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A few thoughts on entanglement

  1. Jan 5, 2006 #1
    These are probably old ideas (or, perhaps, just stupid), but recently thinking about non-locality it seemed to me that

    (a) non-locality clearly shows that time's arrow IS invariant. Physics texts often point out that if you were to make some kind of movie of a physical event such as the collision between two particles, and play it backwards, that the resulting 'backwards' movie would be equally plausible from a physical viewpoint.

    Thus, a photon being absorbed by an atom can be played 'backwards' as a movie and then we will see an atom spontaneously emit a photon; an entirely plausible physical event.

    Taken further, it has often been proposed that antiparticles can be seen as time-reversed particles. A movie of a positron played backwards shows the path of an electron, for example.

    But it occurred to me the other day that entanglement provides a truly non-reversible phenomenon. Consider two photons initially produced in an entangled state such as by an atomic cascade transition. Then these two photons separate in spacetime. Subsequently, measurements are made on one or both photons, (e.g by passing them through a pair of opposed polarisers), destroying their entanglement.

    Reversing this process, we would see two photons, spacetime separated, passing through a pair of polarisers, and becoming spontaneously entangled, something which, as far as I know, is physically impossible. Entangled particles are produced at a single point in spacetime and subsequently become spacetime-separated, but not the converse.

    (b) At the time of the big bang, the universe as we know it was 'contained' (if that is a meaningful concept) within a tiny area. Since at the energies involved, all particles must have existed as bosons, in order not to violate the Pauli exclusion principle, is it not possible that they also existed as a single, entangled, wavefunction.

    At some point during the subsequent expansion, this wavefunction decohered, but not before the radius of the universe reached some finite value. Does this not explain the subsequent homogeneity of the resulting mass distribution within the universe without recourse to 'inflation', which seems a dubious hack, with no plausible physical mechanism.

    (c) Since all particles in the current universe once occupied a minute volume of space, presumably non-locality demonstrates that there are indeed more than four dimensions but that, as postulated by string theory, some of these are 'compactified', presumably to the Planck length or thereabouts.

    If so, this implies that, in principle, the collapse of a wavefunction comprising two entangled particles, while clearly propagating (if that is the right word) much faster than c, might still not be infinitely fast, if these extra dimensions are finite in size.
     
  2. jcsd
  3. Jan 6, 2006 #2
    nice thought! :)
     
  4. Jan 6, 2006 #3

    DaveC426913

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    Interesting ideas. I like where you're going. Some thoughts:

    My little understanding of entanglement tells me that two particles, merely by their interaction with each other become, by definition, entangled, since they can no longer be fully described without reference to the other. So, the two particles, coming from separate locations (in the time-reversed movie), collide at one spot, and thus become entangled. How is this not consistent?


    Well, there WERE no particles (no matter at all) until the universe was big enough and cool enough for matter to condense from pure energy.
     
  5. Jan 9, 2006 #4

    vanesch

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    This is because the standard "measurement interaction" in quantum theory is NOT time-reversible (after all, a probabilistic PROJECTION can not be undone 1-1). But we know that there are a lot of paradoxes concerning this projection (it doesn't correspond to a unitary operator, it is non-local, and all the mess you want).

    When you look upon things in a MWI context, using ONLY unitary interactions (including measurement), then the process becomes entirely time-reversible. The reason is that the entanglement is not destroyed, but is now simply in the observers:

    |obs1>|obs2> (|a>|b> + |c>|d>) will have evolved into:

    |obs1a>|obs2b>|a>|b> + |obs1c>|obs2d>|c>|d> through a unitary evolution operator, which is reversible (by definition, a unitary operator is reversible).

    cheers,
    Patrick.
     
  6. Jan 11, 2006 #5
    This is not quite right. There is a perfectly good way of describing things in which this does not happen. The point is to notice that there is an isomorphism between preparations and measurements in quantum theory, so we can obtain a perfectly retrodictive formalism by interchanging their roles. In this case, the polarization measurements become preparation devices, which always produce a product state. The preparation of an entangled state becomes a Bell-measurement, and then we postselect on obtaining a particular Bell-state. The statistics of this are exactly the same as those of the original experiment, so it is a perfectly good way of describing the time-reversal, which does not involve the spontaneous production of entanglement at spacelike separation.
     
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