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I Can spacetime exist in superposition?

  1. May 22, 2017 #21

    Haelfix

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    Sorry, i'm not clear about the setup here or what sort of approximation scheme we are working in. Talking about semiclassical gravity, the semiclassical spacetime would appear to not be in a superposition at all, b/c by assumption the regime is such that the particle states aren't energetic enough to backreact on the ambient semiclassical spacetime. The particles themselves might be entangled, and note that linearized gravitons propagating in the theory would also be entangled. But where the entanglement lies within the fundamental degrees of freedom that defines the full UV path integral is of course unknown. However I would say your question is more a statement about the inconsistency of keeping a classical spacetime as a fundamental unit, b/c if you include the incredibly weak gravitational field of the particles in the state of the system, you would indeed find that if you could make an objective statement about the gravitational field as required by the classical Einstein equations, you would objectively know whether there was a decay or not of the quantum particle, and that can't be allowed by the rules of quantum mechanics.

    Incidentally the form for the path integral measure you mentioned for regular Einstein gravity, seems to hold as well in string theory, except that 'differentiable manifold's is replaced by 'stringy manifolds' (typically Riemann surfaces when working on the worldsheet or some sort of generalized Stringy geometry when working on the target manifold). Background dependance or independance are typically statements about attempts to 'solve' a given theory, they aren't necessarily statements about the fundamental theories themselves.

    Note that in the LQG case, as well as the AdS/CFT case there is a well defined HIlbert space, and so it's much easier to talk about entanglement. In the AdS/CFT case in particular (unlike any spinfoam model i've ever seen), there is also a well defined dictionary between the bulk semiclassical space and this boundary Hilbert space, so we can ask questions about what entanglement might look like. Please see note 21 (review measures of entanglement in QFTs in note 19 for notation etc) here:
    http://www.hartmanhep.net/topics2015/
     
  2. May 22, 2017 #22

    tom.stoer

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    Thank you; I will check the information you recommend.

    Just for clarification: I am talking about the full theory w/o any approximation. I mentioned the spacetime background used in perturbative string theory only to make clear that this is not what I expect at the fundamental level.
     
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