Can’t we explain well the result of the Michelson–Morley experiment only with the Galilean transformation?
In other words, is the speed of light invariant with respect to inertial frame of references even though an other object than light varies its speed relative to them?
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Under a Galilean transformation, the speed of light is not invariant — in a Galilean frame moving at speed $v$ light (moving in the direction of the frame) moves at $c + v$.
Of course, you could posit that everything except light transforms under Galilean transformations, and light is somehow special. But then you run into Occam’s razor; Lorentz transformations don’t require a special rule for light. In addition, this would be contradicted by other known results such as the excellent predictions of special relativity for, for example, particle collider experiments.
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$\begingroup$ I think you meant to say 𝑐-𝑣 not 𝑐+𝑣. But even in a Galilean frame moving at speed 𝑣, light (moving in the direction of the frame) can move at 𝑐 if the speed of light out of this frame is 𝑐+𝑣. You implicitly assumed an unmeasurable speed of light as 𝑐 even though it is impossible to assure that it is not 𝑐+𝑣. $\endgroup$ Commented Dec 28, 2019 at 14:19