Is the concept of a one-way speed of light meaningful and measurable?

[Freixas]

We can measure the two-way speed of light, but not, apparently, the one-way speed. Light could travel at c in every direction or c/2 in one direction and instantaneously in the other. Nature does not provide us with a way of determining the one-way speed.

I can follow some of the basic reasoning as to why trying to measure the one-way speed of light requires knowing the one-way speed of light. But let's say I have an observer in a spaceship that we consider to be at rest. There is another ship circling this one at a constant distance of 299,792,458 meters (1 light second). By definition, we begin with the two ship's clocks synchronized with respect to the rest observer. It's not important that we do this—it just makes the numbers in my example easier to state.

We will also assume that the speed of light is 2c in one direction and instantaneously in the other. Let's say that when the experiment begins, the orientation of the two ships is such that the light from the moving ship is traveling toward the rest observer in the direction where it travels at c/2 and where the clocks read 0. The light reaches the rest observer at rest time 2 seconds.

The moving ship moves slowly around the circle. At some point, it is located where the light will reach the rest observer instantaneously. At this point, the rest observer notes that the traveling ship's time equals the rest time.

Because the moving ship is moving relative to the rest observer, we could expect some slowing of the moving clock from the rest observer's view. I'm suggesting that the ship move slowly enough that this slowing is minimal. It would seem that the rest observer would see a trend of the observed clock slowing down and speeding up. If the speed were c in every direction, the rest observer would always see the moving clock lag his own by 1 second (plus a small, but slowly increasing delay from the motion).

I'm sure I'm making a big mistake and that the experts here will clear it up. Thanks!

Originally, this started out from thinking about viewing the night sky. If the one-way speed of light were slower one way than the other, then one direction would show a younger universe than the other, and I started wondering if this would be detectable.

 

[PeterDonis]

I can follow some of the basic reasoning as to why trying to measure the one-way speed of light requires knowing the one-way speed of light.

That's not the basic reasoning. The basic reasoning is that trying to measure the one-way speed of light requires adopting a simultaneity convention, which means that what you end up "measuring" is not telling you anything about physics, it's just telling you about the simultaneity convention you adopted.

 

[PAllen]

Applying what @PeterDonis said to the given case is interesting to elaborate. The first question to answer is whether defining a closed curve by constant round trip times for light is taken to be a circle. Answering yes is equivalent to adopting Einstein synchronization. Further, the assumption of constant time dilation ratio between the rocket and the center is also an assumption of isotropy. With an anisotropic simultaneity convention that is consistent with observation, the rocket path would not be a circle, and the time dilation of the rocket compared to the center would not be constant. These effects ”conspire” to ensure that the observed clock rate of the rocket by the center is constant.

 

[Ibix]

Here's an attempt to explain the one way speed of light issue with spacetime diagrams. First, here's a spacetime diagram showing five clocks at mutual rest (red worldlines). The left hand clock emits a pulse of light which reaches the right hand one and is sent back (yellow worldlines). The clocks are Einstein synchronised and the events where they tick $t=0,\ 1,\ 2$ are shown. Additionally, I have marked in blue the periods during the out-bound and in-bound legs of the light's travel.

So far so good, I hope.

Now, I've drawn the exact same situation again - the same five clocks and the out-and-back light pulse. The only difference is that I've synchronised the clocks differently. The clocks lag a bit with respect to their Einstein synchronisation, and the lag grows as you move to the right.

This small change has a large effect on the definition of "during" the out- and in-bound legs - you can see at once that the two parts of the blue line are different lengths. But the distance the light travels is the same in each direction, so we conclude that the one-way speeds are different. So the one-way speed of light is an artifact of your choice of clock synchronisation.

Note: although the lines of simultaneity are slanted in the second diagram, rather like a boosted coordinate system, I've kept the same time direction - parallel to the red lines. So there exists a regular Einstein frame that will use this anisotropic frame's notion of simultaneity, but it will not share the notion of stationary. I've tried to illustrate the difference in the axes below.

The key point here is that whatever scenario you dream up, the one-way speed of light depends only on your clock synchronisation convention. So you can always simply draw a Minkowski diagram of your scenario (the one in the OP has a helical worldline and a vertical one, I think, exchanging light pulses) and tilt the plane of simultaneity. Doing so should immediately let you see where you go wrong. In this case, the moving ship's onboard clock will drift with respect to local anisotropic-synchronised clocks at a non-uniform rate, just the correct clock drift to counteract the expected variation in pulse arrival time. And it must always work out like that (no matter how many bells and whistles you add to the scenario) because there is no change of physics between an isotropic and an anisotropic frame - the only difference is the choice of slant on our simultaneity planes.

