Ok, so I know there have been some variations of this passed around and answered already, but I still can't quite understand how this works, so I want to clarify some particular points in this.
Lets start with Einstein's relativity of simultaneity thought experiment. Specifically the variant where a person stands in the middle of a train car with a lightbulb and another one is stationary on the ground next to the train as it passes by. When the moving observer lights the lightbulb he will wee the light reach both ends of the rail car at the same time. Meanwhile the stationary observer will see the light reach the rear end of the train car first.
I get the experiment itself. However I can't quite understand how it works if we start trying to measure the difference in relativity. Say we put a light detector and an attosecond-accurate clock in each end of the train car and sync the clocks before the experiment (when both observers start in the same "stationary" frame of reference and can agree that the clocks a synced). When the light detector registers a photon, the clocks save the current timestamp and send it to a central computer. When the central computer receives both timestamps it compares them and outputs "EQUAL" or "DIFFERENT" on a screen.
In the original thought experiment we talk of the observers "observing" all the events take place, so, using the same terminology, the observer in the train car will, obviously see the light hit the detectors at the same time. The detectors will both be showing the same time (both will be showing t0 for example) when the light reaches both of them. He will, therefore, see the detectors record identical timestamps at that moment and send them to the central computer.
The stationary observer will observe the light hit the detectors at different moments in time. As both clocks are in the same frame of reference there is no time dilation between them, and the stationary observer will see them showing the same time at any specific point in time (even if they are slightly diverged from a similar clock he might have). Therefore he will see them both showing, say, t1 when light hits the first one, and both showing t2 when light hits the second one, which is fundamentally different from the first case. He will see them record different timestamps and send them to the central computer.
So now we have one person who saw the computer receive 2 identical timestamps, and another who saw it receive 2 different timestamps. So they will observe the computer perform the calculations and output different answers.
I understand there must be an error in such logic, but I can't understand where and why. Theoretically both observers could see the whole process happening up to and including the displaying of the result on the screen. At the same time, if the train stops and both observers walk up to the screen you would expect them to agree as to what is output on it.
Basically the specific questions I want to understand are:
- If you are the stationary observer, then you should theoretically be able to observe the whole process and see "DIFFERENT" on the screen. Or if not, then how could you see anything else?
- If you are the moving observer, then you should theoretically be able to observe the whole process and see "EQUAL" on the screen. Or if not, then how could you see anything else?
If anyone can explain this I would be extremely grateful, because this is frying my brain.