement of the one-way speed of light.

Basically, but I would weaken this a little. There is a real experiment that can be performed, but as noted in my #73, you can consider it verification of agreement clock synch convention (as predicted by SR), or as a measurement of one way light speed (also as predicted by SR - that any reasonable measurement approach will yield c), but not both. That it is a different convention means there is real verification and possibility of falsification of SR; that it is still a convention limits the information it provides.

Finally, as we both know, there are experimentally equivalent theories (or interpretations) to SR that have anisotropic light speed, but predict that no measurement can discern this. Perversely, unless SR is wrong, no experiment can ever rule out such interpretations.

 

[lugita15]

Einstein's synchronization convention is purely arbitrary and a tautology and if we had just that, then we really couldn't measure the one-way speed of light because we would be merely repeating back the time we arbitrarily set on the remote clock.

The only thing I'd nitpick is that only statements can be tautologies, not procedures. So Einstein synchronization is not the tautology; the tautology is the statement that Einstein synchronization yields an isotropic one-way speed of light.

In contrast, the slow transport of a clock is not arbitrary, it always yields the same time and so it allows us to experimentally determine the one-way speed of light.

I would say that slow clock transport is just as arbitrary as Einstein synchronization, at least in the sense that you're free to use it or not, but personally I see it as more natural and intuitive. And I don't know what you mean by "it always yields the same time." But it is true that a measurement of the one-way speed of light using slow-transport synchronized clocks is a nontrivial experiment., in contrast to Einstein synchronized clocks.

The fact that it is identical to Einstein's synchronization now puts the latter on a proven basis so that we can now say that Einstein's synchronization convention does indeed permit a legitimate meaurement of the one-way speed of light.

I'm not sure what you mean by putting Einstein synchronization on a proven basis. As to your statement that "we can now say that Einstein's synchronization convention does indeed permit a legitimate meaurement of the one-way speed of light" - that's essentially my position, but I'd phrase it slightly less boldly:

(*)Since a method which happens to be equivalent (empirically equivalent in our universe, not logically equivalent) to Einstein synchronization allows for a nontrivial measurement of the one-way speed of light, Einstein's second postulate is arguably an empirically grounded fact about our universe.

I put the word "arguably" here, because I definitely agree with the point that LET is empirically indistinguishable from SR, and reasonable people can choose to focus on this point rather than what I said in (*). That's why I've said it's an issue of semantics or interpretation.

 

[ghwellsjr]

I'm confused. I want to take the concepts one at a time. First, you both used the word "tautology" in reference to Einstein's synchronization. My simple question is: If we just consider Einstein's 1905 paper which only allows for synchronizing a distant clock using light signals and not slow transport (or any other experiment), then are you saying that it is impossible to measure the one-way speed of light?

 

[PAllen]

I'm confused. I want to take the concepts one at a time. First, you both used the word "tautology" in reference to Einstein's synchronization. My simple question is: If we just consider Einstein's 1905 paper which only allows for synchronizing a distant clock using light signals and not slow transport (or any other experiment), then are you saying that it is impossible to measure the one-way speed of light?

If you only use light for synchronization, then turning around and using thus synchronized clocks to measure one way light speed is tautological (the answer is built into the synchronization). If you have an additional method of clock synch available, then you can perform a substantive experiment. You can use this method to measure one way light speed (and if you get the isotropic c in all directions, in all inertial frames, immediately infer that your alternate clock synch will always agree with Einstein sync); or you can simply compare clocks synchronized using the two methods, and if they agree in all cases in all inertial frames, infer that one way light speed would be measured as isotropic and constant in all inertial frames (using the alternate clock synch).

From here, look at my post #69 for limitations on the conclusions you can draw from all of this, and some different philosophical ways of characterizing the result.

 

[ghwellsjr]

If you only use light for synchronization, then turning around and using thus synchronized clocks to measure one way light speed is tautological (the answer is built into the synchronization). If you have an additional method of clock synch available, then you can perform a substantive.

