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The Lorentz transformation is linear in $x,y,z,t$.

Are there are any non linear space transformations that leaves the speed of light constant in all inertial frames? The possibility being that space or matter might not transform in a simple homogeneous way.

Such a transformation which leaves the Maxwell equations invariant I imagine is unlikely.

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  • $\begingroup$ Possible duplicates: physics.stackexchange.com/q/12664/2451 , physics.stackexchange.com/q/105379/2451 , physics.stackexchange.com/q/155363/2451 , physics.stackexchange.com/q/253356/2451 and links therein. $\endgroup$
    – Qmechanic ♦
    Commented Jan 9, 2017 at 11:28
  • $\begingroup$ The question and the respective answer by Qmechanic pointed out by ACuriousMind explicitly assume that (1) there is a spacetime viewed as a (2) differential manifold equipped with (3) a metric constructed by exploiting the constant light velocity postulate. The question above does not assume all these physical hypotheses. I do not believe that it is a duplicate even if some overlap exists. $\endgroup$
    – Valter Moretti
    Commented Jan 9, 2017 at 11:55
  • $\begingroup$ Agree with Valter Moretti comments. I am thinking of non linear transformations. The possible duplicates referred to deal more with proving the linearity of the LT I think, a different subject. $\endgroup$
    – user1894243
    Commented Jan 9, 2017 at 12:08

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