• apokrisis
    The cosmological principle states that each constant-time hypersurface of the universe ('this spacetime') is homogeneous and isotropic at the large scale.andrewk

    Aren't you neglecting that the matter density must be uniform? You have to count the contents too. Spacetime won't be flat unless the matter is presumed to be evenly spread.

    .The Wiki article on the cosmo principle does note that the sun is different from the earth, so that the cosmo principle doesn't apply at such small scales.fishfry

    And remember that Linde's eternal inflation would presume that each bubble universe would start off at a planckscale energy density and so the initial state would be a relativistic gas, a quark-gluon hot soup. So the material content would be at thermal equilibrium. The only fluctuations - the seed forming inhomogeneities that result in the later gravitational/material structure - would be thermal quantum ones.

    So both protons and electrons, stars and galaxies, are local inhomogeneities that pop out way after any such structure has been washed clean by an initial thermal equilbration.

    Of course that then is a constraint on the odds of the history of a universe actually repeating "particle for particle". However no one wants to talk about the real combinatorial issues here. :)
  • andrewk
    but multiverse theory strikes me as suffering from the same type of problemfishfry
    It's possible to dislike multiverse hypotheses but not blame it on physics, because it's all unfalsifiable and hence doesn't count as science. I regard it as metaphysics.

    Smolin's complaint is that the same applies to string theory. If he's correct (I don't know enough about string theory to comment) then string theory also is not science and so should not be getting large parts of physics funding. Also, it should be called 'String Hypothesis', as a requirement of any 'theory' is that it be falsifiable.
  • andrewk
    Aren't you neglecting that the matter density must be uniform?
    The homogeneity part of the cosmological principle requires that mass-energy be uniformly distributed 'at the large scale'.
  • apokrisis
    It still has to start off homogenous and thermalised at the small scale of the initial conditions. If it was patchy at the start, it couldn’t be now nearly flat. The CMB would not look homogenous and isotropic.
  • fishfry
    ... has been washed clean by an initial thermal equilbrationapokrisis

    Heat is a measure of average energy over a region. Thermal equilibration is a statistical process. My remarks stand.

    However no one wants to talk about the real combinatorial issues hereapokrisis

    I'm perfectly happy to talk about combinatorics. Although I'm ignorant of the specific physics, I gather that the argument takes the form of modeling the number of particles in a region, and all the states they can be in, and figuring out how many possible configurations of all the particles there are.

    But it doesn't matter. The number, whatever it is, is finite. As far as the mathematics, the situation is best modeled by assuming there are exactly two states, heads and tails. Many here are making detailed technical points of physics. But if you had a "zillion" possible states -- Tom objected to that earlier, a zillion is just whatever big finite number of states you like -- then you could code each state in binary and combine them by some rule and you'd map your entire state space into the set of all possible binary sequences.

    Coin flips are exactly the same as fancy physics-y states for purposes of this discussion. Because you could express all the states in binary and have the same conversation.

    Now Tom has claimed in one post that there are infinitely many states. THAT I do NOT believe. There must be finitely many states in order for this particular argument to go through at all. The argument is that there are infinitely many Hubble volumes, and each one can take on one of a bounded set of finitely many states. In other words there's some number S and that's the most states you can have. [In other words you can't have 1 state in Hubble 1, 2 states in Hubble 2, and so forth. There is a max number of states ANY region can have].

    Otherwise this entire argument does not work. There are finitely many states. And when you're making statistical arguments, coin flips work just as well as huge numbers because you can always code any huge number in binary. The specific details of the physics and the calculation of the possible number of states is a huge distraction that's causing people to miss the fact that they are making statistical arguments. Statistics only tell you about populations, and never individuals.
  • Wayfarer
    no one wants to talk about the real combinatorial issues here.apokrisis

    We’re waiting for the quantum computer to come along.
  • SophistiCat
    In an infinite universe, aren't we almost surely guaranteed a world where our doppelgangers walk through walls (the molecules align just right) after saying an incantation? Maybe doppleganger Jesus really did take a stroll on the water.Marchesk

    Yes, I think Vilenkin entertains similar fun scenarios, but frankly, not having followed the derivations, I am a little hesitant to commit to such specific predictions.
  • SophistiCat
    How can anybody assert that the state of some event outside our sphere 'is' in any particular state? Our definition sort of assumes a measurement taken from 'here', and by that definition, those distant events have no measurement and are in complete superposition.noAxioms

    Superposition states are states too (they are also called "mixed" states, as opposed to "pure" states). But I think I get your point: if we haven't been in contact with some remote region of the universe, then within that interval of time its wavefunction has been evolving independently from us, and there is no coherence between us and any one of its branches.
  • tom
    I think the cosmological principle allows such exceptions, but just says that the probability of us being that exception is sufficiently infinitesimal to preclude explanations that require us to be that exception.noAxioms

    This is simply false. In Inflationary cosmology, no assumptions about randomness, or all initial states being instantiated, or probability distributions, or typicality, or mediocrity is required. Inflation guarantees that this type of "exhaustive randomness" is in place.

