Is there EVIDENCE (proof) that time dilation actually occurs in the case of relative UNIFORM mottion (i.e., where no acceleration or decelleration occurs)? By proof, I don't mean mathematically but, instead, in observerable reality. No one answered this simple question. I raise this because to say in such a case that, from BOTH reference frames, the "moving" cliock is ticking slower than the "stationary" clock is a LOGICAL CONTRADICTION . Even invoking relativity of simultaneity where one clock begins ahead of the other, the period of supposed dilation is overlapped by both frames.
We are constantly in communication with GPS satellites, which only work because they take into account time dilation due both to special relativity and general relativity. It turns out that special relativity is the larger effect, so I think this would count as hard evidence.
Edit: GPS devices communicate with GPS satellites via microwave signals. The signals are sent from the GPS satellites with a time stamp, and by knowing how fast the speed of light is along with the current time, the device can determine how far it is from each satellite and thus triangulate its location. In order for this to work, the clocks on the GPS satellites obviously need to be synched with clocks here on earth. Thus, the clocks on the satellites were set to run slightly faster when they were built and launched so that when they got into high speed orbit the satellite clocks would run at the same speed as our own clocks.