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So, I just saw this Youtube video by Veritasium that discusses how it's impossible to measure the one-way speed of light from a light source to a detector, since it's impossible to synchronize clocks in a fashion that would prevent a directional difference in the speed of light from altering clock speeds via relativistic time dilation in such a fashion that it would conceal directional differences in the speed of light. As a result, it's only possible to measure the two-way speed of light, where light passes from a source to a reflector and then back to a detector located at the light source, and it's impossible to rule out a directional difference in the speed of light, which could be as extreme as light traveling at c/2 in one direction, and instantaneously in the other.

However, Veritasium goes on to briefly mention that if there is true, we would observe stars in the direction of the instantaneous speed of light in real time, rather than through a time delay of hundreds or thousands of years. During his papers on relativity, Einstein noted this possibility, and assumed that it traveled at equal speeds in all directions; as a result, this assumption has apparently been called the "Einstein Synchronization Convention".

This suggests to me that if the Einstein Synchronization Convention is untrue, and there is a directional difference in the speed of light, we should be able to notice this through astronomy; if the light takes less time to travel to us from some directions than others, we should see older stars and galaxies in the directions where light travels more quickly than in the directions where it travels more slowly, since we'll be observing them as being closer to "real time". For instance, if you had galaxies 3 billion light years away from us, but it took light 2 billion years to reach us in one direction and 4 billion years to reach us in the other direction, you'd expect the galaxies in the 2 billion year direction to look 2 billion years older than the galaxies in the 4 billion year direction.

Is this correct, or would a variation in the speed of light invalidate our methods of measuring distance and/or the age of celestial objects? Have there been any astronomical studies investigating this, and if so, what have they found?

To be clear, I am specifically asking about detecting directional variations of the one-way speed of light using astronomy. I don’t want answers that discuss variations of the speed of light due to the velocity of their emitters (which was disproved by experiments prior to Einstein). I don’t want answers talking about clocks or simultaneity, since they’re not really directly relevant to this question.

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    $\begingroup$ The Einstein synchronization convention is a process for synchronizing clocks within a single reference frame. The assumption being made is that it works, essentially. The wiki article has more on the "round trip conditions" which are the focus of your question. $\endgroup$ – J. Murray Oct 31 '20 at 13:41
  • $\begingroup$ Well, it's a convention, and other conventions are possible without affecting what we can actually observe. You may enjoy reading what John D. Norton has to say on this topic. pitt.edu/~jdnorton/teaching/HPS_0410/chapters/… $\endgroup$ – PM 2Ring Oct 31 '20 at 15:16
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    $\begingroup$ You should replace every occurrence of "the Einstein synchronization convention" in the question with "Einstein's second postulate".since that's what you're really asking about. $\endgroup$ – benrg Oct 31 '20 at 16:02
  • $\begingroup$ Here's an older question (with a nice answer) on Reichenbach synchronization: physics.stackexchange.com/q/257665/123208 $\endgroup$ – PM 2Ring Nov 1 '20 at 9:04
  • $\begingroup$ @PM2Ring Yes, that Answer very succinctly points out many of the same facts as the Veritasium video I linked to. $\endgroup$ – nick012000 Nov 1 '20 at 9:39
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if the Einstein Synchronization Convention is untrue, and there is a directional difference in the speed of light, we should be able to notice this through astronomy; if the light takes less time to travel to us from some directions than others, we should see older stars and galaxies in the directions where light travels more quickly than in the directions where it travels more slowly

This is a good question. Neglecting the CMB dipole anisotropy, we see a very nearly isotropic large scale structure to the universe. So your question is, how could a non-isotropic synchronization convention possibly explain the observed isotropy?

As you say, light from the “fast” direction would have a shorter delay than light coming from the “slow” direction. So the fast light would give more recent data and the slow light would give more ancient data. Since both directions show galaxies of roughly the same age, that means that there is an anisotropic cosmological gravitational time dilation. Galaxies in the fast light direction age more slowly and galaxies in the other direction age faster.

Yes, such a convention would be very cumbersome and inconvenient, which is why it is not used. But it would be self consistent and also consistent with the cosmological data.

