Is there an experiment where they tested if c is constant to any observer moving at any speed in any direction? Am I correct that to check the speed of light for two observers (and letting both observers know each other's results) we would need to exchange information in between the two observers, and that the exchange of information can only be done also with max c speed? So how would we let the other observer know of our results if we can send information only with max c speed?
[Physics] How to experimentally prove that speed of light $c$ is constant to any observer
experimental-physicsinertial-framesobserversspecial-relativityspeed-of-light
Best Answer
There have been countless studies on the topic. The easiest for me to understand are the interferometry studies. In these studies, you shine a laser at a semi silvered mirror which splits the beam into two beams at right angles. These each bounce off a mirror and recombine, interfering with each other. You can then move this apparatus in one axis and not the other or rotate it and show that the interference pattern does not change (intuition, such as that gained by thinking about throwing a ball on a train, leads to a different answer).
The most famous of these was the Michaelson-Morley experiment, which showed that the speed of light did not vary with direction or velocity by using the earth's own motion and rotation.
These interference experiments could be though of a a single observer showing that difference in reference frame velocities do not change the velocity of light. If you want it proven with two observers, it may be easier to instead focus on proving that time dilation occurs. That is another expected outcome of relativity. For that, you need to go no further than your local GPS receiver in your phone. Your phone actually has to account for relativistic effects such as time dilation when it is calculating your location. It can be shown that, without that correction, your GPS would be more inaccurate than it is today!