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I have read this question:

It follows that the two-way speed of light is invariant (in the context of relativity, "invariant" is understood to mean "invariant with respect to Lorentz transformations").

Meaning and validity of the mass-energy equivalence valid if we don't know the one-way speed of light?

The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity

https://en.wikipedia.org/wiki/One-way_speed_of_light

Now the first answer specifically states that SR postulates the two way speed, which can (and has been) experimentally proven. The second one says otherwise, and is saying that it (assumedly the one-way speed of light) is a postulate, that cannot be proven.

However, when I look at the papers of SR itself, either on wiki, or some original papers (I can only find very limited versions), the postulate itself does nowhere mention any specific one or two way versions of the speed of light. It just simply says the speed of light.

https://en.wikipedia.org/wiki/Special_relativity

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_relativity.pdf

Question:

  1. Does SR intend to postulate the one- or two-way speed of light?
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  • $\begingroup$ Does thermodynamics intend to postulate Fahrenheit or Celsius? $\endgroup$
    – WillO
    Commented Jan 14, 2022 at 23:02
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    $\begingroup$ @WillO I'd say that those are just two different temperature scales while whether SR regards the one-way or two-way constancy of speed of light changes the ontology of the theory, its derivations, and its range. If our theory only regards the one-way speed of light as a postulate then this will be present throughout its conclusions and interpretations of observables. However, anisotropic depictions similar to SR exist but with constant two-way speeds of light that allow for experimental indistinguishability. I wouldn't say 'that' theory would be the same as SR. $\endgroup$ Commented Jan 14, 2022 at 23:39
  • $\begingroup$ How would you define the two-way speed of light? $\endgroup$
    – DanielC
    Commented Jan 14, 2022 at 23:44
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    $\begingroup$ "However, when I look at the papers of SR itself, either on wiki, or some original papers (I can only find very limited versions), the postulate itself does nowhere mention any specific one or two way versions of the speed of light." As Dale points out, the establishment of Einstein synchronization between distant clocks (such as in Einstein's original paper) is what sneaks in the convention that the one-way speed of light is the same in all directions. $\endgroup$ Commented Jan 15, 2022 at 0:09
  • $\begingroup$ @Thevictorioustruther The speed of light is constant but it could be measured in kilometers or miles. $\endgroup$ Commented Jan 15, 2022 at 1:36

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The Einstein synchronization convention produces a one-way speed of light that is c. So the second postulate is based on the one way speed. This is justified by the isotropy of the two way speed of light and the isotropy of all known laws of physics.

In Einstein’s seminal paper he says “we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.” Where those two times are the one-way times and setting them equal makes the assumption that the one way speed equals the two way speed.

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  • $\begingroup$ Thank you so much! $\endgroup$ Commented Jan 15, 2022 at 4:09
  • $\begingroup$ @dale just out of interest...the slow transport method of clock synchronisation is practically equivalent to the Einstein method for very low v. If you adopted the Reichenbach method, with an extreme value (0 or 1) of the synchronisation parameter, would the slow clock method yield a different result? $\endgroup$ Commented Jan 15, 2022 at 8:06
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    $\begingroup$ @MarcoOcram if you are using Einstein synchronization then clocks remain synchronized after slow transport. If you are using any other synchronization then clocks are no longer synchronized after slow transport. $\endgroup$
    – Dale
    Commented Jan 15, 2022 at 12:40
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    $\begingroup$ @MarcoOcram no, it just means that under other synchronization conventions the expression for time dilation of a moving clock has a term that is first-order in v. There is no a priori reason to forbid such a time dilation law $\endgroup$
    – Dale
    Commented Jan 15, 2022 at 13:20
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    $\begingroup$ @dale many thanks! $\endgroup$ Commented Jan 15, 2022 at 13:22
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There is no experiment which can measure the one-way speeds of light. Standard SR adopts the Einstein clock synchronisation procedure, which tacitly assumes that the one-way speeds of light are equal to the two-way speed (i.e., the round-trip speed).

