Is there any theoretical proof for the constant speed of light in all frames of references? I know it is experimentally proven but just curious.
Answer
As WillO says, one has to state one's theory precisely through a definition of one's axioms (and allowable rules of inference).
But something you may find intellectually fulfilling is the following. Beginning from very basic symmetry principles - homogeneity and isotropy of spacetime as well as continuity of transformations between frames and continuous dependence on relative velocity and, finally, causality, see the Pal and Levy-Leblond papers I cite in my special relativity resource recommendation answer here. One can prove from these assumptions that there must exist a frame-invariant speed $c$ (it could be infinite i.e. Galilean relativity is included in the possible outcomes) and also one derives the form of the Lorentz transformations.
One then experimentally finds that $c$ is finite because the speed of light is experimentally found to behave in this frame invariant way.
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