why there is time difference due to change in height by microseconds?

Question

suppose there are 2 watches kept ..........one above the 5 metre self and the 2nd one above 15 metres... .............we would observe that the 2nd watch would move faster than the first one by micro or miliseconds? plz try it..............its an un belivable truth???????????and try to ans this ,,,,,,,,,,,,,,,,,,it has something to do with the gravitational force?

Answer 1

The fractional change in the rate of the running of time with height difference is given by

gh/c^2.

So, in the vicinity of Earth, the relative difference in rates at positions separated by only 10 metres would be given by:

9.81*10/(3 x 10^8)^2 = 1.09 x 10^(-15).

Thus the TRUTH is that even after a HUNDRED THOUSAND years (10^5 x 3.16 x 10^7s), the higher watch would be faster by only

0.00344...s, or 3.44ms.

This all follows from Einstein's analysis of the behaviour of time in a gravitational field. Already in 1911, before he had the full theory of general relativity in hand, he had used the equivalence principle to show that time ran differently at different heights, and that the local fractional effect is given by ∆ φ /c^2, where φ is the gravitational potential. The sign of the effect is such that the clock that is deeper in a gravitational well runs SLOWER.

This same effect is responsible for the so-called "gravitational red-shift," as photons climb out of those same potential wells.

Incredible though it may seem, this prediction was tested at Harvard in the early 1960's, in a tower of some 70ft in height. The ingenious experiment, which exploited the recently discovered Mossbauer effect, won its designers the Nobel Prize.

Live long and prosper.

Answer 2

This is due to gravitational time dialation, covered by the general theory of relativity. Time travels slower in a stronger gravitational field. The higher clock sees just a wee bit less gravity than the lower one, so time moves just a wee bit faster for it.