# Does General Relativity actually explain gravity?

1. Dec 8, 2011

### nhmllr

So the principle of equivalence states that any effects due to acceleration must also occur with gravity, as it's impossible to tell the two apart. I get that, but it assumes that gravity exists and you know how much it accelerates objects.

But that explanation just predicts what will happen in a gravitational field, which is fine and dandy, but I keep hearing over and over that GR "explains" gravity which I don't see happening.

This might just be some language thing but I need to know

Thanks

2. Dec 8, 2011

### PAllen

Explaining gravity is too much of an expectation. I would say what Einstein accomplished was to replace two disconnected laws with one. Instead of the law of inertia (unless acted on by some force, objects travel in a straight line) and Newton's law of gravity, there is only a modified law of inertia: objects not subject to force travel on the straightest possible line in spacetime. A bit more could be said to be accomplished: having derived his field equations explaining how mass/energy connects to spacetime geometry, it turns out the the modified law of inertia can be derived; it is not needed as a separate assumption or law. Thus, ultimately, both the law of inertia and the law of gravity are replaced with a set of equations relating mass/energy and spacetime geometry.

3. Dec 8, 2011

### PatrickPowers

I have read that GR assumes inertia and derives gravity. But I don't know how and take it on faith.

It IS possible to tell real-world gravity from ordinary acceleration by tidal effects and such things, but from the point of view of GR the difference is not significant.

4. Dec 8, 2011

### PatrickPowers

You seem to be saying it is also possible to assume gravity and derive inertia.

5. Dec 8, 2011

### PAllen

Yes. This was first done by Einstein, Infeld, and Hoffman in the 1940s, and by numerous more rigorous methods in the decades since. The geodesic equation of motion for test bodies (which encompasses both the Newtonian law of gravity and the law of inertia) can be derived from the Einstein field equations relating mass/energy to geometry. Since the 1940s, it is no longer considered an independent assumption in GR.

6. Dec 9, 2011

### tom.stoer

It depends what you mean by "explain".

A physical theory is a mathematical model (equations + rules how to apply them) from which certain predictions can be derived which are subject to experimental verification or falsification.

In that sense Newtonian physics "explains" gravity via the equation F ~ mM/r².

This model has several shortcomings, e.g. it is not compatible with SR (finite, universial speed of light), it cannot correctly predict bending of light rays (near stars, gravitational lensing), it does not predict perihelion precession, it does not predict gravitational waves etc.

Einstein introduced a new model using 4-dim. pseudo-Riemannian manifolds plus two equations (the Einstein field equations, the equation for geodesics) again "explaining" gravity (this new theory contains Newtonian gravity in a certain limit).

But again "explain" means nothing else but to have a model which predicts physical phenomena. The model itself cannot be explained.

7. Dec 9, 2011

### Staff: Mentor

Well said. GR explains gravity, but it doesn't explain itself.

8. Dec 9, 2011

### Naty1

ditto on the last two posts.

So Einstein gave us some additional insights, for example linking space and time with gravity and energy and pressure with gravity, but not a final and complete description of gravity. Two remaining voids that come to mind: Gravity has not yet been incorporated in the standard model of particle physics; Quantum theory seems incompatible with the Einstein description of space and time.

The effort to combine these in a single theory is underway but incomplete: quantum gravity.

9. Dec 9, 2011

### harrylin

It's certainly a language thing and no explanation is total; moreover, the equivalence principle only concerns phenomena (appearances).

However, GR does more than using the equivalence principle and giving a set of equations, it's definitely a field theory. This implies that there is no immediate action at a distance but instead gravitational actions are local, due to the properties of space. In other words, there has to be something acting in "empty space" that determines the local speed of light and the acceleration of objects. It's hard to deduce much more with our limitations to observe, and it's not customary in modern physics to speculate on what cannot be measured.

A rather well-known exception on this is Einstein's Leiden inauguration speech, in which he did elaborate on what we may logically infer from GR:
http://en.wikisource.org/wiki/Ether_and_the_Theory_of_Relativity

Last edited: Dec 9, 2011
10. Dec 9, 2011

### Fredrik

Staff Emeritus
By my terminology, GR provides a definition of the term "gravity". Newton's theory provides another. If we use the latter definition, then GR can be said to "explain gravity", because it explains why Newton's theory works so well. If we use the former definition, then GR doesn't "explain gravity". It just makes predictions about how things will move. To be more precise, it describes exactly how things would move in a general relativistic universe, and the description can be interpreted as a prediction (assumed to be approximately correct) about how things will move in our universe.

When "gravity" is defined by GR, the only thing that can "explain gravity" would be a new theory that makes better predictions about motion than GR. Such a theory would explain why GR works so well, but it would also give us a new definition of "gravity", and if we use it, then we would need another new theory to "explain gravity".

Last edited: Dec 9, 2011