Einstein told us that the speed of light must always, not only appear, but BE the same in every frame of reference no matter how fast we are moving towards or away from it. So even if you are moving at half the speed of light towards a light beam, the entire universe must conspire to either "speed up" or slow down your "time" to account for this difference.
If that makes sense to you, you are no longer sane. You cannot create scenarios of two mutually exclusive events at the same time and call that reality. This is fundamental to reason.
To show this contradiction, consider you are running away from a light beam and towards another at the same time. You move at half the speed of light. Of course in real life you will encounter the light you are moving towards first, but in Einstein's universe both beams MUST (in your world) hit you at the same time. However, in Einstein's universe, someone else will see them hit you at different times because they also MUST see light travel at a certain speed. This is just plain fucking stupid.
At best you can have an illusory effect, but to confuse that with a real difference in simultaneity is to truly give up on reason itself.
Explain why the calculations work in the real world, then.
I can explain many, but I actually don't need to. If I can show a theory is self contradictory and defies the very foundation of reasoning itself (that there is objective truth) then I've exposed it as horrendously flawed.
It's certainly possible to make some correct calculations from a horrible illogical theory. I could create math that assumes Earth accelerates upward and come up with some useful calculations for kinematics of falling objects, but then it will fail miserably elsewhere.
edit: Despite that valid disclaimer, I can show that SR doesn't work for time dilation. As Herbert Dingle and Ron Hatch have already illustrated , under SR there is no one sided time dilation which is found in GPS. So the apparent clock slowing on GPS satellites is only calculated by Lorentz (as Ron Hatch notes) and not Einstein (who requires two symmetrical equations).
Relativity is contradiction after contradiction that its adherents paper over with bad and inconsistent logic. One relativist will give you one excuse to weasel out of a contradiction, compared to another relativist who provides another. Neither are valid. Specifically for the problem of asymmetry in Einstein's time dilation applied in GPS they have multiple excuses all of which are wrong.
"It involves acceleration, therefore is a non-intertial frame" The problem with this excuse is it means the phenomena is no longer governed by SR which does not account for acceleration.
"This is covered by GR which involves acceleration". No further detail is given and if asked for a derivation of this time dilation from GR using acceleration they cannot because it does not exist. SR is the basis for velocity based time dilation, using equations with constant velocity. But since they are bound by velocity being "relative" the effects must be symmetrical and only apparent.
You’re going to have to prove the existence of an objective external reference frame to disprove the reproducible observational effects of relativity.
Objective reality is the basis for reason. Without it you might as well abandon all logic and wander off into madness trying to create your own reality.
Also any philosophy claiming there is no truth can't be true, based on logical deduction. So SR can be thrown out on that alone.
I already explained the failure of SR on one very important alleged observational effect. So on empirical data alone that's sufficient debunking. But the philosophical point is actually more important and more true.
So… no answer, then. Nothing. You can’t prove the existence of an objective external reference frame.