by XVX » Tue Oct 17, 2006 7:19 am
The fundamental difference is that QM is quantitized indeterministic and GR is continuous deterministic.
One might say that the continuous nature of GR is because the quantization is so finely spaced, we don't notice it. This is "second quantization" where you quantitize a continuous field into a quantum field theory.
This has been done and that is how they postulate the graviton. If the graviton exists, then QM wins and Einstein is wrong.
If QM wins, then the gravitational force is determined by bosons (gravitons) just like all other quantum field theories. Which means that Einstein's "interpretation" of spacetime geometry determining the gravitational force........is wrong. The success of his theory, almost being reduced to "amazing coincidence".
The theories cannot both be correct. They have ENTIRELY different explanations of the same phenomena. Either spacetime is smooth and continuous as Einsteins Equations predict or its a bubbling sea of gravitons that are quantum mechanically created and annihilated, causing the gravitational force.
What Einstein did was pure genius and quantum field theory has yielded the most accurate results ever. They both stand high on the pedestal and at least, one is wrong.
I tend to think that the graviton is false and thus quantization of Einsteins field equations is inappropriate, since they are nonrenormalizable unlike the EM equations.
QFT has its version of the "Ultraviolet Catastrophe" that becomes very important at high energies, causing the nonrenormalization. This is where string theory comes in and tries to make the connection between QM and GR.
While I tend to think string theory has gotten carried away, this is definitely where new physics will be found.