 

[Freixas]

Thank you so much for your detailed response.

So you can always simply draw a Minkowski diagram of your scenario (the one in the OP has a helical worldline and a vertical one, I think, exchanging light pulses) and tilt the plane of simultaneity. Doing so should immediately let you see where you go wrong.

If I were you, I would, indeed, immediately see where I've gone wrong. Not being you, it won't be so immediate. :-) Please bear with me.

I didn't want to try to draw a a three-dimensional Minkowski diagram, so I simplified the problem to a 2 dimensional one. This has the advantages that there are some cases where the moving and rest ships are co-located.

At time 0, both ships are at the same location. The moving ships is just accelerating and decelerating at 1g. I divided the moving ship's clock time into 10 segments. I then assumed that light moves instantaneously in one direction and 1/2c in the other and drew the worldline of light from the moving ship to the rest ship.

Obviously, I get nonsense. When I get nonsense, I go back and try again. This time, I created the diagram with the one-way speed equal to the two-way speed, as I normally would.

Then I skewed the image in an image-processing program:

Now I have the speed of light as instantaneous in one direction and 1/2c in the other. The observations are the same as the "normal" case, so would it be correct to say that the usual Minkowski diagram itself has a "Einstein synchronicity" assumption?

So you can always simply draw a Minkowski diagram of your scenario (the one in the OP has a helical worldline and a vertical one, I think, exchanging light pulses) and tilt the plane of simultaneity.

I think that's what I did above. I didn't understand what you meant because in a 2D Minkowski diagram I can tilt a line of simultaneity any way I want without affecting the diagram. I think you meant tilt the line of simultaneity for the rest frame--I wound up there eventually.

To go back to the night sky idea, if we received a message from some distant galaxy from a direction from which we somehow knew light traveled instantaneously, based on the comments in this thread there would be no way to establish this by any experiment. As it is untestable, it then becomes a meaningless, even as a thought experiment.

Einstein's 1905 S.R. paper is said to have two postulates, but it appears to me to have three. I assume the reason it is said to have two is because Einstein synchronicity is not essential, just convenient.

 

[Ibix]

I created the diagram with the one-way speed equal to the two-way speed, as I normally would
...
Then I skewed the image in an image-processing program:

Yes, I think this is the correct way to go about it. You may notice that I didn't even bother skewing my diagram - I just used skewed axes. Since the anisotropic system's axes are non-orthogonal I think it's better to represent them with non-orthogonal axes in the diagram, but there's nothing wrong with what you did.

would it be correct to say that the usual Minkowski diagram itself has a "Einstein synchronicity" assumption?

Einstein synchronisation is equivalent to picking orthogonal space and time axes. So if you use those axes (which we usually do on a Minkowski diagram) then you are implicitly using Einstein simultaneity to define your coordinate grid, yes. Once you skew the diagram your non-orthogonal axes in spacetime map on to orthogonal directions on the diagram and you are drawing your non-orthogonal coordinate grid as your grid squares.

I didn't understand what you meant because in a 2D Minkowski diagram I can tilt a line of simultaneity any way I want without affecting the diagram. I think you meant tilt the line of simultaneity for the rest frame--I wound up there eventually.

In a (2+1)d Minkowski diagram surfaces of simultaneity are planes. You pick one direction that you want to be the principal axis of lightspeed anisotropy and tip the planes upwards in that direction.

To go back to the night sky idea, if we received a message from some distant galaxy from a direction from which we somehow knew light traveled instantaneously, based on the comments in this thread there would be no way to establish this by any experiment. As it is untestable, it then becomes a meaningless, even as a thought experiment.

Yes. Say I look at a galaxy 5 Mly away and see a little green man waving at me and I wave back. Normally you would say he was waving five million years ago and will see me wave back in five million years. You can say he's waving now if you want, but then you also have to say he won't see me wave back for ten million years. Either way it makes no difference to what I do and he's waiting ten million years for an answering wave.

Einstein's 1905 S.R. paper is said to have two postulates, but it appears to me to have three. I assume the reason it is said to have two is because Einstein synchronicity is not essential, just convenient.

