The discussion centers on the relationship between Lorentz invariance and Einstein's clock synchronization convention within the framework of Special Relativity (SR). It establishes that the Lorentz transformation, which preserves the Minkowski metric, is essential for maintaining the invariant speed of light (c) across inertial frames. The conversation highlights that while conformal transformations can preserve angles, they do not maintain lengths, making them incompatible with the physical requirements of SR. Ultimately, the Einstein synchronization convention is affirmed as the only method that aligns with the Lorentz transformations, ensuring consistent time measurement across different inertial frames.
PREREQUISITESPhysicists, students of theoretical physics, and anyone interested in the foundations of Special Relativity and the implications of time synchronization in inertial frames.
I believe it simply shows that in the aforementioned condition Einstein's synchronization convention is consistent (i.e. 'simultaneous' according it defines actually an 'equivalence class').PeroK said:What does that achieve? That's hardly worth a paper.
Well, if Weyl proved that in 1923, then it's a waste of time now.cianfa72 said:I believe it simply shows that in the aforementioned condition Einstein's synchronization convention is consistent (i.e. 'simultaneous' according it defines actually an 'equivalence class of events').
In MINUL pag 10 they claim to remove an assumption (namely ##z=0##) Weyl employed to show that Einstein's synchronization convention is consistent. In section 4 they show that from ##2c \Rightarrow (z=0)##. Hence since from ##L/c## follows ##2c## then they give a proof of ##L/c \Rightarrow 1c## (note that the latter is actually a two folded statement).PeroK said:In any case, it's clear if you read the paper that they believe they have proved way more than that.