Derivation of space-time interval WITHOUT Lorentz transform?

[m4r35n357]

No, the relativity principle does not give us a "top speed", because infinity is not a top speed, it is a word meaning there is no top speed. Galilean relativity does not have a top speed, and therefore it doesn't exhibit relativity of simultaneity or time dilation or length contraction or a null cone structure or any of the other unique features of special relativity that arise when there is a top speed, and yet it is perfectly consistent with the relativity principle.

No, Maxwell's equations do not give us invariant light speed, because they do not, in themselves, contain any information as to how relatively moving systems of coordinates in which Maxwell's equations hold good are related to each other. (Also, we know that Maxwell's equations are not correct, see QED.)



Not even the people (including you) who have explicitly claimed that we can dispense with the light postulate?



Yes.

I most certainly did not specify Galilean relativity, and I don't know why you think I did. In fact I was referring to the Lorentzian solution (I was picked up earlier because I "left it to be determined by experiment") which does specify a top speed. I also explicitly stated that I am not attempting to dispense with the light postulate.
It would appear you have misunderstood me as much as I have you, so I will save you the effort of arguing against stuff you think I said & just leave it. Sorry it didn't work out.

 

[TrickyDicky]

Going back to the fractional linear transformations, I think it is important to stress that their unphysicality is not sufficiently granted just by the homogeneity of the space but also by its flat geometry (euclidean in the galilean case or minkowkian in the SR case) as it is explicit in Pauli's quote from the mathpages link :"All writers start with the requirement that the transformation formulae should be linear. This can be justified by the statement that a uniform rectilinear motion in K must also be uniform and rectilinear in K’. Furthermore it is to be taken for granted that finite coordinates in K remain finite in K’. This also implies the validity of Euclidean geometry and the homogeneous nature of space and time."

 

[strangerep]

Going back to the fractional linear transformations,
[...]
Pauli's quote from the mathpages link :"All writers start with the requirement that the transformation formulae should be linear. This can be justified by the statement that a uniform rectilinear motion in K must also be uniform and rectilinear in K’. Furthermore it is to be taken for granted that finite coordinates in K remain finite in K’. This also implies the validity of Euclidean geometry and the homogeneous nature of space and time."

I'd be interested in a discussion about the LFTs and the extent to which one may be reasonably justified in relaxing some of the criteria mentioned in that quote. But such a discussion would certainly diverge too far from the original topic of this thread. Also, it is not a mainstream subject, hence probably belongs over in the BTSM forum. :-)