# Is gravity a force, or the curvature of space?

1. May 24, 2013

### Thomas1989

After some light reading, I'm more confused than ever. Is gravity just a byproduct or effect of the curvature of space? Is it a force that would exist if space didn't curve, even in the presence of mass? (probably a stupid question, sorry!)

I've seen various diagrams of the earth revolving around the sun in a sort of 'curved space bowl' if that makes sense. I understand how these 2 could effect each other, but why is Andromeda moving towards us then? Is it because of gravitational pull? That's what I've been led to believe, but some sources are telling me gravitational pull doesn't even exist, and that it's a consequence of the curvature of space (not some independent, omnipresent force)

Cheers,
Tom

2. May 24, 2013

### Staff: Mentor

Forget that "curved space bowl" analogy because it does more harm than good - if you want a non-mathematical visual image that will help you understand, search the relativity sub-forum for member A.T.'s really excellent video clips.

And with that said, gravity as a force and gravity as a curvature effect are two different mathematical treatments of the same physical phenomenon. It's like the centrifugal force that pushes you sideways when you're driving a car very fast around a tight curve; we could say that there's a force pushing you towards the outside of the curve, or we could say that inertia is just trying to keep you moving in a straight line while the car is forcing you inwards onto the curved path.

The first description (there's a force) is the classical Newtonian model. The second is the model of Einstein's general relativity. Where they're both applicable, they agree (of course!) but GR works in a number of situations where classical theory doesn't.

3. May 24, 2013

### yenchin

As Nugatory said, "force" and "curvature" are *mathematical* models/constructs used to model *physical phenomena*. Deep down, if you ask, what gravity really is, I am afraid no one would be able to give you the answer. For example, there exists other geometrical formulations of general relativity that does *not* involve any curvature, but they have other geometrical quantities like torsion, but at the physical level they are equivalent to standard general relativity [I am talking about the Teleparallel Equivalent of General Relativity (TEGR)]. In other words, gravity can be modeled by various mathematical models, as long as the models give correct physics that conform with experiments, they are all "good".

4. May 25, 2013

### WannabeNewton

The geometry of space-time serves as both a descriptor of gravitation and the backdrop on which other fields can propagate and on which particles can follow paths, all of these roles dynamically affecting the other. For this reason, the metric tensor which describes this geometry (and allows one to calculate the various curvature quantities of interest) is usually called a dynamical quantity, but keep in mind that there is no one curvature quantity that solely describes gravitation. As for your second question, space-time must curve in the presence of mass-energy distributions and as far as GR is concerned, it is not a force (this is a consequence of the strong equivalence principle).

5. May 31, 2013

### phildukephd

How gravity works and why it works as it does are two different questions. I am very pleased by Wannabe Newton's Post, it is all excellent, and I especially like the statement "...it is not a force..." Of historical interest, in Sir Isaac's Letters to Bentley he stated clearly that he did not believe in action at a distance.

6. May 31, 2013

### Staff: Mentor

Curved spacetime is just another way to represent a force which is proportional to inertial mass. Newtonian gravity can be expressed geometrically also.

7. May 31, 2013

### pervect

Staff Emeritus
Gravity can be thought of as the curvature of space-time in classical General Relativity.

People often forget about the 'time" part - but it's very important!

Note that there is *some* pure spatial curvature. Loosely speaking, you can think of space-time curvature as a unified way of viewing the following effects, all wrapped up in one neat mathematical package:

1) The traditional "Newtonian" force idea (as an excellent approximation).
2) Magnetic like gravitational "forces" that bear somewhat the relation to gravity that magnetism does to the electrostatic Coulomb force. These tiny effects cause frame draggig (as observed on the recent gravity probe experiments).
3) Gravitational time dilation
4) Spatial curvature - the "bowl" effect, that causes extra deflection of light, the Shapiro effect, and which influences (though is not the only explanation for) Mercury's perihelion precession.

If you'll look around the forums, you'll see explanations of "geodesic deviation", which might give you a better idea as how space-time curvature causes what appear to be at first glance "forces".

You can also see how the force concept does NOT directly cause effects 3 and 4 - "forces" don't cause time dilation, nor do they cause spatial curvature, not unless you add something extra to the concept.