Can I assume that your answer to my question is "yes"? Please answer this question with "Yes." or "Nope". No more than four letters, please.

 

[PAllen]

Can I assume that your answer to my question is "yes"? Please answer this question with "Yes." or "Nope". No more than four letters, please.

OK: Yes; it is impossible to measure one way light speed if light signals are your only method of clock synch. I could add, not so much impossible as tautological, as the answer is built into the synch convention, so is pre-determined.

 

[ghwellsjr]

Do you realize you answered yes and no?

 

[my_wan]

Yes, the description is accurate, but it also depends on your synchronization convention. So you are measuring what you assumed via your synchronization convention.

I have disagreed that the synchronization convention is important in terms of the empirical results in the unmentioned thread. You get equally as consistent empirical answer regardless of synchronization convention. Which does not invalidate differing synchronization conventions any more than a coordinate choice physically invalidates an alternate coordinate choice.

 

[my_wan]

OK: Yes; it is impossible to measure one way light speed if light signals are your only method of clock synch. I could add, not so much impossible as tautological, as the answer is built into the synch convention, so is pre-determined.

Though you are correct that it is a tautology the physical consequences remain consistent with any properly formulated synch convention.

 

[Dale]

I have disagreed

Yes, I know. Let's keep it in the other thread so as to not hijack this thread since the OP specifically didn't want our discussion here.

 

[PAllen]

Do you realize you answered yes and no?

I thought you wanted me to answer the following question:

"My simple question is: If we just consider Einstein's 1905 paper which only allows for synchronizing a distant clock using light signals and not slow transport (or any other experiment), then are you saying that it is impossible to measure the one-way speed of light?"

I answered "yes" (but you can go ahead and do it anyway if you don't care about circular reasoning).

 

[ghwellsjr]

I thought you wanted me to answer the following question:

"My simple question is: If we just consider Einstein's 1905 paper which only allows for synchronizing a distant clock using light signals and not slow transport (or any other experiment), then are you saying that it is impossible to measure the one-way speed of light?"

I answered "yes" (but you can go ahead and do it anyway you don't care about circular reasoning).

But if somebody did go ahead and do it anyway, by your answer, it would be appropriate to point out that they were not making a measurement but merely getting back the value they fed in and it would be appropriate to point out that it is impossible to make a measurement of the one-way speed of light using just the process described by Einstein in his 1905 paper, correct? ("Yes." or "Nope" will do just fine as an answer. No "if's", "and's" or "but's", please.)

 

[PAllen]

But if somebody did go ahead and do it anyway, by your answer, it would be appropriate to point out that they were not making a measurement but merely getting back the value they fed in and it would be appropriate to point out that it is impossible to make a measurement of the one-way speed of light using just the process described by Einstein in his 1905 paper, correct? ("Yes." or "Nope" will do just fine as an answer. No "if's", "and's" or "but's", please.)

Yes.

 

[Dale]

My simple question is: If we just consider Einstein's 1905 paper ...

Please answer this question with "Yes." or "Nope". No more than four letters, please.

("Yes." or "Nope" will do just fine as an answer. No "if's", "and's" or "but's", please.)

I don't think that this rhetorical approach is productive. By limiting the question and the response in the way you are demanding, you will get the answer you want but it will be to a question that was never of interest nor in dispute.

 

[ghwellsjr]

Yes.

Thank you.

Now I want to ask you about an experiment. But I want to put this in a context prior to Einstein's 1905 paper. I want to put this even prior to MMX. I want to put this at the time when Maxwell realized that light was a wave in the electromagnetic field his equations described and he believed it would be possible to detect the Earth's motion through this field by measuring the one-way speed of light.

