# About the theory of relativity

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?

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possible duplicate of physics.stackexchange.com/q/33816/11062 – Waffle's Crazy Peanut Mar 27 '13 at 16:16
Just to comment on your last sentence: yes we can completely depend upon experimental results and indeed we must. Only nature itself is always right and any theory must agree with experiments. This little remark aside, it is a good question. – Wouter Mar 27 '13 at 16:26
@Wouter why is it a compulsion to believe upon the experimental results ? There might have been error while doing experiments or next day we can prove it wrong.. I think it is appreciable if there is a postulate which is valid both experimentally and theoretically. – newera Mar 28 '13 at 13:31
@kiranadhikari There is no other truth than that. Nature is what it is, it cannot be wrong. Theory can. Of course experiments can be completely erroneous, but we don't just depend on any old experiment. We only trust results that are replicable and we only trust them within the boundaries of the measurement errors. Naturally, it's one thing to get the data, it's another to interpret it. And the interpretation of experimental results can be wrong, even though the data is completely solid. – Wouter Mar 28 '13 at 16:06
The last sentence of your comment above almost makes it look like you think I'm saying the two are mutually exclusive. Of course they are not and indeed there are plenty of postulates out there which agree with experiment (though often only within a certain field). But you must always remember that a postulate can only be physically acceptable if it does not contradict experimental data. – Wouter Mar 28 '13 at 16:12

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.

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