Speed of Light is a Property of Massless Particles or Space?

[strangerep]

So there is more than just one postulate in his paper in order to reach the conclusions he did.

Yes. Apart from the RP, spatial isotropy (and then spatiotemporal homogeneity) there are also assumptions about continuity, including the assumption that the transformations form a Lie group.

I'd be able to assume if all physics is the same (inertial) that would imply isotropy and homogeneity of where / when the "physics" plays out.

Sorry -- I don't know what you mean. The RP does not imply isotropy or homogeneity by itself.

That said I understood it as the invariance of c speaks to isotropy and homogeneity of space.

One requires only the RP, spatial isotropy, and the mathematical features above involving continuity, to deduce the invariant constant c.

 

[strangerep]

Whether max speed & it's invariance were determined separately. or is one assumed because of the other?

The assumed Lie group property of the velocity transformations gives rise to an invariant speed c. Imposition of the group multiplication property gives rise to a velocity addition formula, from which the role of c as a limiting relative speed becomes obvious.

"The universal constant happens to be an upper limit on relative speed." seems to brush over the difference between invariance and maximum. For me, the "universal constant" is really universal constancy in the order of "co-located" events, or said differently the isotropy / homogeneity of spacetime.

The velocity transformation formulas are derived between observers for which the origins of their frames of reference are collocated (and suitably rotated so that the spatial axis direction coincide).

Is his paper not circumnavigating the out right stipulation of the invariance of c postulate, while relying on its key features?

No.

Perhaps you should try another treatment, such as that in Rindler's textbook on special relativity. I get the feeling you have not yet worked through the math, pen-in-hand? There's not much more I can say until you at least attempt this.

 

[strangerep]

It didn't seem tricksy to me (maybe I've fallen for it). [Pal] seems to be saying that if K<0 then it is possible to find frames where the transform does not reduce to the identity operation in the case of zero velocity. He notes that there are similar problems in the Einsteinian K>0 case for velocities greater than c, but observes that those frames are rendered inaccessible by the relativistic velocity addition law. In contrast, the velocity addition law for K<0 doesn't protect you from having to consider the problematic frames.

OK, yes, that's the basic idea. I just felt the way he expressed the argument could be strengthened.

 

[strangerep]

The case K<0 is weird, you get supraluminal velocities by adding three subluminal velocities, or even infinite ones, e.g. $3x(c/\sqrt{3})=\infty$ and the invariant speed is imaginary. Not very appealing but perhaps it has in interpretation.

I think it has no good interpretation, but rather hints at a guiding principle. I'm not sure if it already has a name, but I call it the "Principle of Physical Regularity". The idea is as follows: the relative parameters that we think of a kinematical (or dynamical) variables, such as velocity, spatial orientation, spatial displacement, temporal delay, etc, characterize how one inertial observer differs from another, and hence the particular transformation which must be performed to convert one observer into the other. If (say) observer B has (finite) relative velocity $v_{AB}$ relative to A, and observer C has (finite) relative velocity $v_{BC}$ relative to B, it must be the case that $v_{AC}$ is finite also, else we do not have a good physical theory. Moreover, this must hold for all (relative) velocities in a nontrivial open neighbourhood of $v=0$.

Appealing to this principle is essentially equivalent to what you described: for K<0 it is possible to choose velocities whose composition yields $\infty$. Such embarrassment is only avoided if we restrict the allowed relative velocities to $v=0$, which makes the "theory" trivial.

 

[nitsuj]

I get the feeling you have not yet worked through the math, pen-in-hand? There's not much more I can say until you at least attempt this.

You're absolutely right I have not worked through the math. I can't read math, so is why I was asking about the relations, assumptions ect most of which is likely explicitly shown (or easily deduced from) in the math.

Thanks for explaining it to me, but yea I really should put effort into the math. Concepts & their relations just get to a point where...it's "more than words" are capable of communicating a clear 'n concise way. lol