General/special relativity-a measurement problem

[ofer]

1. The problem statement: all variables and given/known

Describe a Non-Local Expirement that will lead to the conclusion that a body is in fact in a revolving system and not a system of constant acceleration. Non-Local meaning that the expirement uses 2 measurement instruments at 2 different points in space or 1 instrument with a segnificant size. describe what these instruments are and where they are placed.


2. this was given as a final part of a question involving describing the proper time of a body in a revolving system with SR due to gravitational potential. meaning not yet gotten to GR.




3. The Attempt at a Solution :
I tried to think of this something like the moon revolving around the earth, where the moon is the revolving system captured in the gravitational pull of the earth. somewhere 2 measurement instruments must be placed to variffy that the moon is revolving around the Earth and not being accelerated by some other constant force.
i'm really lost though on how to do this. i have a pretty good notion that an accelerometer should be used somewhere, or maybe clocks and something to do with proper time diffrences between the systems... really lost/

appriciate any kind o help.
thanks.

 

[AJ Bentley]

http://en.wikipedia.org/wiki/Coriolis_effect

 

[ofer]

hmmm, so you meen a viewer outside of the rotating frame of reference would observe the coriolis effect.
thats true' although it feels kind of like cheating, because one could say that a viewer outside the system would actually see the object rotating..
how would he measure it though?

 

[HallsofIvy]

It's NOT a matter of an "external observer". If you and another person are moving at a constant velocity, throwing a ball back and forth would be no different that if you we both stationary (relative to the "outside"). But if you are accelerating, because acceleration is NOT "relative" strange things may happen. In particular, if you and the other person are rotating around a point between you, throwing a ball toward the other person, you and the other person will see that ball curve away from the other person.

 

[paranormal]

I understand that the concept of relativity, both general and special, can be complex and may lead to measurement problems. In this specific case, the problem statement is to determine whether a body is in a revolving system or a system of constant acceleration. To address this, a non-local experiment is proposed, which involves using two measurement instruments at two different points in space or one instrument with a significant size. This experiment would help in verifying whether the body is in a revolving system or not.

To design such an experiment, we first need to understand the concept of proper time in special relativity. Proper time is the elapsed time measured by a clock that is at rest relative to the observed body. In a revolving system, the proper time would be affected by the gravitational potential, which is the potential energy per unit mass due to the gravitational field. This means that the proper time would be different at different points in space, depending on the gravitational potential.

To determine the proper time of a body in a revolving system, we can use two measurement instruments – a clock and an accelerometer. The clock would measure the elapsed time of the body, while the accelerometer would measure the acceleration of the body. These instruments should be placed at two different points in space, with a significant distance between them. This distance should be large enough to observe any differences in the proper time and acceleration measurements.

If the body is in a revolving system, the proper time measured by the clock at the two points in space would be different due to the different gravitational potentials. This would also affect the acceleration measurements by the accelerometer. However, if the body is in a system of constant acceleration, the proper time and acceleration measurements would be the same at both points in space.

By comparing the measurements from the two instruments, we can conclude whether the body is in a revolving system or a system of constant acceleration. This non-local experiment would provide evidence that the body is indeed in a revolving system, as the proper time and acceleration measurements would be different at the two points in space.

In conclusion, the concept of proper time in special relativity can be used to design a non-local experiment to determine whether a body is in a revolving system or a system of constant acceleration. This experiment would involve using a clock and an accelerometer at two different points in space, with significant distance between them. By comparing the measurements, we can conclude that the body is in a revolving system, providing a solution to the measurement problem.