# Gravity and Speed

*Most recent answer: 10/22/2007*

Q:

If you cant go faster then the speed of light explain this:
If you had a mass near a planet or sun or whatever (somthing with gravity) and that mass was attracted to it it would continue to accelerate eventuly going past the speed of light
Would this work?

- James

U.S

- James

U.S

A:

Nope. The speed limit applies to the motion of an object as seen by
another which it is passing by. It applies under all circumstances that
we know of.

You are asking about something else- the speed assigned to the object by some remote viewer back where the object was coming from. It would seem like very strong gravity could make the object speed up to greater than c. Your sense that something odd happens is right. Gravity, it turns out, is not best described as a force within Euclid’s space but rather as an effect on the geometry of spacetime itself. A very massive compact object creates a black hole, a region of spacetime from which no objects can depart. That’s pretty weird, but it’s not the same as beating the speed limit in the ordinary sense.

Mike W.

General relativity starts with the idea that small bits of spacetime act as ordinary, "flat" spacetime where the effects of gravity are small. It turns out that there is no set of flat Lorentzian coordinates which works over large pieces of spacetime when gravity is allowed. So the speed limit of special relativity, when written in GR context, is that nothing can fly past something else at a speed which exceeds c. But if you are comparing relative speeds of objects that are separated by large distances or large times, the gravitational warping of space can make your statements about their relative speeds different.

The universe is expanding, and if it is uniform on very large scales (and it seems to be), then galaxies and stars that are beyond our horizon are indeed moving away from us at a speed faster than the speed of light in our coordinates. But nothing about them lets them move faster than the speed of light in their local coordinates. A description of this is provided in this which is fortunately available online at least for the moment. It’s in the March 2005 Issue.

Tom

You are asking about something else- the speed assigned to the object by some remote viewer back where the object was coming from. It would seem like very strong gravity could make the object speed up to greater than c. Your sense that something odd happens is right. Gravity, it turns out, is not best described as a force within Euclid’s space but rather as an effect on the geometry of spacetime itself. A very massive compact object creates a black hole, a region of spacetime from which no objects can depart. That’s pretty weird, but it’s not the same as beating the speed limit in the ordinary sense.

Mike W.

General relativity starts with the idea that small bits of spacetime act as ordinary, "flat" spacetime where the effects of gravity are small. It turns out that there is no set of flat Lorentzian coordinates which works over large pieces of spacetime when gravity is allowed. So the speed limit of special relativity, when written in GR context, is that nothing can fly past something else at a speed which exceeds c. But if you are comparing relative speeds of objects that are separated by large distances or large times, the gravitational warping of space can make your statements about their relative speeds different.

The universe is expanding, and if it is uniform on very large scales (and it seems to be), then galaxies and stars that are beyond our horizon are indeed moving away from us at a speed faster than the speed of light in our coordinates. But nothing about them lets them move faster than the speed of light in their local coordinates. A description of this is provided in this which is fortunately available online at least for the moment. It’s in the March 2005 Issue.

Tom

*(published on 10/22/2007)*

## Follow-Up #1: Faster than c beyond the horizon?

Q:

I would reproduce what has been said above
"galaxies and stars that are beyond our horizon are indeed moving away from us at a speed faster than the speed of light in our coordinates."
Now my question is:-
If the speed of light in our coordinate system is constant 'c', then how come galaxies and stars that are beyond our horizon moving at a speed faster than 'c' in our coordinate system.

- Indrajit

New Delhi

- Indrajit

New Delhi

A:

There is an old saying, "Out of sight, out of mind" that is relevant in this case. Since "beyond the horizon" means just that, you can't see past the horizon to measure any speed or anything at all. So the question of whether or not there exist things exceeding the speed of light out there is meaningless.

LeeH

I'm not sure it is exactly meaningless. Conceivably, some unlikely cosmological change would bring things back in from outside the horizon. Then we could try to describe their hypothetical past. In practice, it won't happen, so Lee is certainly right that we won't observe the answer. Mike W.

LeeH

I'm not sure it is exactly meaningless. Conceivably, some unlikely cosmological change would bring things back in from outside the horizon. Then we could try to describe their hypothetical past. In practice, it won't happen, so Lee is certainly right that we won't observe the answer. Mike W.

*(published on 06/04/2010)*