# Interpretation of GR

1. Jul 17, 2006

### kvantti

Is it justified to state that GR is "just" a geometrical theory to calculate the paths of objects in spacetime?

Just because GR states that "gravity is a property of spacetime itself" doesn't necessary mean that spacetime is curved; just that the paths of objects in spacetime are curved in a gravitational field.

What I'm after is that as we all know, GR is just an approximation of the yet-to-be-discovered quantum theory of gravity, which might not deal with the "geometry of spacetime" at all.

2. Jul 17, 2006

### robphy

Your statement only describes the kinematical aspect of GR... how the geometry determines the geodesics.
Another aspect [via the field equations] is that [Ricci] curvature is related to the local matter density.... figuratively, "matter tells spacetime how to curve". The gravitational field is dynamical.

There are two notions of curvature in this passage.

"A spacetime path is curved" means that the path is not a spacetime geodesic... it has a nonzero 4-acceleration... it is being influenced by something nongravitational. Free particles are inertial and travel on geodesics (with zero worldline curvature).

"A spacetime is curved" means that the Riemann-tensor is not everywhere zero. This means that geodesics may be focusing... figuratively, initially parallel lines may intersect.

Now, it may be that you are trying to suggest that, for example, particle motions are curved in some higher-dimensional noncurved spacetime.

It may be that the geometric interpretation may be applicable only on classical scales, and may be inappropriate at the small scales.

3. Jul 17, 2006

### pmb_phy

This question is rather easy to address since Einstein himself addressed this question. In a letter to Lincoln Barnett on June 9, 1948 Einstein wrote
Steven Weinberg said something similar to this in his GR text.

Pete

4. Jul 17, 2006

### pervect

Staff Emeritus
As I've remarked in other threads, if you have a space-time, AND the usual metric, you can calculate a mathemetical entity (the curvature tensor) which shows that the space-time cannot be flat.