Quantum Gravity

[ydoaPs]

In Quantum mechanics, position is an operator while time is just a parameter. In Quantum Field Theory, time and position are both parameters.

 

For a successful Quantum Gravity theory, shouldn't space and time be operators? Have there been any notable attempts at a quantum theory with space and time as operators instead of parameters?

[Riogho]

LQG is the best bet right now.

 

String Theories are basically screwed as they agree completely with SR, and are background independent anyways.

 

It'd be real nice to have a fresh new idea pop up sometime though.

 

Start thinkin'!

[ajb]

That is a problem. In any canonical approach one needs to cut space-time into space and time. This is the origin of the problem. Time usually plays a distinguished role. Even in quantum mechanics, time is not a hermitian operator.

 

That is why path-integrals are the best way to proceed with a relativistic quantum field theory.

 

Something related you might be interested in is multisymplectic geometry. It is the geometric setting for covariant Hamiltonian field theory. The idea being to formulate a classical theory with does not use the space-time cut. However, as far as I know due to the issues with Poisson brackets no canonical or deformation quantisation procedure exists.