There are four postulates, really, the two numbered ones plus unstated assumptions that spacetime is homogeneous and isotropic. On top of that he does explicitly state his synchronisation convention, which is not necessary for SR (you can certainly do SR in non-orthogonal coordinates) but probably is necessary to do SR with the mathematical tools Einstein had in 1905.

 

[Freixas]

Yes, I think this is the correct way to go about it. ... etc. ...

Thank you!

Yes. Say I look at a galaxy 5 Mly away and see a little green man waving at me and I wave back. Normally you would say he was waving five million years ago and will see me wave back in five million years. You can say he's waving now if you want, but then you also have to say he won't see me wave back for ten million years. Either way it makes no difference to what I do and he's waiting ten million years for an answering wave.

I was actually wondering if there might be some way to tell if the view in one direction was somehow younger from the view in the other.

I'll make up a silly example to illustrate my idea: Say that we develop almost impossibly sensitive receivers that pick up transmissions clearly coming from a billion light years away. It's TV from that little green man (and friends), with educational channels showing exactly how they've determined the age of the universe (with enough info to convert their units to ours). Employing the same methods, we find out that we get the same age as they do, even though we would normally expect their number to be 1 billion less than ours.

Another example would be directly detecting a particle that could only exist seconds after the Big Bang, but only when looking in one direction.

 

[PeterDonis]

I was actually wondering if there might be some way to tell if the view in one direction was somehow younger from the view in the other.

What does "younger" mean?

It means you've chosen some simultaneity convention that defines which events on the worldlines of the objects that are on opposite sides of the sky happened "at the same time". Only with such a convention does it make any sense to ask which object was "younger" when the light from it that you are seeing now was emitted. So "younger" is not telling you anything about physics; it's telling you about the simultaneity convention you adopted.

 

[Freixas]

What does "younger" mean?

In the sense I used, I was thinking that the universe has an age and that that age might be discernible.

Assume that a cohort of people were born at the same time, all at my location (just to avoid questions of simultaneity). At a young age, they all move away, traveling at the same rate and for the same amount of time, but each in a different direction. They don't go very far away or travel for very long. They settle into the spot they reach. Years later, I train telescopes on them. If in one direction, I saw people not much older than when they left, and in the other, much older, I would know something fishy was going on.

After thinking about my original question and looking at the skewed Minkowski diagram again, I suspect that the events I described wouldn't be possible. Even if the the aliens reporting on the age of the universe shared an inertial frame with us, if the skew were there so that light traveled instantaneously to us, they would report the age of the universe as 1 billion years less than we would, exactly as they would if we assumed no skew and that the TV signals took a billion years to arrive.

Seeing something that exists only seconds after the Big Bang is just another variation of the above.

Back to the cohort: that one is definitely odd, but if we assume no trickery involved in the description, it's odd because I don't believe it can physically happen.

 

[PeterDonis]

In the sense I used, I was thinking that the universe has an age and that that age might be discernible.

The universe does have an age, and it is discernible. That has nothing to do with the concept of "younger" you appeared to be using.

At a young age, they all move away, traveling at the same rate and for the same amount of time

What do "at the same rate" and "for the same amount of time" mean?

The latter can be given an invariant meaning--the same amount of time elapses on each person's clock--but the former cannot. "Speed" has no invariant meaning: it's frame dependent. And in a curved spacetime, you can't even use "speed relative to some particular object", which is invariant in flat spacetime, because in curved spacetime there is no such invariant concept (except within a small local patch of spacetime in which the curvature can be ignored). So you still don't have an invariant scenario here.

They don't go very far away or travel for very long.

Again, "not very long" can be given an invariant meaning (use the elapsed time on each person's clock), but "not very far away" cannot, since distance is frame dependent.

Years later, I train telescopes on them. If in one direction, I saw people not much older than when they left, and in the other, much older, I would know something fishy was going on.

In such a hypothetical scenario, you would not be finding out anything "fishy" about the one-way speed of light. You would be finding out something "fishy" about the curvature of spacetime in between you and the people you are looking at through the telescope.

If you assume spacetime is flat, you can prove that no such "fishiness" is possible, without assuming anything about the one-way speed of light, just based on invariants.

If you don't assume flat spacetime, it's still easy to see that whatever "fishiness" you observe can't be due to "fishiness" in the one-way speed of light: just watch the people continuously through the telescope and have them emit pulses of light, say, every second by their clocks. You will see a time-varying shift in the intervals by your clock at which the pulses arrive. Any "fishiness" in the apparent ages of the people will be exactly matched by corresponding "fishiness" in the shifts you see, and will tell you that there is something "fishy" about the spacetime geometry in whatever region the people are passing through. Everything is invariant and there is no one-way speed of light anywhere.

