Non-local manifold

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Is it possible to create a non-local manifold that co exist with the spacetime manifold? The non-local manifold being where quantum correlations took place. How do you make the two manifolds co-exist?
 

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  • #2
andrewkirk
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What do you mean by a 'non-local manifold'?

Certainly the spacetime manifold can be embedded in manifolds with sufficiently higher dimensionality. In fact, infinitely many spacetime manifolds can be thus embedded in the same higher-dimensional space.
 
  • #3
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What do you mean by a 'non-local manifold'?

Certainly the spacetime manifold can be embedded in manifolds with sufficiently higher dimensionality. In fact, infinitely many spacetime manifolds can be thus embedded in the same higher-dimensional space.
A manifold where c is not the limit.. to account for possible quantum correlation channel.. so how do you embed manifolds where c is the limit to one where c is a billion times the limit?
 
  • #4
PAllen
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A manifold has no geometric content, only topology. You can equip a given manifold with many different metrics, giving it different geometries. Normally, Newtonian physics is considered to be defined by a fiber bundle rather than a manifold with metric because there is no non-degenerate metric. The most famous embedding results are about isometric embedding of arbitrary lower dimension Riemannian manifolds in higher dimensional manifold with Euclidean metric.

Relativity has a pseudo-Riemannian metric. The signature (not all +) is what gives an invariant speed.

So, it seems you are asking about ways of embedding a pseudo-Riemannian manifold in a fiber bundle (or a manifold with degenerate metric of a certain type). I have not heard of any results of this kind. Perhaps someone else can answer this re-phrased question, if it is representative of what you are after.
 

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