Answered February 4, 2018 · Upvoted by David Tregurtha, PhD Physics, University of Bath (2014) and Suraj Saha, M.Sc Physics (2017)
Why did Einstein assume the speed of light as constant in a vacuum?
Two reasons.
One is theoretical: A constant speed of light is predicted by Maxwell’s equations of electrodynamics so long as the electromagnetic properties of the vacuum are treated as constants of nature. If different observers, moving at different speeds, measured different values for the speed of light, that would mean that the properties of the vacuum (its electric permittivity and magnetic permeability) would not be the same for these observers. This made little sense.
The other is experimental: Einstein probably knew about the result of the 1887 Michelson-Morley experiment that showed that the measured speed of light is not affected by the Earth’s motion in space.
In terms of modern language, we know that the vacuum Maxwell equations are “conformally invariant”: they do not change under an arbitrary “angle-preserving” transformation in four-dimensional spacetime. If we also allow charges, this symmetry is reduced to an invariance under a subset, namely the Lorentz-Poincaré group of four-dimensional hyperbolic rotations and translations. Special relativity, fundamentally, is the physics that ensues once we assume Lorentz-Poincaré invariance, which, for all practical intents and purposes, is equivalent to assuming that the speed of light is constant.
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