An astronaut, in a space ship capable of accelerating from zero to C instantly ( to reduce complex math to get an easy to understand answer below ).
The space ship will only travel around earth, meaning, it won't get further and further away, but basically always be at a constant distance from earths center point.
To keep example simple, the astronaut will only travel a quarter of a spin around earth.
Ready, steady, go.
The observers with their high tech equipment on earth can calculate in advance what time the astronaut is expected to arrive after a quarter of a spin. Lets call it
Now, so can the astronat. In fact, I believe their calculations show the same time. Lets call it
Time dilation states that after this experiment, and when both stop to compare watches, earth, since they are the observers (
although who is actually spinning, earth or the astronaut is a good question), that
Xearth will be lets say
At the same time. Calculations prior showed that the astronaut can expect his watch to be
2019.fraction.of.a.nano.second while on earth, since they considered not themselves being the observers, also expected the astronaut to be there
How do we address this paradox? What time is it on earth after the astronaut makes this trip?
- Addressing in advance a response I might get immediately. Namely that since he is spinning around earth, there is no observer and their time should be equal indeed, but that would go against my understanding of the special relativity. It cares not where or what trajectory of the speeding astronaut is, it only cares about what speed he is traveling.
Please try to stick to this example when answering the question.