KJW

Special Relativity is embedded in Maxwell's equations. Maxwell's equations indicate that electromagnetic waves propagate at the speed of light, expressed in terms of the permittivity of free space and the permeability of free space. Maxwell's equations are invariant to Lorentz transformations, indicating that the speed of light is also invariant to Lorentz transformations. That is, the speed of light is the same for all inertial observers regardless of their velocity relative to some specified frame of reference. Thus, the notion of an absolute frame of reference is denied by Maxwell's equations. However, Special Relativity does go beyond Maxwell's equations and electromagnetism in general. Indeed, the speed of light in Special Relativity should not be regarded as specifically about light, but rather about the relationship between space and time. In principle, underwater creatures could determine the speed of light in a vacuum without measuring the speed of light in a vacuum by measuring the speed of light in both stationary and moving water, applying the relativistic velocity-addition formula. In this case, the speed of light in water is an "ordinary" speed, distinct from the c that appears in relativistic formulae.

Good day, Markus. Yes, it is me from The Science Forum. It seems that The Science Forum has finally died. It did seem like an inevitability for quite a long time. But I did stick with it till the very end. Anyway, I joined this site earlier today, posted some stuff. I notice you are still using the generalised Stokes theorem as your signature. 😉

You are correct. There is the question of "invariant to what?". For example, Special Relativity is invariant to Poincaré transformations, whereas General Relativity is invariant to all coordinate transformations, a much bigger group. But if the group of transformations for which the laws of physics are invariant is limited, and that the laws of physics are not invariant to transformations outside this group, then it becomes impossible to state what these varying laws of physics are because one doesn't have a reference against which one can state which laws of physics apply to which location in the space to which the transformations apply. But if the laws of physics are invariant, then they can be stated unequivocally due to that invariance. For example, if the laws of physics are expressed entirely in terms of partial derivatives, then they will vary according to the coordinate system. But the coordinate system is not actually known, so one can't know which laws of physics apply. But if the laws of physics are expressed entirely in terms of covariant derivatives, then they will be invariant to coordinate transformations, and therefore one no longer needs to know the coordinate system because the same laws of physics apply to all of them. I often see the question "What is time?". The answer I give is "Time is what a clock measures.". But what is a clock? A clock is defined by the instructions that are used to construct it. While this may not be particularly helpful in understanding the nature of time, time is nevertheless well defined by the instructions.

In what way are these different devices clocks? In what way are these measurements that disagree with the proper time of general relativity time measurements? I'm not discarding these devices as false, only your assertion that they measure time. It is my belief that it is the most fundamental principle of reality that the laws of physics are invariant. For without invariance, there are no laws of physics.