Gravity and acceleration

[Enola Straight]

According to Einstein, geavity and acceleration are the same thing.


If I am in a fast car and really punch it, accelerating forward at 1g, I can see where I'm accelerating to.

If I lay down flat on the grass and look straight up, which way am I accelerating?

[Surlethe]

Here's a different statement of the principle: being at rest in a gravitational field is indistinguishable from being at rest in an accelerating frame of reference. The opposite holds true: free fall in a gravitational field is indistinguishable from being at rest.

For example: suppose you are in an elevator that is an incredibly smooth ride. How can you tell that the elevator is at rest in the Earth's gravitational field instead of accelerating upward at 9.8 m/s/s in outer space? Once you're in the elevator, there is no way of conducting a test that can tell the difference. Similarly, if the elevator cable snaps, how do you know that you're falling instead of simply sitting in outer space at rest (or at a constant velocity)?

To your question: under Einstein's formulation of general relativity, when you are lying on your back, you are actually accelerating upward at 9.8 m/s/s. This is because space is not Euclidean, but curved; thus, a "straight line" is one in which you are in gravitational free-fall. In terms of GR, you are actually in an accelerated reference frame, with the force of the ground pushing on you accelerating you.

[Darth Wong]

According to Einstein, geavity and acceleration are the same thing.


If I am in a fast car and really punch it, accelerating forward at 1g, I can see where I'm accelerating to.

If I lay down flat on the grass and look straight up, which way am I accelerating?

If you sit in a train with no windows and it accelerates at 1g, what do you see? You see the interior of a train. It's not moving closer to you, nor is it moving farther away. Yet you feel a force pulling you back into your seat, don't you? Much as you feel a force pulling you toward the ground?

[Kuroneko]

Despite being more than adequately answered, I think this could use some elaboration...

According to Einstein, geavity and acceleration are the same thing.

Well, yes, but with an important qualifier of this being the case only locally. That's why, as in the previous poster's examples, thought experiments regarding a smooth acceleration always mention sealed and windowless trains or elevators, etc.--if one is allowed to look at one's surrounding environment, be it the ground or astronomical bodies or whatnot, it typically becomes obvious whether the acceleration is caused by gravity or an engine. Thus, the principle of equivalence is not that is that they are physically indistinguishable in all cases (this would be silly), but only over small spatial and temporal intervals. In particular, acceleration related to rotation/centrifugal force is particularly easy to distinguish from gravity given "large enough" intervals of spacetime even if there are no convenient astronomical bodies nearby.

If I am in a fast car and really punch it, accelerating forward at 1g, I can see where I'm accelerating to. If I lay down flat on the grass and look straight up, which way am I accelerating?

Good question, and Surlethe's answer is right on the dot, but just to elaborate on the physics: because when one doesn't feel one's own weight when in freefall, freefall frames of references are actually inertial, i.e., unaccelerated (this is actually a reformulation of principle of equivalence). So, to ask where you're accelerating to, let's restate: if there is an inertial (freefalling) observer right beside you, what will your trajectory look like in that reference frame? You will appear to be accelerating upward, of course, although you might prefer to say that you are stationary and that the observer is going downward. Hence, you are actually accelerated upward in that scenario.

It may be counter-intuitive at first, but GTR reverses the usual expectation: an object in freefall is inertial, while a stationary object in a gravitational field is accelerated. Just like rotating reference frames have a fictitious "centrifugal force", according to GTR the "force of gravity" is a similarly fictitious effect of having an accelerated reference frame. And just like with centrifugal force, we can transform our coordinates to make it disappear, we can do the same with gravitational force. There is a significant difference, however, in that, as per above, we are can only make it disappear "locally".