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Gravity Probe B

Testing Einstein's Universe

Special & General Relativity Questions and Answers

Does time pass for all massive bodies at the same rate?

According to Einstein's general relativity, it is not necessary for clocks to be in motion in order to experience 'time dilation'. If two clocks are subject to different gravitational fields, they will appear to run at different rates. This key prediction of general relativity was confirmed in 1959 by Harvard physicists Pound and Rebka. By performing a sensitive experiment to examine the so-called Mossbauer Effect, they detected a slight difference in the frequency shift of gamma rays over a difference in height of 22.6 meters. This difference in frequency was only 2.5 parts in 1000 trillion, but was exactly in accord with the prediction by general relativity.

According to general relativity, the amount of 'time dilation' between two clocks in which one is inside a gravitational field and one is deep inside a gravitational field is:

 T(inside)  = ---------------------
               ( 1 - 2GM/(rc^2) )^1/2

This is reflected in the fractional change in the frequency of the light emitted near the surface of the body with a mass of 'M' at a distance of 'R' from the center of mass according to:

              Change in frequency               G M
 Shift =    -----------------------  =   -   ---------
                  frequency                     R c^2

Where the 'frequency' is the frequency of the light far from the body, and the minus sign indicates a 'redshift'. As an example of the kinds of gravitational redshifts that are possible for objects that are multiples of the solar mass ( 2 x 10^30 kilograms), here is a list:
Object             Distance          Mass           Shift
                 (kilometers)      (Solar Mass)
Sun                6.9x10^5           1.0         0.0000021
White Dwarf        10,000             1.0         0.000146
Neutron Star         20               1.0         0.0733
Black Hole            3               1.0         0.48
For the Black hole case, we did the calculation at a distance of 3 kilometers from the center. Since the event horizon is located at 2.9 kilometers, we are just outside. If we had crossed over the horizon, the gravitational redshift, calculated properly, would have been 1.0 which means that the time dilation effect would have been infinite as we see from the first equation above.

So, the rate at which time passes is different depending on where you are relative to a local gravitational field, but for most normal bodies, the differences are only a few parts per million!

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.