Question on Einstein original paper

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1. Dec 16, 2015

DrSirius

Hi, I am reading the Einstein original paper on Special Relativity, in this link (English translation), I am having difficulties on this sentence:

"We have now to show, that every ray of light moves in the moving system with a velocity c (when measured in the moving system), in case, as we have actually assumed, c is also the velocity in the stationary system ; for we have not as yet adduced any proof in support of the assumption that the principle of relativity is reconcilable with the principle of constant light-velocity."

Why does he need to show that c is constant also in the moving system if that is a principle? Is it necessary? Is it done for completeness or really he does need to show to complete the demonstration?

2. Dec 16, 2015

Staff: Mentor

Because, as he says at the end of the quote, he needs to prove that the principle of relativity--by which he means here basically the rules of how to transform quantities from the stationary system to the moving system--is consistent ("reconcilable") with the principle of $c$ being the same in all frames. Assuming the constancy of $c$ as a principle does not automatically guarantee that it is consistent with other principles that are assumed.

3. Dec 16, 2015

Staff: Mentor

[Moderator's note: adjusted thread title to be more descriptive of the actual topic.]

4. Dec 16, 2015

DrSirius

I see, so it is a kind of "sanity check". But then all kind of paradoxes happen and you would need to check them one by one, so, once he proves that the proposition ( c being constant ) is satisfied, he can be sure that the theory is self-consistent? Could that be proved by simply mapping the entire spacetime? I mean, when you get the Lorentz relationships, you see that for every point (x, y, z, t) there exists a set of coordinates (x', y', z', t') which describe that very same point. Wouldn't it be sufficient? For example, if you say that it is c/2 which is constant, and you maintain c as the fastest speed, used in the synchronization of clocks, you would surely arrive to a logical inconsistency when trying to establish the relationships of coordinates. If you don't arrive to any inconsistency, you are done with everything, including any apparent paradox. In fact, if a paradox arises, then you are surely discovering a new physical effect: for example, the transversal Doppler effect. It is predicted solely on Einsteinian relativity grounds, and does not exists in classical electrodynamics.

5. Dec 16, 2015

Staff: Mentor

I'm not sure what you mean here.

He didn't "prove that the proposition is satisfied"; he proved that assuming it to be true is consistent with the principle of relativity, by showing that if all light rays move at $c$ in one inertial frame, they also move at $c$ in any other inertial frame. That is sufficient to show that the two postulates are consistent with each other.

6. Dec 17, 2015

DrSirius

Yes, I see that and I think that I understand your point of view. However, if we go to the part of velocity composition, we could also check that "c + c = c" ( "+" is, in fact, the composition sign), but my point in this commentary is that it is not really necesary.

With the paragraph that I was discussing, I think that the same principle could be applied: namely, that because we have started by assuming that we can have a speed "c = constant", (indeed, a maximum speed - being this speed physically that of light, but this point is not so necesary to the theory from a theoretical-mathematical point of view), then we only need to assure that we obtain a transformation or mapping from (x,y,z,t) to new coordinates (x',y',z',t') and that we, indeed, don't need to check that c = constant, because the only fact of obtaining those coordinates, having started with the assumption of c = constant is just enough to assure that. (I am not sure if I am explaining right here).

7. Dec 17, 2015

Staff: Mentor

The assumption that c = constant in the moving system was not used to derive the transformation from the stationary system to the moving system; only the assumption that light moves at c in the stationary system was used. So you still need to check that light moves at c in the moving system. That's what Einstein is doing.