How does gravity affect time? It turns out that time runs slower in gravitational fields. Time runs slower for a person standing on the ground on Earth, than for a person standing on top of the highest mountain. Let’s visit our friend Jackie to see why.
Imagine that you and Jackie are floating freely in space at different ends of a spaceship. Both of you have synchronized watches that flash every second. Because both you and Jackie are weightless and there is no relative motion between the two of you, we can conclude that you are in the same reference frame. In this case, you would see each other’s watches flashing at the same rate.
Now, let’s say you fire your spaceship engines and start to accelerate, where you are still at the front of the spaceship, and Jackie at the end (see figure F-5-2). When the ship accelerates, you are not weightless anymore, and your speed is constantly increasing relative to an outside observer who is weightless. This means that both you and Jackie are constantly changing reference frames.
The light flashes from your watch will reach Jackie a little faster than when you were stationary, because the spaceship is carrying Jackie toward the point at which your watch emitted a flash. Jackie, then measures less than 1 second for each of the flashes from your watch. From your perspective, you are being carried away from the flashes of Jackie’s watch and that light takes a little bit more than 1 second to reach you. You would conclude that Jackie’s clock is ticking slower and she would conclude that your watch is ticking faster.
Notice that you and Jackie agree! Time is running faster at the front of the ship and slower at the end of the ship. If we now apply the equivalence principle, where effects of acceleration are equivalent to those of gravity, we can conclude that time runs slower in strong gravitational fields . Time runs slower at lower altitudes than at higher altitudes. This effect is called Gravitational Time Dilation .
The effect of gravitational time dilation is stronger in stronger gravitational fields (or greater curvature of spacetime). Therefore, time runs slower on the surface of Sun, than it does on the surface of Earth.
The Moon has the lowest mass, so it would have the lowest gravity on its surface and time would run fastest there. Notice that the white dwarf, neutron star and the black hole are all highly compressed objects making their surface gravity very strong.
Passage of time has been precisely measured at different altitudes on Earth and confirmed by many experiments. Time indeed passes more slowly at lower altitudes and the measurements are in precise agreement with general relativity.
Gravitational Time Dilation is NOT Symmetrical
In special relativity time dilation is symmetrical. When you and Jackie were floating weightlessly in spaceships each of you measured that the other’s time is slower. Jackie concluded that you were the one moving at 0.7 c while she was stationary and that your clock ran slower. You concluded that Jackie was the one moving and that her clock ran slower than your stationary clock. But gravitational time dilation is not symmetrical!
Looking back at the example of Jackie at the front and you at the end of the accelerating spaceship (see previous figure), she measures your time to tick slower, while you measure her time to tick faster. The two of you actually agree that the clock in a stronger gravitational field ticks slower.