Thread: Real Gravity vs. Pseudo-Gravity

I'm sorry to make so many topics on this issue. I'm trying to come to terms with GR. My latest confusion is the clock postulate. Apparently the acceleration of other objects does not cause us to observe them to be time dilated beyond the time dilation associated with their velocity. (But there's no time dilation from their acceleration.) If you yourself are accelerating, you will perceive other objects to be time dilated as a result of your own acceleration, however.

However, if you are an observer outside a gravitational field (by which I mean far enough away that the field's strength approximates to zero) looking in, objects inside the gravitational field will appear time dilated to you. So clearly there is a difference between gravity and acceleration. How does one go about understanding this difference? Does anyone know of any good analogies or descriptions?

Doesn't the equivalence principle say that in a closed environment, there is no way to tell the difference between acceleration and gravity without an outside reference.

Originally Posted by kojax

I'm sorry to make so many topics on this issue. I'm trying to come to terms with GR. My latest confusion is the clock postulate. Apparently the acceleration of other objects does not cause us to observe them to be time dilated beyond the time dilation associated with their velocity. (But there's no time dilation from their acceleration.) If you yourself are accelerating, you will perceive other objects to be time dilated as a result of your own acceleration, however.

However, if you are an observer outside a gravitational field (by which I mean far enough away that the field's strength approximates to zero) looking in, objects inside the gravitational field will appear time dilated to you. So clearly there is a difference between gravity and acceleration. How does one go about understanding this difference? Does anyone know of any good analogies or descriptions?

OK, here is my explanation. If you are inside an elevator, whether it is being accelerated by gravity downward or in outer space and accelerated by a continuously applied force, to you there could be no difference since in both cases you are simply being accelerated in a linear direction.

But when looking outside your frame of reference, speeds of objects moving toward the gravitational field, closer to the center of the gravitational field, or moving faster relative to a gravitational field, will appear more time dilated than your reference frame. If you were able to measure the time dilation of an outside object relative to yourself, you still could not determine where the center of gravity was in your field unless you also knew the variation in vector direction of the outside object with yourself, and also could know at least your own or the other objects motion relative to the center of gravity.

So there could be no difference between the affects of gravity or acceleration concerning the person or object itself, but there would be a difference concerning the time dilation, or lack thereof, of exterior persons or objects.

Sound right?

Originally Posted by kojax

Apparently the acceleration of other objects does not cause us to observe them to be time dilated beyond the time dilation associated with their velocity. (But there's no time dilation from their acceleration.) If you yourself are accelerating, you will perceive other objects to be time dilated as a result of your own acceleration, however.

I think it's best to set acceleration aside for a moment, and say if you're moving fast relative to another observer, you see him as time dilated, and he sees you as time dilated. Yes you need to accelerate to be moving fast, but this symmetrical time dilation is the result of relative motion rather than acceleration per se. This is at the heart of the "Twins Paradox", but it's no more of a paradox than two observers separated by distance who each deem the other observer to look smaller than themselves.

Originally Posted by kojax

However, if you are an observer outside a gravitational field (by which I mean far enough away that the field's strength approximates to zero) looking in, objects inside the gravitational field will appear time dilated to you.

The big difference is that two observers both agree that clocks run slower where gravitational potential is lower. The observer at the surface of the earth agrees that your clocks are running faster than his. The time dilation isn't symmetrical.

Originally Posted by kojax

So clearly there is a difference between gravity and acceleration. How does one go about understanding this difference? Does anyone know of any good analogies or descriptions?

It's really simple actually – you cannot transform a real gravitational field away. But IMHO you have to understand the distinction between SR time dilation and GR time dilation first, and then come back to that. IMHO the best way to understand SR time dilation is to imagine that each observer is carrying a parallel-mirror light clock. Imagine you're zooming across space in front of me and I look at your parallel-mirror light clock through my gedanken telescope. I have to pan to do this, which means I no longer notice that the light in your clock is zigzagging relative to me like this /\/\/\/\/\. Instead it looks like it's going straight up and down like this ǁ, and it looks like it's going slower. You can similarly look at the light in my parallel-mirror light clock. For GR time dilation imagine that we have no relative velocity, but that I'm on the surface of a planet whilst you're up in space. We each look directly at the other's light clocks and see the light moving like this ǁ and we both agree that my light is moving slower than yours. In GR the coordinate speed of light varies in a non-inertial reference frame, and that's what we're seeing.

If the universe is limited it seems that the Big-Bang theory is nearly reasonable.
But if the universe is infinite such theory maybe looks like redundant.

Originally Posted by kojax

However, if you are an observer outside a gravitational field (by which I mean far enough away that the field's strength approximates to zero) looking in, objects inside the gravitational field will appear time dilated to you. So clearly there is a difference between gravity and acceleration. How does one go about understanding this difference? Does anyone know of any good analogies or descriptions?

Suppose you're at rest in a uniform gravitational field. It would be impossible for you to distinguish whether you were at rest in such a field compared to being in the absense of a gravitational field but being in a rocket accelerating at the same rate as the local acceleration of the field. In that sense acceleration and gravity are equivalent.