    Which is why I have been describing the initial conditions as ERGODIC from the beginning.
  • noAxioms
    Superposition states are states too (they are also called "mixed" states, as opposed to "pure" states). But I think I get your point: if we haven't been in contact with some remote region of the universe, then within that interval of time its wavefunction has been evolving independently from us, and there is no coherence between us and any one of its branches.SophistiCat
    A type-1 alternate universe is just like a type-3 in that we might share a common portion of past history, but we can effectively no longer interact, ever. One is a past statement, and one is the future. The future makes it type-1, and that indeed is a mixed state. But for there to be a copy of Earth, we need a reasonably identical past, which would be a pure state since nothing can come from outside.

    Neither are bounded by the Hubble-Sphere. The type-1 universe is bounded by the event horizon (which IS frame dependent, despite my expressed hesitancy in the prior post), but the Earth copy requires that pure quantum state which is bounded by the particle horizon.
    The former is a ball about 31 Glyr in diameter (units in proper distance), but the latter is a frame-independent ball about 92 Glyr in diameter, beyond which all quantum states are pure from our standpoint. That means the nearest copy of us is only 92 Glyr away There are closer ones, but there is no coherence between us and them, so they don't really exist in a type-1 sense.
  • noAxioms
    This is simply false.tom
    Could be. You need to reply to those who know this subject better than I. I've been a ball of disproven opinions on this point throughout this thread.
    Comment on my QM thingy instead. I just stated that there is a copy of us quite nearby, to the point of giving a fairly specific figure for it.
  • tom
    They do not say that they are speaking precisely and formally in their books. It is only you that says that. The evidence points to the opposite being the case. The absence of equations is a big clue.

    In any case, the books are not holy scripture and we are not in the helpless position of those trying to interpret holy scripture and work out what the Author intended. Either mathematical analysis supports a conclusion that there does not exist a single level 1 spacetime lacking a duplicate Earth, rather than the set of such spacetimes merely having measure zero, or it doesn't. If it does, you should be able to point to a rigorous proof of the former. So far you have not done so.

    Here's Tegmark being as explicit in one of his papers as in his book:

    "In particular there are infinitely many other inhabited planets, including not just one, but infinitely many with people with the same appearance, name and memories as you. Indeed there are infinitely many other regions the size of our observable universe, where every possible cosmic history is played out. This is the Level I multiverse."

    All relevant papers are available on arXiv.


    For example the abstract of the paper you claimed to have read:

    "A generic prediction of inflation is that the thermalized region we inhabit is spatially infinite. Thus, it contains an infinite number of regions of the same size as our observable universe, which we shall denote as O-regions. We argue that the number of possible histories which may take place inside of an O-region, from the time of recombination up to the present time, is finite. Hence, there are an infinite number of O-regions with identical histories up to the present, but which need not be identical in the future. Moreover, all histories which are not forbidden by conservation laws will occur in a finite fraction of all O-regions. The ensemble of O-regions is reminiscent of the ensemble of universes in the many-world picture of quantum mechanics. An important difference, however, is that other O-regions are unquestionably real.
  • tom
    Superposition states are states too (they are also called "mixed" states, as opposed to "pure" states).SophistiCat

    Actually it's the other way round. Superpositions are pure states, mixed states are statistical mixtures.
  • andrewk
    An article on arXiv is no more holy scripture than a pop-science book.

    I asked you to link to a proof for your claim. Those papers contain no proofs.

    The closest the Vilenkin paper comes is on p7 (2nd para of section IV) where it says:
    All histories consistent with exact conservation laws will have non-vanishing probabilities and will occur in an infinite number of O-regions
    Right there, in that sentence, Vilenkin asserts that E having a nonzero probability in a single trial entails that it is impossible for there to be an infinite sequence of trials in which E does not happen. That is, he simply assumes the conclusion that you assert. He does not prove it.

    That's because he's writing informally. That becomes blindingly obvious in the paragraphs that follow, where he whimsically contemplates things like O-regions in which Elvis is still alive.
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