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(outside)
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!
Return to the Special & General Relativity Questions and Answers page.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.