His only problem was that technology was not available for him to perform the type of experiment that we can perform today but let's imagine that it was. So let's suppose that he took two accurate and stable atomic clocks that were synchronized at one location and slowly moved one of them some distance away and the distance was measured using a rigid calibrated ruler. (Let's stipulate that there was no error in his distance measurement.) Now let's also say that he constructs a tube or pipe that he evacuates with a perfect vacuum and he puts a light source at one end that can log the time from the atomic clock located next to it when the light is turned on and a light detector at the other end that can log the time from the other atomic clock located next to it when the light is detected.

So now he does his experiment and he divides the difference between the two logged times into the measured distance. I believe he will get c as the answer and I believe there is no controversy about this, correct?

But let's also assume that this answer would have surprised Maxwell and so he repeats the experiment at different times of the day and at different seasons of the year. Let's say the experiment was so easy to do that other people repeat the same experiment. They do it in every conceivable location, at the bottom of the deepest valley, at the top of the highest mountain, at the poles, at the equator, even at the bottom of the deepest ocean. They repeat the measurement with the apparatus pointed in all different directions of the compass. Everybody always gets the same value for c, correct? Everybody agrees that this is what would have happened, correct?

So then they put the apparatus on the longest flatbed railway car and repeat the measurement at different constant speeds. I'm assuming that their apparatus has no errors and that the accuracy is good enough that they had every reason to believe that they could measure any motion through the field for the speeds they were traveling. Everybody agrees they still always measure exactly c, correct?

So my question for you is: Is there any reason to believe that the development of science would have progressed any differently than it did as a result of MMX which was a two-way measurement instead of a one-way measurement?

 

[PAllen]

So my question for you is: Is there any reason to believe that the development of science would have progressed any differently than it did as a result of MMX which was a two-way measurement instead of a one-way measurement?

No one would say you can't measure the one way speed of light

More seriously, to say an experiment is meaningful means that it matters how it comes out. If the experiment came out showing anisotropy, physics would be very different. Thus the experiment has content.

[edit: and to contrast with a non-meaningful experiment: between two unsynchronized clocks at a measured distance, measure a two way speed of light (using one of them and a mirror). Then, synch them with Einstein's convention, then 'measure' the one way speed to see if it is different. People would think you were deranged.]

 

[ghwellsjr]

OK, now suppose that the size and delicacy of the atomic clocks prevented a fast transport, do you think that anyone would have figured out that they would have gotten a different experimental result if they did transport the clock rapidly? Please explain your answer. If you were there, what argument would you use to make this prediction?

 

[PAllen]

OK, now suppose that the size and delicacy of the atomic clocks prevented a fast transport, do you think that anyone would have figured out that they would have gotten a different experimental result if they did transport the clock rapidly? Please explain your answer. If you were there, what argument would you use to make this prediction?

They would immediately see the tension between Galilean relativity and the experimental light results. Other experiments would show electric and magnetic fields didn't distinguish inertial frames. Eventually someone would figure out the Lorentz transform, showing it preserved the form of Maxwell's equations and explained the light speed measurements. Then predictions for time dilation would follow, and would be sought as soon as technology allowed.

 

[ghwellsjr]

Good. But if you really believe the order of events as you just described them, just based on the Lorentz transform, they already had the experimental evidence for time dilation, even without waiting for new technology. They would have concluded that the atomic clocks themselves were subject to time dilation as they moved at different speeds during the course of a day depending on their arbitrarily chosen Frame of Reference. And part of that explanation of the light speed measurements would show them that even transporting a clock at slow speed would result in its time at the new location being different than the one that remained behind and was dependent on the chosen Frame of Reference.

But they would also conclude that the length of the pipe was changing during the course of a day and that would exactly compensate for the difference in the time between the two clocks resulting in them always measuring the one-way speed of light being the same constant value c.

