Gravity Power: What Gives It the Ability to Accelerate Objects?

[harrylentil]

What is the physical property that gravity has that enables it to make an object go faster or, if it is resting on the ground, have weight?

In General Relativity (as I understand it) objects in free fall move in geodesics. Thus an orbiting satellite moves in the curve around the planet that is the geodesic for it given its velocity, etc. If it is in a circular orbit it does not gain or lose kinetic energy (ignoring orbital decay). If it is in any other orbit it gains and loses velocity and its kinetic and gravitational potential energy are constantly rebalanced. It is this latter process whose mechanism puzzles me.

Why does following a straight line in curved space turn potential energy into kinetic energy and vice-versa?

The quantum fields in the standard model each have energy. The gravitational metric field - what is its energy, that it can do these physical things? It is not the whole vacuum energy, as other fields and condensates have a contribution. Please regard that question as part of the whole question in this post. Presumably the gravitational metric field, or curved space-time, must have energy to be physical, and this might be key to its ability to accelerate bodies.

 

[PeterDonis]

What is the physical property that gravity has that enables it to make an object go faster or, if it is resting on the ground, have weight?

Since you have re-posted this question in the relativity forum, you are going to get a different take on it than you got in the Classical (i.e., Newtonian, pre-relativity) physics forum.

From the standpoint of relativity, gravity does not do either of the things you describe. Objects moving solely under gravity are in free fall, feeling no force, feeling no weight, and not changing their motion at all. What causes objects to change their motion and feel weight (force) is something other than gravity acting on them. For example:

The apple "falling" from the tree is actually not accelerating at all; what is accelerating is the Earth's surface. The apple is feeling no force; the Earth's surface is. (Of course the apple does feel a force when it hits the Earth, but that's not what we're talking about here.)

You feel weight when you stand on the Earth's surface because the Earth's surface is pushing up on you, accelerating you, changing your motion from the "natural" motion you would have if only gravity were acting on you.

In General Relativity (as I understand it) objects in free fall move in geodesics.

Yes.

Thus an orbiting satellite moves in the curve around the planet that is the geodesic for it given its velocity, etc.

A curve in spacetime, yes. Not in space. In spacetime the satellite's path is a helix, and is a geodesic in the curved spacetime the satellite is moving in.

Why does following a straight line in curved space turn potential energy into kinetic energy and vice-versa?

First, it's curved spacetime, not space.

Second, when you view things in terms of potential energy and kinetic energy, you are implicitly changing viewpoints from the "natural" viewpoint I gave above. You are treating an object moving relative to Earth (technically, relative to the center of an idealized non-rotating Earth) as having "kinetic energy" that depends on its speed relative to Earth, and an object at some height above the Earth as having "potential energy" that depends on its height. But you don't have to do this to describe the object's motion, and you don't have to treat either of these energies as "real". You can ignore them completely and still make accurate predictions about all aspects of the satellite's motion.

The reason we generally don't do this is convenience: it makes the calculations simpler and makes things conceptually easier in some ways to do things in an imaginary reference frame in which the (idealized, non-rotating) Earth is at rest and motion with respect to the Earth's center counts as "real" motion, and potential energy due to height above the Earth counts as "real" potential energy. But when we do this, we are not figuring out anything about gravity; we are just adopting particular conventions to make the calculations easier. So asking why "gravity" converts potential energy to kinetic energy and vice versa is a mistaken question; gravity isn't doing any of that. We are, by adopting this particular imaginary reference frame for purposes of our calculations.

It's also important to realize that this convention adopted for convenience is not always available. The case of a single, idealized, non-rotating massive body that is spherically symmetric, for which this convention works, is a very special case. Most curved spacetimes in GR do not even admit such a coordinate system, and do not even have a well-defined "potential energy" or a well-defined "center" that we can consider to be at rest, at all.

 

[harrylentil]

Thanks for that. I have a way to go before I understand it. Is this the case? Free fall is not motion because a freely falling object feels no acceleration. Rest on the ground is motion because an object stationary on the ground is accelerating (and feels weight). Will you help me over a big hurdle and explain why the ground is accelerating in all directions but the planet is not thereby expanding?

 

[A.T.]

Will you help me over a big hurdle and explain why the ground is accelerating in all directions but the planet is not thereby expanding?

A mass spinning in a circle on a string is accelerating towards the center, but the string is not getting shorter. So even in classical mechanics accelerating towards a point doesn't imply getting closer to it.

In GR accelerating away from a point doesn't imply getting further away from it. To understand why, look into the difference between proper acceleration and coordinate acceleration.

For a more intuitive view, check out the space-time cone in this video:



The world-lines of constant height are curved, so you experience proper acceleration when advancing along them (green). But they are not "curving upwards" so you don't get further away from the center : see the rolled up version at 1:05 min.

 

[Ibix]

Free fall is not motion

Motion (or not) is relative - you have to specify what it is you are moving relative to. Free fall is, typically, motion with respect to the surface of the Earth, for example. What free fall is not is proper acceleration. Proper acceleration is acceleration you can detect yourself ("proper" here is used in the sense of "one's own", like "property" or if you speak Spanish "propio") if you are locked in a box, because you are pressed against a wall. If you are in free fall you don't get this effect - see astronauts floating around a ship or look up the "vomit comet". If you are not in free fall you will be pressed against a wall (or the floor, typically, as my weary legs will attest today).

 

[PeterDonis]

Free fall is not motion because a freely falling object feels no acceleration.

"Motion" is the wrong word to use; as @Ibix pointed out, motion is relative. Free fall means the object feels no acceleration; that's the only invariant thing you can say about it.

Rest on the ground is motion because an object stationary on the ground is accelerating (and feels weight).

Again, "motion" is the wrong word. "Feels acceleration" is the key thing.

Will you help me over a big hurdle and explain why the ground is accelerating in all directions but the planet is not thereby expanding?

The ground feels acceleration, but that is not the same thing as "accelerating" in the sense of "moving faster". Again, "motion" is the wrong word to use and the wrong way to think about this, at least globally.

Locally, as I said, you can view the Earth's surface as accelerating upward (because it's being pushed upward) towards the apple, and the apple as being at rest (because it feels no force). But this only works locally. There is no way to view the Earth's surface globally as "accelerating upward" or apples in free fall all around the Earth as all "being at rest".

 

[PeroK]

Thanks for that. I have a way to go before I understand it. Is this the case? Free fall is not motion because a freely falling object feels no acceleration. Rest on the ground is motion because an object stationary on the ground is accelerating (and feels weight). Will you help me over a big hurdle and explain why the ground is accelerating in all directions but the planet is not thereby expanding?

Consider this. Two objects, spacecraft say, are at rest relative to each other in gravity-free space. One spacecraft accelerates for a time and then switches off its engines. I.e. stops accelerating and cruises at constant velocity.

The two spacecraft are now in relative inertial motion. But, no experiment will detect any absolute motion of either spacecraft .

So, what has the acceleration achieved? In a sense, acceleration does not result in motion, not in an absolute sense. But, it does imply a change of inertial reference frame.

The spacecraft that accelerated knows that it was changing its inertial reference frame while it was accelerating.

If we now look at the situation with gravity, this may start to make sense. The acceleration of an object on the ground does not imply motion in the upwards direction, but a change of inertial reference frame. While the object in freefall is not changing its inertial reference frame.

Which object is "moving" depends on your reference frame.

In short: proper acceleration does not imply absolute motion. That's the flaw, IMO, with the argument that the Earth is "expanding in all directions".