| HPS 0410 | Einstein for Everyone | Fall 2024 |
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The observer I is located at the midpoint of the spatial locations of the strikes A and B. Light signals coming from the strikes A and B arrive at this observer I at the same time.
The observer II is located much closer to the strike A. As a result, the light signal from strike A arrives at observer II much earlier than the light signal from strike B.
Observer I sees the signals at the same time; observer II sees them at different times.
Is this difference the relativity of simultaneity of relativity theory? If not, why not?
B. Two identical spaceships pass one another, moving rapidly in opposite directions at the same speed according to an observer on a nearby planet. The planet observer judges that both spaceships have shrunk the same amount due to relativistic length contraction. So they are the same length and, in conformity with this expectation, the planet observer notes that the two spaceships line up perfectly as they pass.
An observer on one of the spaceships, however, finds the other spaceship to be moving rapidly. So that spaceship observer judges the other spaceship to have shrunk relative to the first spaceship. And an observer on the second spaceship comes to the reverse judgment, that the first spaceship has shrunk.
How is it possible for all of of them to come to such different judgements?
C. Judgments of simultaneity are involved in any procedure that measures the length of moving bodies or the times elapsed for processes on them. Consider some procedures for measuring such lengths and times and show how judgments of simultaneity are hidden in them. What if, for example we measure the length of a moving body by timing how long it takes to pass a single observation point, where we use just one clock to time its passage. Its length is just its speed multiplied by the time measured.