Is 2nd postulate of SR necessary?

[Phrak]

To those who have been arguing the point, I fail to see how the exclusion of postulate 2, specifying a finite invariant velocity, would obtain anything but Galilean relativity.

 

[Fredrik]

In fact, that isn't technically quite good enough, because it makes no distinction between orthogonal and skew coordinates, so a bit more is needed to resolve that ambiguity.

The funny thing is that what we need to resolve that ambiguity is something like..."a coordinate transformation from one inertial frame to another maps the light cone at the origin onto itself", but that's a statement that sounds a lot like the second postulate. It just isn't possible to define "inertial frame" in a way that's appropriate for SR without including (some version of) both of the postulates in the definition.

Good post by the way. You noticed a couple of things that I hadn't.

 

[Fredrik]

To those who have been arguing the point, I fail to see how the exclusion of postulate 2, specifying a finite invariant velocity, would obtain anything but Galilean relativity.

The first postulate mentions the equations of electrodynamics explicitly, and Maxwell's equations predict that the speed of an electromagnetic wave is c in all inertial frames. So if we completely ignore that the first postulate actually fails to define what an inertial frame is (which actually seems to be what everyone is doing), then the second is implied by the first.

If we choose to interpret the first postulate as if it doesn't actually include Maxwell's equations (i.e. if we interpret "electrodynamics" as an unspecified theory of electricity and magnetism), then we still don't get Galilean relativity. To get Galilean relativity, we must at the very least postulate that the invariant speed is infinite.

 

[xantox]

To those who have been arguing the point, I fail to see how the exclusion of postulate 2, specifying a finite invariant velocity, would obtain anything but Galilean relativity.

One-postulate derivations such as Levy-Leblond's cited earlier will give a generic transformation law, where depending on the value of some undefined parameter you may obtain both Lorentzian, Galilean and Euclidean transformations.

 

[Phrak]

The first postulate mentions the equations of electrodynamics explicitly, and Maxwell's equations predict that the speed of an electromagnetic wave is c in all inertial frames. So if we completely ignore that the first postulate actually fails to define what an inertial frame is (which actually seems to be what everyone is doing), then the second is implied by the first.

If we choose to interpret the first postulate as if it doesn't actually include Maxwell's equations (i.e. if we interpret "electrodynamics" as an unspecified theory of electricity and magnetism), then we still don't get Galilean relativity. To get Galilean relativity, we must at the very least postulate that the invariant speed is infinite.

Then this is all historical nit-picking over axioms better stated. We could easily have Galilean relativity, compatible with Maxwell's equations within an aether where c is the velocity in the aether. But it Einstein relativity without a finite nonzero invariant velocity.