# Gravitational time dilation - acceleration vs potential

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What I know gravitational time dilation (based on GRT) is dependent on gravity potential and not on gravitational acceleration. That would mean, that for example in center of Earth is the gravitational acceleration zero, but the gravitational potential is bigger than on the surface of Earth, meaning that gravitational time dilation is bigger in center of Earth than on surface of Earth. This is standard mainstream interpretation but what I know, this was never confirmed by experiments.

There were experiments which confirmed gravitational time dilation comparing atomic clocks in different heighs above surface of Earth or by GPS satellites. But what I know there were no tests which confirmed this for different states of gravitational acceleration and gravitational acceleration. Theoretically it could be tested by comparing atomic clock on surface and atomic clock in some deep mine, but there is major problem that gravitational acceleration starts to decline in around 2000 km under surface of Earth, so experiments surface vs deep mine would not deliver detectable difference.

So Im coming to my main question: If we can not confirm this directly by experiment, could it be done is some reverted experiment or observation? Meaning that if gravitational time dilation would depend on gravitational acceleration and not on gravitational potential, this would in theory lead to some specific observable effects, which in theory could be observed, but were not observed in reality?

PeterDonis
Mentor
2020 Award
in center of Earth is the gravitational acceleration zero, but the gravitational potential is bigger than on the surface of Earth, meaning that gravitational time dilation is bigger in center of Earth than on surface of Earth

This is correct.

this was never confirmed by experiments

True, since we have no easy way of sending a clock to the center of the Earth and having it exchange light signals with us on the surface so we can see how its rate of time flow compares to ours.

there were no tests which confirmed this for different states of gravitational acceleration and gravitational acceleration

Yes there are. The GPS satellites are in free-fall orbits. They have zero proper acceleration; we here on Earth's surface have 1 g proper acceleration.

Also, the orbital altitude of the GPS satellites is high enough that the "acceleration due to gravity" there (which the satellites don't feel, since they're in free fall) is significantly lower than it is on Earth's surface. So if the rate of time flow were affected by "acceleration due to gravity" as well as potential, this effect would show up in GPS, and it doesn't.

if gravitational time dilation would depend on gravitational acceleration and not on gravitational potential, this would in theory lead to some specific observable effects, which in theory could be observed, but were not observed in reality?

This experiment has been done: GPS. See above.

Dale
Mentor
2020 Award
Meaning that if gravitational time dilation would depend on gravitational acceleration and not on gravitational potential, this would in theory lead to some specific observable effects, which in theory could be observed, but were not observed in reality?
I am not aware of any theory where time dilation depends on gravitational acceleration. Such a theory would be incompatible with the equivalence principle, so I guess that any test of the equivalence principle would indirectly rule out all such theories.

gravitation force comes from gradient of gravitation potential, i.e. gradient of time dilation. Gravitation force shows direction and magnitude which and how much lower in gravitational position and slower in time dilation.

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pervect
Staff Emeritus
Gravity probe A (the scout rocket tests) would probably be good test of GR's predictions with respect to gravitatioanal potential vs acceleration.

There's a wiki article on the test.

What I know gravitational time dilation (based on GRT) is dependent on gravity potential and not on gravitational acceleration.

I am not so sure but we may be able to say gravity potential depends on or is generated from time dilation thus gradient of gravity potential, i.e. gravity acceleration depends on gradient of time-dilation.

For example say light goes horizontally on surface of planet, in the higher part light goes more than in the lower part due to gradient or time dilation, thus light bends downward by Huygence's principle. This is interpreted as gravity bends light down.

PeterDonis
Mentor
2020 Award
I am not so sure but we may be able to say gravity potential depends on or is generated from time dilation

It's better to say the two of them are different manifestations of the same thing (a particular kind of curved spacetime geometry). Neither one is "more fundamental" than the other.

sweet springs
PeterDonis
Mentor
2020 Award
For example say light goes horizontally on surface of planet, in the higher part light goes more than in the lower part due to gradient or time dilation, thus light bends downward by Huygence's principle.

This is at best a heuristic explanation of why light bends towards a source of gravity. According to GR, this is again a manifestation of a particular kind of spacetime geometry, that results in a particular configuration of null geodesics. There is no need to invoke any particular properties of light, much less a particular model of light (Huygens' Principle, which depends on a particular wave model of light).

sweet springs
haushofer
This is at best a heuristic explanation of why light bends towards a source of gravity. According to GR, this is again a manifestation of a particular kind of spacetime geometry, that results in a particular configuration of null geodesics. There is no need to invoke any particular properties of light, much less a particular model of light (Huygens' Principle, which depends on a particular wave model of light).
Einstein originally calculated the deflection of light by Huygens' Principle, and I saw it a while ago in a GR-textbook (I forget which one it was). So I wouldn't say it is merely heuristic; it's one way to calculate and understand the bending of light.

sweet springs
PeterDonis
Mentor
2020 Award
it's one way to calculate and understand the bending of light

But it only works for a particular model of light. What's more, that model isn't even the one that's usually used in GR to model light rays (normally problems like the bending of light in GR are treated using the geometric optics approximation).

Whereas the geometric model predicts that anything that follows null geodesics will be deflected in a gravitational field; you don't have to know anything about the details of the thing, other than it following null geodesics.