Interpreting GR: Is Spacetime Geometry Necessary?

[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.

 

[robphy]

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

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.

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.

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.

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.

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

 

[pmb_phy]

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.

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

I do not agree with the idea that the general theory of relativity is geometrizing Physics or the gravitational field. The concepts of physics have always been geometrical concepts and I cannot see why the g_ik field should be called more geometrical than f.i. the electrodynamic field or the distance between of bodies in Newtonian Mechanics. The notion comes probably from the fact that the mathematical origin of the g_ik field is the Gauss-Riemann theory of the metrical continuum which we are won't to look at as part of geometry. I am convinced, however, that the distinction between geometrical and other kinds of fields is not logically founded.

Steven Weinberg said something similar to this in his GR text.

Pete

 

[pervect]

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.

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.

See the https://www.physicsforums.com/showthread.php?t=123922"

thread for more discussion. Note that it IS possible to make such redefintions of the metric and get useful theories - one has to take some extra steps to insure Lorentz invariance when one plays with the metric in this manner, because invariance of the Lorentz interval is no longer automatic if the Lorentz interval is not given by the metric.