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yuiop

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This relates to the thread "https://www.physicsforums.com/showthread.php?t=431712"" started by Passionflower, but is hopefully even simpler (but non trivial).

The basic question, is what is the length of a falling elevator (or ruler) that is reasonably rigid, according to:

1) A Schwarzschild observer at infinity.

2) A local observer at r=4m when the falling elevator is passing.

3) A free-falling observer inside the elevator using radar measurements from the top of the elevator.

4) A free falling observer inside the elevator using radar measurements from the bottom of the elevator.

5) How do any of the above measurements compare to two particles initially co-located with the top and bottom of the elevator and released at the same time as the elevator, but unconnected to the elevator and allowed to free-fall naturally.

By "reasonably rigid", I mean the forces that hold the elevator together are significantly stronger than than the tidal forces pulling it apart and the length of the elevator is short enough to minimise the tidal forces.

In trying to analyse this question (as a first step to answering Passion's question in the other thread) I strated by assuming these two statements are true, "Spacetime is locally Minkowskian for a local stationary (accelerating) observer in Schwarzschiuld coordinates" and "An observer in a free-falling elevator would be unable to detect if they are free falling or stationary in flat space, without reference to information external to the elevator".

My initial investigation suggests that the two statements are incompatible and one of them has to be rejected. The second statement has the condition "exluding tidal effects" and I suspect it this condition that allows us to reject the second statement.

I have already asked a lot of questions and I do not expect anyone to answer all of them, but if someone could supply a definitive answer and/or equation to anyone of the questions, that would be a significant start.

The basic question, is what is the length of a falling elevator (or ruler) that is reasonably rigid, according to:

1) A Schwarzschild observer at infinity.

2) A local observer at r=4m when the falling elevator is passing.

3) A free-falling observer inside the elevator using radar measurements from the top of the elevator.

4) A free falling observer inside the elevator using radar measurements from the bottom of the elevator.

5) How do any of the above measurements compare to two particles initially co-located with the top and bottom of the elevator and released at the same time as the elevator, but unconnected to the elevator and allowed to free-fall naturally.

By "reasonably rigid", I mean the forces that hold the elevator together are significantly stronger than than the tidal forces pulling it apart and the length of the elevator is short enough to minimise the tidal forces.

In trying to analyse this question (as a first step to answering Passion's question in the other thread) I strated by assuming these two statements are true, "Spacetime is locally Minkowskian for a local stationary (accelerating) observer in Schwarzschiuld coordinates" and "An observer in a free-falling elevator would be unable to detect if they are free falling or stationary in flat space, without reference to information external to the elevator".

My initial investigation suggests that the two statements are incompatible and one of them has to be rejected. The second statement has the condition "exluding tidal effects" and I suspect it this condition that allows us to reject the second statement.

I have already asked a lot of questions and I do not expect anyone to answer all of them, but if someone could supply a definitive answer and/or equation to anyone of the questions, that would be a significant start.

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