[MikeS (OP)]

If, as General Relativity states gravity is curvature of space time then it is not a force.  If gravity is not a force, there is no such thing as a graviton, so why does GR need to be unified with QM?

[Kryptid]

I can imagine that leaving them seperate causes problems.

Take physics at very small scales, for example. Is space-time quantized? Does it come in discrete "packages" or "particles" in a similar way that matter and energy are quantized? If so, then we need a quantum theory of gravity, since gravity is an emergent property of curved space-time. Apparently, there was some experiment not too long ago that demonstrated that neutrons occupy quantized energy states when falling through a gravitational potential.

I think the idea of anything infinite in physics is a sign of a problem, so if we want to think of space-time (and therefore gravity) as being unquantized, then we can imagine a black hole shrinking down to an infinitely small point. It's much "neater" if we can model black hole singularities as having a very small, but finite size (which could once again arise from the assumption that quantization means that there is a "smallest size" of space-time that the singlurity can't shrink below).

[damocles]

The unification of special relativity and quantum mechanics produced Quantum Electrodynamics, which is one of the best tested and most accurate theories in the whole of Physics/Chemistry.

http://en.wikipedia.org/wiki/Quantum_electrodynamics

It clearly makes sense to try to develop and explore this sort of theory in terms of an extension to general relativity, even though intuition suggests that for small-scale effects the change from SR to GR should have little measurable effect. Often there are unforeseen consequences in this sort of thing.

[JP]

If, as General Relativity states gravity is curvature of space time then it is not a force.  If gravity is not a force, there is no such thing as a graviton, so why does GR need to be unified with QM?

This illustrates a problem with interpreting concepts like "force" too broadly across theories. 

In GR, all forces except gravity live within space-time and act to change the energy/momentum of matter.  Gravity itself acts by the curvature of space-time and the laws of motion across space-time.  It lives in the fabric of space-time itself, so it's different from other forces, hence it's not like the other forces.  It can change the energy/momentum of matter as well, so in that sense it is like a force.

Now, one of the things quantum field theory does is to explain that the energy/momentum changes caused by forces are actually the result of the exchange of virtual particles.  So a goal of quantum gravity is to figure out how to do the same for gravity.  It's very difficult because of the unique way gravity is involved in space-time itself.

[JP]

By the way, there are good reasons to explore quantum gravity even if you don't care about describing gravity as a force or finding gravitons.  Right now, we don't know how to describe gravitational effects on quantum objects because we can't describe how quantum objects interact gravitationally with space-time on quantum-sized scales.  There are interesting phenomena that require a description of gravity on tiny scales: the instants after the big bang and black holes, for example.  Whether or not you want gravity to act like the other forces, these are also interesting questions which require GR to be tied together with quantum theory.

[yor_on]

It is also so that we broadly assume SpaceTime to be a 'closed system'. If you do so then you also have to assume that all that exist inside SpaceTime somehow has a relevance for everything else. And there QM behaves very different from what we see macroscopically, so it is important to find a description that connects small scales to the macroscopic. Without it we have two definitions not joining. I agree on it being geometry though, at least macroscopically. Although, if we define gravity as a geometry we still will need a good description for how it behaves at small scales.