- #1
Hiero
- 322
- 68
If a clock runs n times faster than another clock due to flawed design, then it is logically necessary (and rather trivial) that the other clock runs 1/n times slower than the flawed clock.
I thought the same should be the case for gravitational time dilation; if a clock on a tower runs n times faster than a clock on the ground, then I expected the clock on the ground to run 1/n times slower than the one on the tower.
The formula for uniform gravitational time dilation which I have learned is the clock on top will run faster than the ground clock by a factor (1+gh), but also the clock on the ground will run slower by a factor (1-gh)
So we do not have the n=>1/n relationship ... although we do have that relationship for small h [if we neglect 2nd+ order terms of h, then 1/(1-gh)=1+gh].
I think the {(1+gh), (1-gh)} factors are exact not approximate, but this seems strange to me that they aren't reciprocal.
To make it more clear what bothers me: After 10 seconds on the ground clock, a ground observer might see 11 seconds passed on the tower clock. But then when 11 seconds pass on the tower clock, a tower observer will see only 9.9 seconds passed on the ground clock.
I suppose nothing is wrong with this apparent discrepancy?
I thought the same should be the case for gravitational time dilation; if a clock on a tower runs n times faster than a clock on the ground, then I expected the clock on the ground to run 1/n times slower than the one on the tower.
The formula for uniform gravitational time dilation which I have learned is the clock on top will run faster than the ground clock by a factor (1+gh), but also the clock on the ground will run slower by a factor (1-gh)
So we do not have the n=>1/n relationship ... although we do have that relationship for small h [if we neglect 2nd+ order terms of h, then 1/(1-gh)=1+gh].
I think the {(1+gh), (1-gh)} factors are exact not approximate, but this seems strange to me that they aren't reciprocal.
To make it more clear what bothers me: After 10 seconds on the ground clock, a ground observer might see 11 seconds passed on the tower clock. But then when 11 seconds pass on the tower clock, a tower observer will see only 9.9 seconds passed on the ground clock.
I suppose nothing is wrong with this apparent discrepancy?