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Your question is really about Einstein's second postulate, the constancy of the speed of light, not about the synchronization convention, which is only a convention as the name implies.

Light moving at a constant speed has consequences that are independent of what that speed actually is. It means that light waves won't overtake each other, no matter how far they travel. We can test this in various ways. For example, binary stars and moons in the solar system accelerate over fairly short time scales; if there was even a slight dependence of the speed of light on the speed of the source then we would see distortion in their motion that we don't see.

Once you've convinced yourself that the speed of light is constant (in that sense) by these sorts of observations—which had already happened before Einstein's paper—you can choose to use this property of light to set clocks. If the speed is really anisotropic then clocks that you set this way won't really be synchronized, but that doesn't stop you from setting them this way. You can now ask another question: if you set clock B from A this way, then set C from B this way, is the result the same as if you'd set C from A? You can test this by setting two different clocks at C and comparing them locally. You can repeat this experiment with every possible arrangement of three points at relative rest in three dimensions.

If the speed of light passes that test, then it no longer matters whether it's "really" isotropic or not since it behaves as though it's isotropic. We can assume our clocks to be synchronized, and we can even fix the speed of light in meters per second by definition and use it to define length, as we in fact do. This doesn't prevent us from detecting a violation of our assumptions, because the only physically meaningful assumption that we actually made is that the experiments of the previous paragraphs won't start returning different results in the future, and we didn't assume the existence of "truly" synchronized clocks for those experiments.

We can also take the speed of light to be anisotropic, and the clocks to not be synchronized, but this amounts to doing the same physics in different coordinates, and the result of any calculation in these coordinates will be the same as the transformed result of the calculation in standard coordinates. Taking the age of stars as an example, if the $t$ of the anisotropic coordinates doesn't match cosmological time, then stars at the same distance in different directions have different ages, and this exactly counters the light travel time delay so we see them at the same age. If the $x$ coordinate doesn't match comoving position, then Earth is moving away from the faster light and toward the slower light at just the right speed so that they take the same time to arrive. If both coordinates don't match, it's a combination of both effects. This is similar to the way that length contraction, the relativity of simultaneity, and so forth always conspire to make things consistent in different inertial frames.

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  • $\begingroup$ I’m not asking about variation on the speed of light as a result of the speed of the object emitting it, but based upon the direction it’s travelling (e.g. 2/3c in one direction and 4/3c in the other direction), as a result of our inability to directly measure the one-way speed of light. $\endgroup$ – nick012000 Nov 1 '20 at 3:18
  • $\begingroup$ @nick012000 I just wrote another answer about that. If there exist coordinate systems in which the speed is constant (which there do) then you can always define some other coordinate system in which it isn't. No theory could ever avoid this because it's just a mathematical substitution of variables, so the fact that you can do it has no physical significance. $\endgroup$ – benrg Nov 1 '20 at 3:26
  • $\begingroup$ Reading that answer, I’m not convinced you understood the Veritasium video in the first place, since they’re not just talking about mathematical transformations with no physical consequence- there should be at least one physical consequence that I could think of, and that’s what my question was about. $\endgroup$ – nick012000 Nov 1 '20 at 3:33
  • $\begingroup$ @nick012000 They are just talking about a mathematical transformation with no physical consequence. Take the hollow Earth theory of Mostafa Abdelkader, which starts with geocentric polar coordinates and substitutes $r'=R^2/r$. Can it be falsified? Abdelkader himself thought that if you drilled into the Earth you'd hit empty space. But of course that breaks the coordinate equivalence. (cont'd) $\endgroup$ – benrg Nov 1 '20 at 3:44
  • $\begingroup$ @nick012000 (cont'd) Veritasium isn't cranky like that, I don't think. They'd consistently refute any attempt to falsify the hollow earth by saying it'd have (the transformation of) the same result as the experiment in the standard theory. That's what they do with every proposed experiment in their video. There's no way around it because it's purely a word game. $\endgroup$ – benrg Nov 1 '20 at 3:45
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Veritasium raises the question whether it is possible for clocks on Earth and clocks on Mars to be correlated?

