Undergrad Observers A & B: Rest & Simultaneity

[adosar]

Suppose we have two observers A and B and they are at rest. Observer A observes two objects falling from height H (A has same distance between the two objects). Does observer B will measure different times for the duration of falling of the two objects ? (because the two object are not in the same location therefore a finite time interval must exist for the information of their position to reach B).

 

[Ibix]

You mean that A and B are at rest with respect to one another? In that case no, if the impacts are simultaneous for one then they are simultaneous for both (although strictly the presence of gravity makes this more complicated, we can easily arrange things so we can neglect that). B will certainly receive light from the impacts at different times, but relativity is about what happens after you correct for the travel time of light. Observers in relative motion turn out to get different results if they use the same procedure to correct for the travel time, but observers at relative rest (like your A and B) get the same result.

I assume you've heard of Einstein's train thought experiment? The point is not that the observers receive the light at different times, but that they put different interpretations on what they see.

 

[adosar]

You mean that A and B are at rest with respect to one another? In that case no, if the impacts are simultaneous for one then they are simultaneous for both (although strictly the presence of gravity makes this more complicated, we can easily arrange things so we can neglect that). B will certainly receive light from the impacts at different times, but relativity is about what happens after you correct for the travel time of light. Observers in relative motion turn out to get different results if they use the same procedure to correct for the travel time, but observers at relative rest (like your A and B) get the same result.

I assume you've heard of Einstein's train thought experiment? The point is not that the observers receive the light at different times, but that they put different interpretations on what they see.

I think i get it. The difference come when they move relative to each other. This is why we can't have an absolute time ? Thanks for the response.

 

[Ibix]

This is why we can't have an absolute time ?

Strictly, it's one way to show that a global notion of time is inconsistent with an invariant speed of light and the principle of relativity. You then need to go out and do an actual experiment to see if it's consistent with reality. Which we've done, and so far it is consistent.