The discussion revolves around the constancy of the speed of light as derived from Maxwell's equations and its implications for gravitational waves. Participants explore whether the speed of gravity waves can be similarly derived from pre-Einstein equations and the necessity of postulating the constancy of light speed in the context of special relativity.
Participants do not reach a consensus on the necessity of postulating the constancy of light speed or the historical beliefs about Maxwell's equations. Multiple competing views remain regarding the derivation of gravitational wave speed and the interpretation of Einstein's statements.
There are unresolved questions regarding the historical context of beliefs about electromagnetism and the ether, as well as the implications of different interpretations of Einstein's postulates. The discussion reflects a range of perspectives on the derivation of physical laws and their applicability across reference frames.
Why didn't he say what "he meant"?PeterDonis said:he also meant that "the equations of mechanics" would have to be modified
I think the opposite direction would be nicer. Derive Minkowski spacetime from postulate 1 (the laws of physics are the same in all inertial frames) and postulate 2 (there exists an invariant speed) + assumed linearity. Then derive a theory of electromagnetism from assumed Coulomb’s law +SR.Meir Achuz said:Why is the second postulate needed today?
Source:paper said:ABSTRACT
Maxwell’s equations are obtained by generalizing the laws of electrostatics, which follow from Coulomb’s law and the principle of superposition, so that they are consistent with special relativity.
If "he" means "Einstein", he did. That's the entire point of his 1905 paper "On the Electrodynamics of Moving Bodies", which is where the phrase you quote appears: to show how "the equations of mechanics" must transform in order to be Lorentz invariant, and what the implications of this are.Meir Achuz said:Why didn't he say what "he meant"?
With the 1st postulate alone and the other symmetry assumptions you get Galilei-Newton spacetime or Einstein-Minkowski spacetime. To decide, which one is the correct (of rather the better) description of the spacetime structure you need empirical input. That empirical input at the time when Einstein wrote his paper were Maxwell's equations, summarizing all then known phenomena concerning electromagnetism including its application to optics, and from a purely kinematic point of view the one conclusion from the assumption that Maxwell's equations must look the same in any inertial reference frame is the "constancy of the speed of light", i.e., the independence of the phase velocity of electromagnetic waves in a vacuum of the velocity of the light source wrt. any inertial reference frame.Meir Achuz said:Why is the second postulate needed today?
But he did! In his 1905 paper he gave the modified equations of motion for point particles, though in a very deformed way from the modern point of view, introducing various kinds of "relativistic mass". This was clarified already in 1906 by Planck and finally by Minkowski in 1908, revealing the mathematical structure of Einstein's special-relativistic spacetime model.Meir Achuz said:Why didn't he say what "he meant"?