Both are stopped at the same time in S, but not simultaneous relative to some other frame.Both stop watches are stopped at the exact same time. — flannel jesus
They'd observe the closer runner finishing first. They'd also see that the stoped watches read identical values. All this is true even under Newtonian physics, and the observer in question doesn't have to be moving in S to observe any of this.If there's an observer in some relativistic frame of reference, travelling at some significant fraction of the speed of light to the left or the right (you choose, it doesn't matter), how do they perceive the race? — flannel jesus
Not relative to S', of course not.Do they think the runners ran the same speed? — flannel jesus
The guy running to the right (slow, at about -.286c relative to S') wins the race. The guy running directly left moves at 2/3 c relative to S' and gets to his destination some time after (in S') the first guy does.both runners are running at 25% of the speed of light relative to the people in the audience, they reach their finish lines after 4 seconds of running (so they ran 1 full light-second), and the observer watching the race in a relativistic frame of reference is travelling to the right at 50% the speed of light. — flannel jesus
All this is true even under Newtonian physics, and the observer in question doesn't have to be moving in S to observe any of this. — noAxioms
The part I said was true under Newtonian physics was the bit about which runner was first observed to finish, which is a function of where the observer is at the time of that observation and not at all a function of how fast or what direction the observer is moving. There's a set of events that the light from both runners finishing reaches simultaneously. That set of events forms a 3D hyperplane in spacetime. If the observation of the observer is made on one side of that plane, the one runner is first observed finishing, else the other runner is first observed finishing.In Newtonian physics... I don't know how to do that version of transformation between S and S', but it would seem to me that once you as an observer account for the time it took the light to reach you for each of your observations, wouldn't your results look exactly like they would look from the perspective of a stationary observer? — flannel jesus
The original description doesn't say where the observer is ("in the stands" but where in S are 'the stands'?). Anyone in S would compute that the race was a tie, but the nearer runner would first be observed finishing. For instance, each guy with the stopwatch would see the other runner finish 2 seconds later.And if someone wasn't moving in S, wouldn't they just see the same thing as the original description?
Train has no wheels since relativistic wheels are a whole new problem. So it's sort of a mag-lev situation where the track is there but doesn't touch.Through this process of accelerating, is there any difference in the length of the train *in the reference frame of the train itself* — flannel jesus
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