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I Can spacetime exist in superposition?

  1. Mar 15, 2017 #1
    It's well known that a single particle can exist in superposition, but what about the gravity of the particle? Is the gravity also in superposition? I suppose this makes it difficult to write a wavefunction, since we can't express it in terms of a field over a single spacetime. But what if we naively just assume that gravity is never in superposition and we simply calculate the stress energy density directly from the smeared out wavefunction? What problems would that cause?
     
  2. jcsd
  3. Mar 15, 2017 #2
    I guess a serious problem is that a wavefunction collapse can't be treated covariantly as an event in spacetime. If we have a particle that passes a slit and hits a screen, the wavefunction spreads out as it passes the slit, but then collapses to a small region on the screen, and we don't know where this collapse actually occurred in spacetime.
     
  4. Mar 16, 2017 #3
    You are trying to marry a quantum object (particle) to a classical one (GR gravity). That's probably why it does not work.
     
  5. Mar 17, 2017 #4
    This is fun to think about. It really forces you to try and understand, "what is spacetime?", "what is curvature?", "What is a distance?"......

    Space-time is a structure we can use to organize distances between events. These distances define the communication time associated with the two points. This makes me wonder, if you were just given a collection of N nodes along with the distances between each node, could you determine curvature? Could you determine dimensionality?

    With two nodes (or points, whatever you want to call them), you only have one distance, and dimensionality or curvature can't be determined from that alone.

    Makes sense to me for there to be superpositions of distances between things.
     
  6. Mar 24, 2017 at 6:07 AM #5
    I don't know the details, but Hawking was doing something called "summing over histories" where he applied QM principles to curved spacetime. He tried to show this way that some singularities cancel out.

    So yes, there are theories where spacetime can be superposed (added).
     
  7. Mar 24, 2017 at 1:53 PM #6
    I should also say, that Wheeler's superspace is more easily thought of in superpositions than spacetime. Go ahead and look that up.
     
  8. Mar 24, 2017 at 2:18 PM #7

    mfb

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    Probably. If an object is in superposition between two states, a nearby particle should couple to it via gravity, and become part of this superposition. Such an experiment would require a relatively large mass kept in a large macroscopic superposition for a long time - and that is very challenging. Current setups cannot avoid decoherence long enough for such an experiment.
     
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