 

[PAllen]

Good. But if you really believe the order of events as you just described them, just based on the Lorentz transform, they already had the experimental evidence for time dilation, even without waiting for new technology. They would have concluded that the atomic clocks themselves were subject to time dilation as they moved at different speeds during the course of a day depending on their arbitrarily chosen Frame of Reference. And part of that explanation of the light speed measurements would show them that even transporting a clock at slow speed would result in its time at the new location being different than the one that remained behind and was dependent on the chosen Frame of Reference.

But they would also conclude that the length of the pipe was changing during the course of a day and that would exactly compensate for the difference in the time between the two clocks resulting in them always measuring the one-way speed of light being the same constant value c.

Sure, but that would all be inferences from experimental observation. The whole point of theory is to explain observations. An observation explained does not become a non-observation.

Anyway, I think a lot has been well discussed in this thread. I don't see anything new being added since around post #69-#75. If you have some new insight on this, I will respond further, otherwise I probably won't.

 

[ghwellsjr]

But I was saying the same thing back in post #66 which contained quotes from #35 and #52 which got ignored then just like now. Your idea that it is possible to measure the one-way speed of light using the slow transport of clocks is at odds with virtually all the literature on this subject including those in wikipedia and this one, for example:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#one-way_tests

 

[PAllen]

But I was saying the same thing back in post #66 which contained quotes from #35 and #52 which got ignored then just like now. Your idea that it is possible to measure the one-way speed of light using the slow transport of clocks is at odds with virtually all the literature on this subject including those in wikipedia and this one, for example:

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#one-way_tests

You don't seem to understand my position, no matter how many ways I explain it. The following first sentence from your link:

"Note that while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic."

is something I have said six ways from sunday (including, with great emphasis, in #69). But the logical completion of this statement is that a large class of possible theories are ruled out as well. An experiment that rules out possible theories is a real measurement with content. (As opposed to measuring one way lightspeed after Einstein synch, which has no content). Further, as an interpretational bias, given a choice between an interpretation that has unobservable anisotropic ligthspeed , and an interpretation that takes observable ligthspeed as the only quantity of theoretical merit, I prefer the latter (still fully accepting that the former cannot be ruled out).

I believe I have said exactly this at least 6 times. I am confident my view is actually not in conflict with expert opinion, only with overly narrow interpretation of limited quotes of expert opinion.

[edit: Right from #69:
"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).
"]

 

[ghwellsjr]

I used to think that the rationale for the slow transport of clocks was based purely on the final result being the same as Einstein's synchronization but that the process was really different. It took some time for me to understand that it was the process that was also identical. Since you believe that Einstein's convention does not allow for the measurement of the one-way speed of light but yet you do believe that slow clock transport does allow for the measurement of the one-way speed of light, it only shows that you do not yet understand that the process is the same for both of them. Don't you have any curiosity as to why some of us keep emphasizing this point? It has nothing to do with alternate theories. Please try to think about this in another way.

I will ask you a question: why do you believe that when you move a clock at a slow speed, the time on that clock has not shifted in some unknown way? We know that if you rapidly move a clock from A to B and back to A, the time on it will be different than the time on a clock that remained at A. So we know that moving a clock can affect the rate of its ticking.

Now it's not like we have two clocks that aren't ticking and they both display noon and we move one around and when it gets back to the first clock it still displays noon on it. These clocks are constantly changing their times. How can you say that just because they track when together, and they track after slowly taking one of them on a round trip, that they continue to track when they are separated? How do you know that as you move one of them from A to B, it runs slower than the stationary one and so has a different time on it when it gets to B and then when you bring it back it runs faster so that it now has the same time on it when you compare it to the first clock?

Until you can prove that this isn't happening, then you have no justification that the slow transportation of clocks results in them having the same time on them at the remote location. And if you can't prove that, then you can't prove that your measurement of the one-way speed of light is actually measuring what you claim to be measuring even if you get a constant value of c.

