One problem with the "Twin" thought experiment, where one twin travels close to the speed of light, twin on Earth ages, etc., is that - according to the theory - there is no absolute reference, so which twin is traveling? One could say that the twin in the rocket remained motionless and the Earth traveled near light speed.
The problem is this is Theoretical Physics. It's all mathematical conjecture.
“The problem is this is Theoretical Physics. It’s all mathematical conjecture.”
No, relativity was only “theoretical” in that Einstein conceived it mainly as a thought experiment; it can actually be tested by a variety of experiments.
Obviously we can’t approach anywhere close to the speed of light, but we can demonstrate the time dilation effects he predicted on a smaller scale.
Relativity was made popular because it's a good scientific theory that explains our observations and has passed every test we've thrown at it. It's right.
"The problem is this is Theoretical Physics. It's all mathematical conjecture."
Relativity is physics. Its effects are measured and used, and our technology depends upon it. It is not conjecture.