Reconciling Quantum Interactions and Spacetime: Is a Manifold Necessary?

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Discussion Overview

The discussion centers around the relationship between quantum interactions and the necessity of a manifold in describing these interactions, particularly in the context of general relativity and quantum gravity. Participants explore whether tensors can be utilized to represent quantum effects without relying on a geometric background of spacetime.

Discussion Character

  • Exploratory, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions whether tensors can describe quantum interactions on a macroscopic scale without necessitating a spacetime manifold.
  • Another participant asserts that tensors are inherently linked to manifolds, particularly in general relativity, and suggests that if one wishes to use tensors, a manifold is required.
  • This participant also notes that formulating a theory of quantum gravity without a manifold is not ruled out, but emphasizes the current lack of a consistent theory in this area.
  • A third participant shares a reference to literature that may provide additional insights into the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of a manifold for the use of tensors in describing quantum interactions. There is no consensus on whether a manifold is essential or if alternative formulations could exist.

Contextual Notes

Participants acknowledge the complexity of the topic, with one expressing a desire for simpler mathematical explanations and the potential for varying interpretations of quantum gravity theories.

rustynail
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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.
 
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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.
 
Thank you robphy! Very interesting indeed.
 

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