 

[PAllen]

I used to think that the rationale for the slow transport of clocks was based purely on the final result being the same as Einstein's synchronization but that the process was really different. It took some time for me to understand that it was the process that was also identical. Since you believe that Einstein's convention does not allow for the measurement of the one-way speed of light but yet you do believe that slow clock transport does allow for the measurement of the one-way speed of light, it only shows that you do not yet understand that the process is the same for both of them. Don't you have any curiosity as to why some of us keep emphasizing this point? It has nothing to do with alternate theories. Please try to think about this in another way.

I will ask you a question: why do you believe that when you move a clock at a slow speed, the time on that clock has not shifted in some unknown way? We know that if you rapidly move a clock from A to B and back to A, the time on it will be different than the time on a clock that remained at A. So we know that moving a clock can affect the rate of its ticking.

Now it's not like we have two clocks that aren't ticking and they both display noon and we move one around and when it gets back to the first clock it still displays noon on it. These clocks are constantly changing their times. How can you say that just because they track when together, and they track after slowly taking one of them on a round trip, that they continue to track when they are separated? How do you know that as you move one of them from A to B, it runs slower than the stationary one and so has a different time on it when it gets to B and then when you bring it back it runs faster so that it now has the same time on it when you compare it to the first clock?

Until you can prove that this isn't happening, then you have no justification that the slow transportation of clocks results in them having the same time on them at the remote location. And if you can't prove that, then you can't prove that your measurement of the one-way speed of light is actually measuring what you claim to be measuring even if you get a constant value of c.

I believe I have answered this in many ways in prior posts, and will not take more time to repeat myself. As I said, in #69, consensus in this thread is unlikely. I was actually pleased that all participants in this thread other than you did reach consensus that my point of view is a defensible formulation.

 

[PAllen]

Ok I will answer some more, but have no optimism that this will get anywhere.

I used to think that the rationale for the slow transport of clocks was based purely on the final result being the same as Einstein's synchronization but that the process was really different. It took some time for me to understand that it was the process that was also identical. Since you believe that Einstein's convention does not allow for the measurement of the one-way speed of light but yet you do believe that slow clock transport does allow for the measurement of the one-way speed of light, it only shows that you do not yet understand that the process is the same for both of them. Don't you have any curiosity as to why some of us keep emphasizing this point? It has nothing to do with alternate theories. Please try to think about this in another way.

It is not the same process, and I believe this has been accepted others. It is a process that is equivalent in our world, but would not ncessarily be equivalent if different physical laws held.

I will ask you a question: why do you believe that when you move a clock at a slow speed, the time on that clock has not shifted in some unknown way? We know that if you rapidly move a clock from A to B and back to A, the time on it will be different than the time on a clock that remained at A. So we know that moving a clock can affect the rate of its ticking.

We don't. We propose it as a convention (as I have said numerous times in this thread), and examine the consequences of this convention. SR and equivalent theories say this convention should match light syncrhonization. To validate these theories (versus other theories), we check this prediction experimentally.

[EDIT: and one form of performing this validation is to explore the isotropy and frame independence of one way light speed measurements that don't use light synchronization.]

 

[Histspec]

Note that while these experiments clearly use a one-way light path and find isotropy, they are inherently unable to rule out a large class of theories in which the one-way speed of light is anisotropic. These theories share the property that the round-trip speed of light is isotropic in any inertial frame, but the one-way speed is isotropic only in an aether frame.
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#one-way_tests

So let us compare light-synchronized clocks with slowly transported clocks:

a) When we find no difference, then this is in agreement with all theories in which the two-way speed is isotropic, regardless of whether the one-way speed is anisotropic or not.

b) When we find a difference, then all theories in which the two-way speed of light is isotropic are refuted

Therefore, comparing light-synchronzied clocks with slowly transported clocks says a lot about the two-way speed, though nothing about the "one-way speed" - the latter is only a useful convention helping us to simplify the arrangement of our experiments, but it's isotropy or anisotropy can never be proved nor refuted.

