I don't think they've proved the theory of relativity. Please provide the Best single proof that?

Question

a)light cannot change speed no matter how much you change your speed relative to it

or

b)gravity affects time

Answer 1

The Michelson Morley experiment proved that the speed of light is constant. The Ether was thought  to be a frictionless solid, at that time it was believed that light travelled in wave form, so it needed a medium to wave through, we now know that this not the case. Gravity does not effect time, very high speed causes it to dilate. The famous equation, E=MC2 led to the development of the fusion bomb.

Answer 2

GPS satellite system provides a lot of data on the subject

google 'GPS relativity' for reams of information

the fact it still gets people where they're going is testament to the accuracy of the predictions.

A cornerstone of SR is that the laws of physics should be the same for everyone, no matter what they're doing, how fast or where...

i think that came from maxwell's equations, which give the speed of light to be a function of permitivity and permeability of free space.  these are just constants for space.  there was no obvious reason for that to change for someone moving or whatever. how does your moving affect space?    If you take that point, and consider the speed of light to be the same for everyone no matter what they are doing, then you end up with SR.      

something to bear in mind is 'how do you measure this?'

so you might feel that it is ridiculous that time could be variable for different people doing different things.  but how do you measure it?   and your body has processes which depend on the same laws of the universe as any clock, and everything else.

Answer 3

There is tons of evidence, and mathematical proof for that matter.  

I believe that they have flown planes around the Earth with clocks on them to show that time slowed down.

Also if you want a lot of proof you have to look at things that move really quickly, which electrons do a nice job of.  If you study advanced quantum mechanics there are always adjustments that need to be made to calculations based on relativity, all experimentally verified.