Reconciling Quantum Interactions and Spacetime: Is a Manifold Necessary?

[rustynail]

Hello forum!

I would like to begin by stating that I am no expert in general relativity, nor in physics or mathematics, although I have some basic understanding of calculus and linear algebra. So if you can keep the math simple, I would appreciate. Also, please correct me if I'm wrong.

As I understand so far, tensors are used to describe the curvature of spacetime due to the presence of mass. But this would imply that quantum effects are taking place on a manifold.
My question is the following : Could tensors be used to describe the direction of quantum interactions on a macroscopic scale without the need of a spacetime with it's own geometry in the background?

Thank you for your time.

P.S : If this is in the wrong sub-forum and should be in ''Quantum Physics'', I apologize.

 

[Matterwave]

Tensors exist on a manifold. The manifold in GR is spacetime. If you still want to use tensors, then you have to have a manifold. You could replace the spacetime manifold with something else if you want, but as long as you want tensors around, you need to have a manifold.

If you want to try to formulate a quantum gravity without a manifold, then you will be without tensors. Nobody says that this is impossible. Nobody has found a consistent and compelling theory of quantum gravity yet, so I don't think we can rule things out at this point.

 

[robphy]

Possibly interesting reading:

"Einstein Algebras" by R. Geroch (CMP, 1972)

http://projecteuclid.org/DPubS?verb...e=UI&handle=euclid.cmp/1103858122&page=record

 

[rustynail]

Thank you robphy! Very interesting indeed.