Proof of Lorentz transformation

[murshiddreamengineer]

What are the supporting arguments for the assumption that space and time are homogeneous?

 

[Dale]

What are the supporting arguments for the assumption that space and time are homogeneous?

It is the simplest assumption, and it is consistent with all observations in the absence of tidal gravity.

 

[Nugatory]

What are the supporting arguments for the assumption that space and time are homogeneous?

Two things:
First there's pretty much no evidence to the contrary. The laws of physics don't change even though the earth is in a completely different place in winter and summer, the spectral lines from distant astronomical objects show that time and space works the same there as here, no matter which direction I point my laser I will find that the round trip time from laser to a fixed mirror and back is the same.....
And second, there's no plausible theory that starts with an inhomogeneous spacetime yet predicts the same observations.

(As a digression, there are implausible theories that do exactly that. The homogeneity assumption is also the assertion that these theories are implausible).

 

[Mister T]

What are the supporting arguments for the assumption that space and time are homogeneous?

Things derived from that assumption match observation and experiment.