Thought experiments are very common in Special and General Relativity (SR,GR). Usually a thought experiment is structured as follows:
- We present a setup in a frame of reference
- We apply principles of SR or GR to derive what must happen
- We then shift perspective to another frame of reference
- We state that both observers should agree on what's happening
- We at last draw the conclusions
This structure lets us derive directly from the postulates effects like Time Dilation, Light Bending in a Gravitational Field and so on.
My problem regards the point 4.: In every thought experiment we state that observers should agree on what is happening in some way. Problem is that this is not always true! If I state that observers in different frames should agree on simultaneity, for example, I am obviously in the wrong. But if I state that both observers should see a mug breaking I am probably correct.
My question is: The fact that both observers, in different frames, should agree on events is a principle? If so what is the precise wording of this principle? Does this principle have a name?
