Can Acceleration and Gravity Equally Affect Time Dilation?

[Maartenn100]

(This is just a hypothesis which can be totally wrong)

I will combine three ideas here:

The equivalenceprinciple
Gravitational timedilation
Special theory of relativity

The equivalenceprinciple says that a gravitational force on a system is indistinguishable from an acceleration of that system. Whether you are on Earth or you are accelerating in a spaceship with 1 g, there is no way to tell the difference. (general theory of relativity)

So, the equivalenceprinciple must tell us: (I'm sorry for my bad English)

The decreasing timeflow of a body with a constant acceleration of x g in respect to the timeflow of a body at rest is equivalent with the decreasing timeflow of a massive body with a gravitational field of x g in respect to uncurved spacetime with zero gravity (f.e. intergalactic space).

To simplify the idea:
Accelleration versus being at rest = gravity versus zero gravity (intergalactic space f.e.)


We all know that a clock in the spacehip of lower orbit (hence in a region of stronger gravity) runs more slowly then a clock in the other ship. (gravitational timedilation).

So a prediction can be:
If we had a telescope to see a hypothetical clock in intergalactic space we would see it ticking faster and faster and faster to infinity.

If we were in intergalactic space and would see through a telescope, we would see a clock on Earth ticking slower and slower and slower to infinity.

Thank you for the interesting feedback.

 

[PeterDonis]

(This is just a hypothesis which can be totally wrong)

It is--at least, your prediction is. See below.

The equivalenceprinciple says that a gravitational force on a system is indistinguishable from an acceleration of that system. Whether you are on Earth or you are accelerating in a spaceship with 1 g, there is no way to tell the difference.

Locally, this is correct (though a bit sloppily stated). More precisely, it's correct over small enough ranges of space and time that tidal gravity is negligible.

The decreasing timeflow of a body with a constant acceleration of x g in respect to the timeflow of a body at rest

Here you're starting to go wrong. What is "a body at rest"? "At rest" is frame-dependent; there's no invariant way of saying that one body is "at rest" and another is "in motion".

You could say "a body with a constant acceleration of x g relative to a body moving inertially, feeling no acceleration"; that would be OK. But the analogy you are trying to draw with a gravitational field still isn't valid, because of the qualifier I put in above on the equivalence principle. See below.

is equivalent with the decreasing timeflow of a massive body with a gravitational field of x g in respect to uncurved spacetime with zero gravity (f.e. intergalactic space).

No, it's not, because, as I just noted, the equivalence principle is local, not global. The fact that, locally, you can't tell whether you're on the surface of the Earth or in a rocket accelerating at 1 g in deep space, does not mean you can't tell, period.

Suppose, for example, there was someone in a spaceship very, very far from Earth, but at rest with respect to it, and we sent light signals back and forth. The relative "timeflow" of us on Earth with respect to the spaceship would be *constant*, not decreasing, because we can remain at rest relative to each other even though we are accelerated at 1 g and the spaceship is in free fall. That's because of tidal gravity: the acceleration it takes to stay at rest in the Earth's gravitational field is not constant, it decreases with increasing distance.

Now suppose a second spaceship is sitting next to the first one, very, very far from Earth (and all other gravitating bodies), and it suddenly turns on its rockets and accelerates away at 1 g. This spaceship will not, and cannot, remain at rest relative to the first one; its velocity away from the first one will increase, and increase, and its "timeflow", as seen by the first ship, will get slower and slower. That's because of the lack of tidal gravity: there is no way for the second ship to maintain 1 g in deep space, far from all gravitating bodies, without continually increasing its velocity relative to the first ship.

So the two situations, while analogous locally, are not analogous globally, so the comparison you're trying to make doesn't work.

So a prediction can be:
If we had a telescope to see a hypothetical clock in intergalactic space we would see it ticking faster and faster and faster to infinity.

If we were in intergalactic space and would see through a telescope, we would see a clock on Earth ticking slower and slower and slower to infinity.

These predictions are both wrong; see above. We haven't tested them with a clock in intergalactic space, but we *have* tested them plenty with clocks that are far, far out of the gravity well of the Earth (and the Sun), such as those on the Voyager spacecraft and other interplanetary probes. The predictions of relativity, which are as I described above, have always proved to be correct.

 

[Maartenn100]

ok, thank you very much.