time dilation in a gear chain system

Question

Thought experiment...

suppose we have a mechanism connecting two chain gears as follows:

gear A rotates at 2 rpm. gear B is near a massive star. because of time dilation, time is slower at B, lets say half the time at A. therefore, as seen from observer at A, the gear at B will rotate only 1 rpm.

therefore there is mismatch of speed on each gear, how to explain this?

disregard elasticity/ mass of chain/ or friction... thank you

Do you notice that in preparing your figure you have assumed the existence of an external observer whose time is absolute? Do you see how this is a problem? All observer will see both gears as having the same speed, but they will disagree on what that speed is. — dmckee --- ex-moderator kitten, Jan 23 '17 at 09:40

score 0 · Answer 1 · edited Apr 13 '17 at 12:39

1) Special Relativistic Effects (for relative velocity) for observer at A
1a) Belt (and wheel) travelling towards them appears time dilated and length contracted.
1b) Belt (and wheel) travelling away from them appears time dilated and length contracted.

2) General Relativistic, (gravitational effects) for observer A
2a) B appears time dilated due to acceleration against gravity
2b) Belt at B and gear at B appears stretched, due to the warping of space.

you can find more about effect 2b) here length contraction in a gravitational field

time dilation in a gear chain system

1 Answers1