@3ammo So here is why its a convention and not a postulate… simply speaking if you pick some other convention that ensures the round-trip is unchanged but it is asymmetrical, all the math we do will give the same final results. Thus its a convention because it doesnt really matter since everything is eventually a round-trip anyway, so we just pick the easiest way to get the answer.

As an example imagine a world at the most extreme asymmetry where light travels at c/2 in one direction and instantaneous in the other. If you use this convention and then apply the new form of lorentz transformations to any thought experiment that could be carried out as a literal experiment, you get the same result as you would get if c was symetrical. What happens is the error is just enough that it cancels out and produces the same results.

Consider communicating with a distant astronaut and how we perform the very simple lorentz transformation there to synchronize time. Lets assume we know the real time (I will abbreviate it RT) and lets assume there is a meassured time, ill call this MT.. here is how it works out assuming C is symetrical.

  1. Astronaut flys 1 light hour away, experiment starts, RT 0:00

  2. Earth sends light signal to astronaut saying “The time here is 0:00” (RT)

  3. Astronaut receives message claiming time is 0:00, he knows he is one light hour away so he now sets his clock to 1:00 (MT), he then replies “message received, I have now set my clock to 1:00” and sends this back home.

  4. Home base gets the message saying the astronauts MT is 1:00, knows again it is one light hour away so concludes after lorentz transformation that the MT is now 2:00. Looks up at his clock, the RT, and sees it says 2:00. Concludes the astronaut clock and home clock are set to the same time.

But now lets look at the same scenario where the speed of light is c/2 in one direction and instantanious in the other, but the scientist dont know this so use the convention that c is symmetric. Being just a convention it should all work out (if it were a postulate then it would be meaningful and thus effect results and things would break here).

  1. Astronaut flys 1 light hour away, experiment starts RT 0:00

  2. Earth sends light signal “The time here is 0:00” (RT)

  3. Astronaut receives signal, assumes c is symetric, therefore performs the same lorentz transformation as before and determines that the time must be 1:00 (MT), in reality because c/2 the RT is 2:00, so the astronauts clock is technically off by an hour. Astronaut replies “I have now set my clock to 1:00”.

  4. Home base again gets the message of the astronaut claiming the time being 1:00, home base again assumes time is symmetric so gets the same result he did in the earlier experiment assuming that the astronauts clock must be 2:00 by the time they hear the return message (which took an hour to get to them).. sure enough they look up at the wall and it matches RT of 2:00… but in reality the signal was not symmetric and the return time for the light signal was instantaneous instead. That means by the time homebase heard “my clock is set to 1:00” and they assumed it was RT 2:00 by the time they heard it this was wrong, the reply was instantaneous and in reality the astronauts clock was 1:00 by the time they got their response and their transformation was wrong, and the clock is still slow by 1 hour. However it appears to them everything is correct, the full round trip time was still c, they got all the same answers at all the same times they would have if it was symmetrical. So even though it is technically wrong, the results work just as well

In fact you can pick any arbitrary asymetrical convention you want, so long as the round-trip results in a average speed of c, and you will get the exact same results and both sides of the communication would be unable to tell any difference at all.

This is why its a convention, you can pick any asymmetry you want and none of the results will ever change, therefore a convention is picked arbitrarily to be easy. No one needs to say “this is how it is” because nothing changes whether it is that way or not

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@3ammo By the way even einstein said that the idea that C is symmetric in both directions is by definition (convention) and not as a postulate. Here is his own words on the matter in one of his published papers.

First he says:

“But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B.”

In this sentence he points out that we can not experimentally or otherwise theoretically conclude anything about these individual times without making an assumption, which implies it is arbitrary. He goes on to say (he put by definition in italics not me):

“We have not defined a common ‘time’ for A and B, for the latter cannot be defined at all unless we establish by definition that the ‘time’ required by light to travel from A to B equals the ‘time’ it requires from B to A”

In other words the symmetry of light is by definition, and not an assertion as to what is, namely, a convention.. he never says “we assume light to be”.. he says “establish by definition”, which is exactly what a convention is.

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