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Quantum tunneling from nothing

  1. Mar 13, 2015 #1
    General Relativity allows a potentially infinite number of spacetimes that are inaccessible to each other (except perhaps at the event--presumably lacking either duration or extent because of its instantaneity-- of their formation), as far as I can recollect from my sketchy reading of Sklar's analysis of GR (-his book called "Space, Time, and Spacetime"). False-vacuum inflation seems to have taken it over the version known as chaotic inflation, per the Planck Satellite group's intro to their data release earlier this year.

    However, Guth and Vilenkin both describe a problem getting the false-vacuum bubble (the volume acting like a vacuum which isn't quite the lowest-density vacuum possible) into our spacetime from wherever/whenever it originates, due to its tendency to collapse into a black hole under its own externally-attractive gravity. (Its interior is filled with the repulsive gravity that accounts for inflation, i. e., exponentially accelerated expansion.) Both overcome this by quantum "tunneling", which I understand to be a change not requiring either physical or temporal motion. Vilenkin calls his version "quantum tunneling from nothing", which he claims is allowed by well-established principles of QM.

    I know that inflation tends to lead into a multiverse where innumerable replicas of myself occupy innumerable replicas of my observable region, but the person I call "Continuous/Contiguous Me" is distinct from its replicas, and doesn't consider that anything that happened longer ago than it took electromagnetism to cross C/CM's synapses exists. So I'm wondering whether the "nothing" Vilenkin visualizes could be physically interpreted as "the past", or (equally well) as "the future". Sorry for all the detail, but I'm hoping it will help people with a clearer knowledge of physics tell me just why it might or might not be.
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  3. Mar 13, 2015 #2


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    In the context of GR, this isn't really a meaningful statement. GR is not a model of a single "multiverse" with a lot of different spacetimes in it that may or may not be connected. It is just a framework for constructing many individual models of individual spacetimes. In GR terms, a "multiverse" is just one single spacetime; it may have different parts that we label as different "universes", but that's a matter of labeling, not physics. Physically, a multiverse is one spacetime in GR terms.

    That's not really what they're describing, as I understand it; as I understand it, they're talking about problems with how the transition from false vacuum to "true vacuum" (what our universe has now) is induced. The transition itself does not "move" anything from one spacetime to another; in spacetime terms, the transition is just a particular region (or regions) of spacetime in which certain parameters are sharply changing value. But I would need a specific reference to a paper or discussion by Guth and Vilenkin to know for sure whether or not my understanding is correct.

    At the quantum level, "motion" itself is not really well-defined anyway. You don't have objects moving; you have wave functions or quantum fields that take different values at different spacetime points. "Tunnelling" is just a label for a certain kind of configuration of wave functions or quantum fields, driven by a certain kind of potential (which is a term in the equation to which a wave function or quantum field distribution is a solution).

    This is too strong, isn't it? Everything in the past light cone of C/CM can also be considered to "exist", can't it? Or perhaps to "have existed"--are you just trying to draw a distinction between "present" and "past"?

    Since any "quantum tunnelling" event or region that produced our current observable universe would be in the past light cone of us here on Earth today, it could be considered as part of our past. But it couldn't be part of our future, because that region of spacetime is not in our future light cone.
  4. Mar 13, 2015 #3
    Thanks; the clarifications on terminology are very helpful, and the exclusion of "the future" as a possible equivalent of Vilenkin's "nothing" makes it more intuitively comprehensible (-for instance, compatible with the possibility that our reality is a simulation).

    Vilenkin's initial mention of his "quantum tunneling from nothing", in his popularization "Many Worlds in One", is currently visible through "google books" online, on its p.180. It does, however, seem to refer to the initial appearance of the false vacuum (as does Guth's mention of the problematic collapse of the false-vacuum bubble, in the "Creation of Universes" chapter of his own popularization, the book "The Inflationary Universe"), rather than those local endings of inflation which result in such "pockets" (to use Guth's term) or "islands" (to use Vilenkin's) as our own "local universe".

    Please add or elaborate if you all feel like it. I may not get another chance to look at it before Monday. Thanks again.
  5. Mar 13, 2015 #4


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  6. Mar 15, 2015 #5
    PeterDonis asked whether I was trying to draw a distinction between the present and the past, but that wasn't actually my purpose; rather, I was trying to establish whether physics allows an endless sequence of recurrent multiverses, or of recurrent universes (if, as Chronos mentions, the multiversal version of the inflated cosmos is not the correct one ), each with its own past and future light cones (or, if the multiverse is the correct version, its own set of past and future light cones).

    It seems to me that this would be possible if the "nothing" from which the false vacuum tunneled would equate to a phenomenological present (or, much more probably, to some combination of phenomenological presents) no longer extant, at least on its original scale. (The phenomenological present, in differing examples each being experienced by one or another of the multi-celled beings like ourselves, would presumably be larger than the infinitely thin physical present, because it extends over the span traversed by electromagnetic signals within each being during the time it takes to traverse them: I'm guessing that the integration of any one of them with the spacetime of physics would be "fiendishly complicated", and would be more-or-less the holy grail of biology.)

    The elaboration of any views to the contrary would be much appreciated.
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