Even if the the aliens reporting on the age of the universe shared an inertial frame with us

What does "share an inertial frame" mean?

Seeing something that exists only seconds after the Big Bang

Exists only seconds after the Big Bang at what location?

 

[Dale]

Because the moving ship is moving relative to the rest observer, we could expect some slowing of the moving clock from the rest observer's view. I'm suggesting that the ship move slowly enough that this slowing is minimal.

This is actually not possible. If the one way speed of light (OWSOL) is anisotropic, so is the time dilation. And what is more, the accumulated time dilation does not go to zero at any speed, no matter how slow, depending on the direction. So as the moving ship gets to the "instantaneous" direction the stationary ship will instantaneously receive their highly time dilated signal, and as they get to the "slow light" direction the ship will receive their anti-dilated signal slowly.

Using Anderson's convention the metric in anisotropic coordinates is: $$d\tau^2 = dt^2 + 2 \kappa \ dt \ dx - (1-\kappa^2) dx^2 - dy^2 - dz^2$$ so we can easily calculate the time dilation in these coordinates by $$ \left(\frac{d\tau}{dt}\right)^2 = 1 +2 \kappa \frac{dx}{dt} + \kappa^2 \left(\frac{dx}{dt}\right)^2- \left(\frac{dx}{dt}\right)^2- \left(\frac{dy}{dt}\right)^2- \left(\frac{dz}{dt}\right)^2$$ $$\frac{1}{\gamma} = \sqrt{ 1+2 \kappa \ v_x + \kappa ^2 \ v_x^2 - v^2 } $$

Note in particular that the $2 \kappa \ v_x$ term is first order, so it doesn't go away at low speeds like the second order terms do. Also, note that it can be positive or negative, so unlike normal time dilation it can make the moving clock go faster than the stationary clock. At low speeds, this term dominates over the second order terms, and it exactly compensates for the changing in the OWSOL so that the clock at rest gets a steady stream of signals.

 

[Freixas]

This is actually not possible. If the one way speed of light (OWSOL) is anisotropic, so is the time dilation. And what is more, the time dilation does not go to zero depending on the direction. So as the moving ship gets to the "instantaneous" direction the stationary ship will instantaneously receive their highly time dilated signal, and as they get to the "slow light" direction the ship will receive their anti-dilated signal slowly.

Using Anderson's convention the metric in anisotropic coordinates is: $$d\tau^2 = dt^2 + 2 \kappa \ dt \ dx - (1-\kappa^2) dx^2 - dy^2 - dz^2$$ so we can easily calculate the time dilation in these coordinates by $$ \left(\frac{d\tau}{dt}\right)^2 = 1 +2 \kappa \frac{dx}{dt} + \kappa^2 \left(\frac{dx}{dt}\right)^2- \left(\frac{dx}{dt}\right)^2- \left(\frac{dy}{dt}\right)^2- \left(\frac{dz}{dt}\right)^2$$ $$\frac{1}{\gamma} = \sqrt{ 1+2 \kappa \ v_x + \kappa ^2 \ v_x^2 - v^2 } $$

Note in particular that the $2 \kappa \ v_x$ term is first order, so it doesn't go away at low speeds like the second order terms do. Also, note that it can be positive or negative, so unlike normal time dilation it can make the moving clock go faster than the stationary clock. At low speeds, this term dominates over the second order terms, and it exactly compensates for the changing in the OWSOL so that the clock at rest gets a steady stream of signals.

Thanks, Dale,

The example I posted was from before @Ibix's response, so, yes, I agree (even without the equations) that whatever invariants come out of my example are independent of the choice of simultaneity convention.

 

[Mister T]

By definition, we begin with the two ship's clocks synchronized with respect to the rest observer. It's not important that we do this—it just makes the numbers in my example easier to state.

Well, whether we synchronize them or not we need to be able to know, at the location of one of the clocks, what the reading is on the other clock. As soon as we do that we have adopted a simultaneity convention that depends on the very thing we are trying to measure.

 

[Freixas]

That's not the basic reasoning. The basic reasoning is that trying to measure the one-way speed of light requires adopting a simultaneity convention, which means that what you end up "measuring" is not telling you anything about physics, it's just telling you about the simultaneity convention you adopted.

Duly noted.