Regards,

 

[PAllen]

So let us compare light-synchronized clocks with slowly transported clocks:

a) When we find no difference, then this is in agreement with all theories in which the two-way speed is isotropic, regardless of whether the one-way speed is anisotropic or not.

b) When we find a difference, then all theories in which the two-way speed of light is isotropic are refuted

Therefore, comparing light-synchronzied clocks with slowly transported clocks says a lot about the two-way speed, though nothing about the "one-way speed" - the latter is only a useful convention helping us to simplify the arrangement of our experiments, but it's isotropy or anisotropy can never be proved nor refuted.

Regards,

I have no disagreement with the above (and I don't believe anything I have said disagrees with it). However, note that once an observation of one way anisotropy refutes that two way isotropy holds in all frames, it is no longer (necessarily) true that the one way measurement is limited in the information it provides. When testing SR, you should not assume the information limitations implied by the theory you are testing.

One side note is that measurement in one particular frame that two way speed happens to be isotropic but one way speed is not, is sufficient to disprove the equivalence of inertial frames. Thus, in a hypothetical universe where the principle of relativity is false, use of one way light measurements with slow transport might establish this using only single frame, while two way measurements could require two frames to establish this.

Further, note that possible anisotropy is inherently unobservable in SR equivalent theories; while all measurements of c, two way or one way, will be c. Adopting an interpretation in which you attach significance to the unobservable anisotropy only complicates such things as interpreting Maxwell's equations. As long as one understands that you can't rule out such formulations, you are free ignore them for practical convenience.

 

[harrylin]

[..] I want to put this at the time when Maxwell realized that light was a wave in the electromagnetic field his equations described and he believed it would be possible to detect the Earth's motion through this field by measuring the one-way speed of light.

His only problem was that technology was not available for him to perform the type of experiment that we can perform today but let's imagine that it was. So let's suppose that he took two accurate and stable atomic clocks that were synchronized at one location and slowly moved one of them some distance away and the distance was measured using a rigid calibrated ruler. (Let's stipulate that there was no error in his distance measurement.) Now let's also say that he constructs a tube or pipe that he evacuates with a perfect vacuum and he puts a light source at one end that can log the time from the atomic clock located next to it when the light is turned on and a light detector at the other end that can log the time from the other atomic clock located next to it when the light is detected.

So now he does his experiment and he divides the difference between the two logged times into the measured distance. I believe he will get c as the answer and I believe there is no controversy about this, correct?

So far it looks correct.

But let's also assume that this answer would have surprised Maxwell and so he repeats the experiment at different times of the day and at different seasons of the year.

Thus you propose two (extremely!) stable clocks that are once calibrated and synchronised, after which measurements are done at different times of the year. Such an experiment is still to be done I think (and perhaps still out of reach).

Let's say the experiment was so easy to do that other people repeat the same experiment. They do it in every conceivable location, at the bottom of the deepest valley, at the top of the highest mountain, at the poles, at the equator, even at the bottom of the deepest ocean. They repeat the measurement with the apparatus pointed in all different directions of the compass. Everybody always gets the same value for c, correct? Everybody agrees that this is what would have happened, correct?

Sorry but no, that's certainly wrong: according to theory they must find deviations for c, due to the fact that the clocks were not re-synchronised.

So then they put the apparatus on the longest flatbed railway car and repeat the measurement at different constant speeds. I'm assuming that their apparatus has no errors and that the accuracy is good enough that they had every reason to believe that they could measure any motion through the field for the speeds they were traveling. Everybody agrees they still always measure exactly c, correct?

No, still faulty for the exact same reason!

So my question for you is: Is there any reason to believe that the development of science would have progressed any differently than it did as a result of MMX which was a two-way measurement instead of a one-way measurement?

Probably the development of science would have progressed quite similarly; however it could be that textbooks would present a theory that started out from positive results a little different from a theory that started out with negative results.