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Aether

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It isn't so much that it is unclear, it is that I am unwilling to risk absorbing this while the larger questions of Lorentz symmetry, tensor notation, etc. are still outstanding. When those issues are fully resolved, then I will be in a better position to absorb or reject some of these other notions in an informed way. Let's come back to these lesser issues later.JesseM said:I'm not talking about a selecting a simultaneity convention, I'm just asking about physical measurements on a physical system of rulers and clocks. How many times do I have to say "you are not obligated to use a coordinate system where the clocks are synchronized" before it sinks in? Again, analyzing a physical situation involving a physical system of rulers and clocks which have been "synchronized" using the physical procedure known as the Einstein synchronization convention does not magically force you to use a coordinate system with a simultaneity convention that says the clocks all read the same time at a given t-coordinate, any more than analyzing the behavior of the physical clocks in the twin paradox would magically force you to use a coordinate system where each twin's clock reads the same time at every t-coordinate (which would be impossible once they reunite anyway).

But I've been saying this over and over and you still don't seem to get it. Can you explain which part of the above is unclear?

This is such an important issue that I would like to fully understand it before proceeding with the rest of the discussion. Since Newton's laws are expressed using 3-vectors rather than 4-vectors, I don't see how they could be Lorentz covariant/invariant. Also, if Lorentz covariance/invariance is specifically tied to the Lorentz transforms then it may not be as fundamental of a physical concept as we have given it credit for above (e.g., what about the LET transforms?). I would question whether or not Poincare covariance/invariance isn't the more general physical symmetry; I'm not saying that this is so, but these are questions that I would need to know the answers to before leaving this subject.I'll look around for something like this, although as I said I'm not too knowledgeable about group theory or tensor mathematics. Doing a bit of quick googling, it seems the term "Lorentz covariance" is synonymous with Lorentz symmetry, and this page has a quote by Einstein where he defines Lorentz covariance in terms of the equations of physics being unchanged by a Lorentz transformation (which I hope you'd agree is equivalent to my statement that the laws of physics are measured to work the same in the different inertial systems of rulers and clocks described by Einstein in his 1905 paper, since the two postulates can be used to prove that the positions and times assigned by these systems must be related by the Lorentz transformation): And this page from the Springer Encyclopaedia of Mathematics says: So both these sources define the notion of Lorentz covariance/invariance simply in terms of the laws of physics being unchanged under a Lorentz transformation, which I would think means they are talking about the non-tensor form of the laws, since I had thought thatanyphysical law (including, say, Newton's laws) could be expressed in a "generally covariant" tensor form in which it would work the same way in all coordinate systems (for example, see the last section of this page), although I could be misunderstanding things here.