About the theory of relativity

Question

Why is speed of light constant in every non inertial frame of reference? Is there any theoretical explanation behind this postulate Since we cannot completely depend upon the experimental results?

Answer 1

The idea is that if you are moving inertially and someone else is moving inertially, then each of you should be able to write your laws of physics in a way that looks the same. You might place your origin in different places and so disagree on your coordinates, you might place your x-axis in different directions and so disagree on where something is on the x-axis, but you agree on what the laws themselves look like.

Some of those laws are Maxwell's equations:

$\nabla \cdot E =\rho /\epsilon_0$,

$\nabla \cdot B =0$,

$\nabla \times E =-\frac{\partial B}{\partial t}$,

$\nabla \times E =\mu_0(J+ \epsilon_0\frac{\partial E}{\partial t}).$

These laws, including the values of the constants $\epsilon_0$ and $\mu_0$ should be the same in all inertial frames, and that is a matter of principle. A principle that so far has been affirmed by observation. Then we notice that these laws permit a travelling wave at speed $\sqrt{\frac{1}{\epsilon_0\mu_0}}$, and so every inertial observer predicts they will see waves that travel at a speed $\sqrt{\frac{1}{\epsilon_0\mu_0}}$. We do measurements on the speed of light and notice that light moves at that speed, so maybe those waves are what light is. If so then we predict there are also other colors of light invisible to the human eye and when we do the experiments we detect them (infrared, UV, radio waves, gamma rays, microwaves). So we really think these waves, the ones described and predicted by the laws describing electric and magnetic fields are exactly what light is. So light moves at the same speed in every frame because the laws of electromagnetism are the same in every frame, including the values of the constants in those laws.