I first learned about the one-way speed of light from a YouTube video with the click-bait title "Why No One Has Measured The Speed Of Light". The author of the video is Dr. Derek Muller, who is said to have "completed a degree in Engineering Physics from Queen's University in Canada, and a PhD in physics education research at the University of Sydney."

The video begins with the problems of attempting to measure the one-way speed of light and why the attempts fail. What it doesn't tell you is that a one-way speed of light measurement is just a choice of an arbitrary simultaneity convention.

Starting at about 11:45, the video starts talking about the one-way speed of light as thought there is a true one-way speed that we simply can't ever find out. In fact, Muller suggests that Einstein's synchronization convention could be an "error". At around 14:20, he builds on this with the idea that when we look at Mars, we could be looking at it "right now, in real time."

He should have asked the fine folks at PhysicsForum to review his video.

The one-way speed of light page on Wikipedia correctly summarizes the issue: "The 'one-way' speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector."

However, it then goes on to cite a list of experiments that attempted to measure the one-way speed. If physicists all understand that it's just a choice of a convention, why are they trying? Here is the last citation:

Will, Clifford M. (1992). "Clock synchronization and isotropy of the one-way speed of light". Physical Review D. 45 (2): 403–411. Bibcode:1992PhRvD..45..403W. doi:10.1103/PhysRevD.45.403. PMID 10014389

Physics Review D claims to be "a leading journal in elementary particle physics, field theory, gravitation, and cosmology and is one of the top-cited journals in high-energy physics." You'd think, if what I'm hearing here is correct, this would be thrown out immediately. According to Wikipedia, the article was refuted five years later.

This isn't something new, is it? It appears that Einstein fully understood that he was just choosing a convenient convention.

Anyway, some of this might explain where I was coming from when I started this post. I stand corrected!

 

[Dale]

This isn't something new, is it?

No, it isn’t new. I believe that Reichenbach first published this stuff in the 1920’s. However, my preferred reference is Anderson from 1998: https://www.sciencedirect.com/science/article/abs/pii/S0370157397000513

Peer review isn’t a panacea. It improves quality of papers, but it remains imperfect. So expecting perfection from a peer reviewed journal is unrealistic.

Will, Clifford M. (1992). "Clock synchronization and isotropy of the one-way speed of light". Physical Review D.

This paper seems to support the points made here. Did you intend it as a counter example?

 

[Freixas]

This paper seems to support the points made here. Did you intend it as a counter example?

Here's what the Wikipedia page says. I've left their citation links in place.

This experiment, carried out in 1990 by the NASA Jet Propulsion Laboratory, measured the time of flight of light signals through a fibre optic link between two hydrogen maser clocks.[31] In 1992 the experimental results were analysed by Clifford Will who concluded that the experiment did actually measure the one-way speed of light.[11]​

​

In 1997 the experiment was re-analysed by Zhang who showed that, in fact, only the two-way speed had been measured.[32]​

If Wikipedia's analysis of Will's and Zhang's papers is correct, Will has it wrong.

 

[Dale]

Well, the abstract says "It is shown that, when properly expressed in terms of measurable quantities, the results of such experiments are independent of the method of global synchronization of clocks." Which is the key point with the OWSOL. I cannot access the article itself, but the abstract seems to be making the correct point that the experimental results are independent of the OWSOL.

 

[PeterDonis]

Here's what the Wikipedia page says.

Wikipedia is not a good source to be relying on for things like this. I would certainly want to read the actual paper by Will before even considering the possibility that Will made the kind of error Wikipedia is attributing to him.

 

[Dale]

In any case, this stuff is not new, and regardless of the actual content of Will's paper it is possible for such things to make it through peer review. Although it is not new, this topic is rather obscure. The non-standard synchronization conventions have no value outside of internet discussions as far as I can tell. It simply isn't something that the scientific community spends any time on, so it is easily possible that two random reviewers at a reputable journal may never have studied this.

 

[hutchphd]

Starting at about 11:45, the video starts talking about the one-way speed of light as thought there is a true one-way speed that we simply can't ever find out. In fact, Muller suggests that Einstein's synchronization convention could be an "error". At around 14:20, he builds on this with the idea that when we look at Mars, we could be looking at it "right now, in real time."

He should have asked the fine folks at PhysicsForum to review his video.

I don't know what you think you have discovered here, but inuendo is never an appropriate tool. I am not expert in Relativity but I can find nothing incorrect in Dr. Muller's efforts on that video Also your characterization of what he says is factually deficient. Your personal opinion is not relevant. If there is an error please point it out.