There are astronomical events that occur in a spike. The emission of energy by a supernova event ramps up, and subsequently decays. By matching the emission profile at a high level of precicion the astronomers can line up the data.

Take for example the case of a Supernova event that reaches the Earth and Mars from a direction perpendicular to the line that connects Earth and Mars at that point in time. This means the light must arrive at Earth and Mars simultaneously. This provides a way to arrive at correlation of the time keeping between Earth and Mars.

This can then be cross-correlated with results from Einstein synchronization procedure.

So: is the above procedure, using arrival time of far-away events, an independent way of correlating time keeping on Earth and Mars?

Well, the light arriving at Mars has not traveled the same path as the Earth. In order to arrive at Mars that light has traveled at an angle with respect to the light arriving at Earth. No matter how small that angle is, that is a velocity component in the direction parallel to the line that connects the Earth and Mars.

I expect that the astronomical observation will line up with the time correlation achieved with the Einstein synchronization procedure, as a consequence of not being independent methods of time correlation.



The fundamental feature underlying this is the following: if all forms of physics taking place occurs in accordance with Lorentz invariance then one-way speed of light is inaccessible to observation.

It is about accessibility to observation. Comparison: Lorentz proposed a form of Aether theory where all forms of physics taking place occurs in accordance with Lorentz invariance. Then that Aether is inaccessible to observation.

In both cases it's the same inaccessibility to observation.




GPS time correlation

Independent of the above: I noticed that Derek says something very odd about the GPS system

Derek says:

This is the same reason GPS synchronized clocks won't work. The whole GPS system is based on the assumption that the speed of light is the same in all directions. If the speed of light is different in different directions,the light pulses from satellites will travel at different speeds so the clocks won't be properly synced.

As far as I can tell Derek is claiming here that the GPS system can't be used to find a one-way speed of light. My best guess is that Derek thinks that the GPS satellites are synchronized using the Einstein synchronization procedure.

However, that is not the case. For the correlation of the time keeping of the GPS satellites the Einstein synchronization procedure is not used.

The time keeping of the GPS satellites is correlated with the Earth global time keeping. Distributed over the Earth there are multiple centers for time keeping, and they maintain a correlated global Earth time, to a very high level of accuracy. This correlated global Earth time does not involve the Einstein synchronization procedure.

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  • $\begingroup$ This seems sort of tangential to the question I'm actually asking? I'm asking if it would be possible to detect a directional difference in the speed of light by observing directional differences in the ages of stars or galaxies a given distance away from us. $\endgroup$ – nick012000 Oct 31 '20 at 16:19
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    $\begingroup$ @nick012000 The current level of astronomical data (a very, very high level) indicates that the Universe is uniform in all directions. No directional difference. This has no bearing on Derek's point, if there is a directional difference in speed of light then that would not show up in the form of differential aging. The very point that Derek is making is that it wouldn't show up in any form whatshowever. Derek has a valid point, but the way he presents it is not transparent $\endgroup$ – Cleonis Oct 31 '20 at 16:29
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This isn't the answer you asked for but :

The question is not about if the synchronization procedure is untrue, it's not, but that it is a convention/postulate rather than fact observable directly. You cannot access the information about the one-way speed of light coming towards you, only the energy that it carries. Any other procedure you employ to figure out the speed of light will involve the two way speed of light, and it is by assertion that $c$ is isotropic.

For example it was believed that emission velocity of the source of light would impart some additional velocity to the light, this would lead to all sorts of weird observable effects in astronomy, like stars not following Kepler's laws, Doppler redshift when stars were receding away and blueshift when stars were approaching, multiple images, etc. Read this for more info

Basically, if one-way light speed was anisotropic,it would manifest experimental effects similar to that described earlier but we don't see such effects. That warrants an explanation. It is because if you say speed of light is anisotropic, you are essentially claiming that you have a way of comparing one-way speed of light information, which you don't. So yeah it might be possible that we are viewing the Universe in real time and that distant quasars actually exist at the edge of the universe.

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