Professor John D. Norton has an excellent website that discusses this topic. Norton is considered an authority on the science of Albert Einstein and the philosophy of science.   As Norton explains, Hans Reichenbach established that you're free to choose another synchronisation convention. For details (including diagrams), please see the Reichenbach's $\epsilon$ section of Norton's site.

In Reichenbach's notation, the standard Einstein synchronisation uses a parameter of $\epsilon=\frac12$, but any values of $\epsilon$ between $0$ and $1$ give valid synchronisation schemes. If you choose any $\epsilon \ne \frac12$ the one-way speed of light in one direction isn't equal to the one-way speed of light in the reverse direction. Nothing is physically different under such a scheme with $\epsilon \ne \frac12$, but the mathematics of the Lorentz transformation becomes messier.

Here's a brief excerpt from Norton's site.

With $\epsilon=\frac12$, light takes 2 units of time to go forward from A to B and 2 units to return from B to A. With the non-standard $\epsilon=\frac14$, things are quite different. Light takes one unit of time to go from A to B. [...] But the light takes three times as long to return from B to A

So while you can do SR using $\epsilon \ne \frac12$, it would not be practical. It's far more sensible to choose $\epsilon = \frac12$, and use the Einstein procedure to synchronise your clocks.


There's no point in asking what's the true value of $\epsilon$. There is no true value. In some ways, it's like asking what's the true velocity of the Earth. Velocity is always relative, a velocity only has meaning relative to some reference frame, and you're free to choose whatever reference frame happens to be convenient. In cosmology, it's often useful to choose the comoving frame of the CMBR (i.e., the frame where the CMBR is isotropic), but that doesn't imply that the CMBR frame is the absolute frame of the cosmos.

Similarly, the $\epsilon = \frac12$ convention is a useful convention, but it doesn't prove anything about the one-way speeds of light.

The one-way speeds cannot be measured independently of a choice of $\epsilon$. So in a sense, those speeds have no physical existence, they're just a mathematical artifact of the $\epsilon$ associated with your synchronisation convention. In contrast, we can measure the round-trip speed of light, and show that it's invariant, and that's the real basis of special relativity.

We can talk about absolute velocities, and one-way speeds of light, but they don't actually correspond to things that are physically observable.

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  • $\begingroup$ Thank you so much! $\endgroup$ Commented Jan 15, 2022 at 4:09
  • $\begingroup$ I posted a question some time ago, asking why stellar aberration is not considered a one-way speed of light measurement. It has no answers so far. I would appreciate if you could answer that one as well: physics.stackexchange.com/q/651542/101743 $\endgroup$
    – fishinear
    Commented Jan 15, 2022 at 11:48
  • $\begingroup$ @fishinear If you choose $\epsilon=\frac12$ then every measurement of light speed (in a vacuum) must be $c$, and that includes measurements derived from stellar aberration. With $\epsilon\ne \frac12$, the planes of simultaneity are tilted (compared to those of the standard $\epsilon=\frac12$ convention), so you get length contraction effects, as shown in the diagrams on John D. Norton's page which I linked in my answer. FWIW, Norton has further info on aberration here. $\endgroup$
    – PM 2Ring
    Commented Jan 15, 2022 at 15:22
  • $\begingroup$ @PM2Ring Norton gives an excellent explanation of stellar aberration, but does not explain why stellar aberration cannot be considered a one-way speed of light measurement. Can you elaborate why the reasoning in my question is not valid? $\endgroup$
    – fishinear
    Commented Jan 15, 2022 at 15:37
  • $\begingroup$ @fishinear It comes down to the same reasoning that Lorentz used to show that the aberration angle is the same whether you consider the Earth to be at rest in the ether and the star moving, or vice versa. You have to choose some $\epsilon$ in order to assign spacetime coordinates to events, and if you choose $\epsilon=\frac12$ then the result that the one-way speeds must equal $c$ is already "baked" into your system. $\endgroup$
    – PM 2Ring
    Commented Jan 15, 2022 at 16:04

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