 

[Freixas]

Wikipedia is not a good source to be relying on for things like this. I would certainly want to read the actual paper by Will before even considering the possibility that Will made the kind of error Wikipedia is attributing to him.

Plus Zhang's critique. The latter appears to be accessible, but you have to create a free account on some site.

 

[PeterDonis]

Plus Zhang's critique.

I don't trust Wikipedia's description of that any more than I trust Wikipedia's description of Will's paper.

 

[Freixas]

Also your characterization of what he says is factually deficient. Your personal opinion is not relevant. If there is an error please point it out.

At 7:42, talking about Einstein's choice for synchronizing clocks, he says: "That sounds a lot more subjective than how I think most people would imagine the speed of light is defined." This makes it sound like Einstein's choice was a whim, rather than that Einstein recognized that the choice was arbitrary.

At 11:33 he says: "Now this may sound like just an academic concern, so I want to go through an example to show just how differently the universe works if the speed of light is not the same in all directions." What I've gotten from this thread is that the universe would work exactly the same--all invariants would be the same--if the one-way speed of light were the same in all directions or different. He then shows examples of the "differences". These examples have the same invariants (what people observe) and differ only in their simultaneity convention.

At 12:49, he says "But Mark [on Mars] doesn't know this..even though on Earth it is now 12:20." The implication is that Mark has the "wrong" time. I believe all that is happening is that the narrator is using a different simultaneity convention than Mark. Mark's time is neither right nor wrong--he is trying to "synchronize" with Earth and so has to choose a synchronization strategy. For Mark, the time on Earth with respect to his choice of simultaneity is correct.

At 14:30 he says: "Mark would be seeing the Earth as it was 20 minutes ago, but Earth is seeing Mars in real time, exactly as it is right now." Again, what Mark actually sees of Earth and what someone on Earth would see of Mars doesn't change because of any choice for the one-way speed of light. Labeling Mark's view as 20 minutes old (instead of 10 or some other number) is just a choice of conventions.

Check out @PeterDonis' response #2 above. The key problem with Muller's video is that it is about the one-way speed of light yet never mentions Peter's point.

 

[PeterDonis]

At 11:33 he says: "Now this may sound like just an academic concern, so I want to go through an example to show just how differently the universe works if the speed of light is not the same in all directions."

It looks to me like the key error being made in this video is equating "isotropy of space", which is an invariant property of spacetime geometry, with "the one way speed of light is the same in all directions", which is dependent on a choice of simultaneity convention. Of course this also means that you can't test for isotropy of space just by testing for the one way speed of light being the same in all directions. Measurements involving light might be relevant to a test for isotropy of space, but not in that simple a way.

What I've gotten from this thread is that the universe would work exactly the same--all invariants would be the same--if the one-way speed of light were the same in all directions or different.

No, that's not quite the point you should be taking away from this thread. The point you should be taking away from this thread is that "the one way speed of light being the same in all directions, or different" is not a meaningful difference at all. The one way speed of light can change from being the same in all directions to not being that way purely by you changing your choice of simultaneity convention. That's not a physical change at all. It's a change in a human convention. It doesn't even make any sense to ask whether "the universe would work exactly the same" in the two cases; that's like asking whether math "would work exactly the same" if we used Roman numerals instead of Arabic numerals. In a sense, of course, the answer is yes, but the question itself is not really well posed.

 

[Orodruin]

Put slightly differently and a bit more generally, the important takeaway is that the OWSOL is a coordinate speed. By picking obscure enough coordinates, coordinate speeds can be anything, they are not invariant.

 

[Freixas]

No, that's not quite the point you should be taking away from this thread. The point you should be taking away from this thread is that "the one way speed of light being the same in all directions, or different" is not a meaningful difference at all. The one way speed of light can change from being the same in all directions to not being that way purely by you changing your choice of simultaneity convention. That's not a physical change at all. It's a change in a human convention. It doesn't even make any sense to ask whether "the universe would work exactly the same" in the two cases; that's like asking whether math "would work exactly the same" if we used Roman numerals instead of Arabic numerals. In a sense, of course, the answer is yes, but the question itself is not really well posed

Sorry, thanks for correcting me. Yes, I have been thinking about it that way, but when I wrote the above, I had just been reviewing the video. It is difficult to shake the idea that there isn't a "real" one-way speed and I started using Muller's language.