• noAxioms
    417
    If they have the same history, and if determinism is the case, then wouldn't they also have the same future?Michael
    That's why I brought up QM interpretations.
    Copenhagen is in theory nondeterministic, but involves faster than light action, and thus destroys the limits of the Hubble volume. It also leaves states in superposition if not measured from an arbitrary observation point. Pull back the camera so to speak and Copenhagen becomes as deterministic as any other interpretation.
  • noAxioms
    417
    No it doesn't. You can't count your clones. Physics tells us that the cardinality of your clones is Aleph_0.

    If you think it is possible to count your clones, I urge you to try.
    tom
    I did in the post to which you replied. Perhaps you think that countable means you can know how many there are, but then the integers are not countable, so you're working from a different rule book.

    I said the Hubble Volumes are INDISTINGUISHABLE not identical.
    I think you need to expand on what you mean by these terms since we seem to be talking past each other.
  • tom
    1.1k
    If they have the same history, and if determinism is the case, then wouldn't they also have the same future?Michael

    If you perform a quantum measurement - e.g. a measurement of z-spin of a particle prepared in x-spin-up configuration, and choose your spouse based on the result, in half your futures you are married to Mary, in the other half it's Jane. Same past different futures.

    Determinism is dead. Long live Unitarity!
  • noAxioms
    417
    If you perform a quantum measurement - e.g. a measurement of z-spin of a particle prepared in x-spin-up configuration, and choose your spouse based on the result, in half your futures you are married to Mary, in the other half it's Jane. Same past different futures.

    Determinism is dead. Long live Unitarity!
    tom
    I thought you pushed the view that you're married to both of them, a deterministic view.
    I just now see Michael's edit where he notes the same view shift.
  • tom
    1.1k
    I thought you pushed the view that you're married to both of them, a deterministic view.
    I just now see Michael's edit where he notes the same view shift.
    noAxioms

    In half your futures you are married to Jane. In the other half, you are married to Mary. Are you suggesting I have ever promoted polygamy?

    Of course I am a determinist, it's just that the picture of how determinism applies in Reality has to take into account quantum mechanics. This is different from classical determinism.
  • noAxioms
    417
    Let's be rigorous about our definition of the state of a type-1 universe, that with which we would need to have copied.

    I think all you need is a specification of an event, frame, and state. The frame is there for future state only, not present state. So:

    Earth CoG at stroke of midnight Y2K, in the arbitrary frame of Earth CoG at that moment, in the state that is the direct causal history of me making this post 17 years later. That defines a temporal line of that point in space that goes out forever. A different Hubble Volume is identical to that one if the wave function of any point along that line is the same in both volumes.
    Does that work? It totally leaves out the definition what is the 'current state' of our volume, and I think it might even be independent of QM interpretation.
  • SnowyChainsaw
    2


    I have recently concluded that whether or not multiverses are real is not a very interesting question since currently we have no way of observing the truth of it.
    However, I do find that considering reality in 10 dimensions, the 7th and beyond relating to multiverses, is a useful tool when determining the characteristics of the universe we can observer by comparing it to the arbitrary characteristics of other "possible" universes.
  • SophistiCat
    253
    I skimmed that article you linked and was interested to note that Vilenkin makes statements like:

    "there are an infinite number of O-regions with identical histories up to the present"

    where I think what he means is "there is almost surely an infinite number of .....". That is, I think he over-simplified his statement, presumably because he wanted to make it more accessible to the non-physicist reader, since it is a non-technical article.

    I note that in your post you included the crucial qualifier "almost certainly", although it does not occur in the paper. Interestingly, Tegmark also omits the qualifier (bottom of first column on page 4 of this article you linked) but, like Vilenkin, gives no explanation for the omission, and his article is also more pop science than academic.

    Do you have a view on why they omitted the 'almost certain' qualifier from their articles?
    andrewk

    Well, I cannot answer for Vilenkin or Tegmark, but I think they were speaking informally.

    How we interpret these results depends on how we think about probability. If we interpret probability as a quantitative measure of credence, or degree of belief, then there isn't really a difference between "almost surely" and "surely": in either case, the credence is exactly zero. This failure to make a distinction between possibility and impossibility may be a deficiency of the epistemic interpretation of probability (not to mention the problems of formal probabilistic modeling that have been raised here).

    But if we further think about our concepts of probability and possibility, this might be argued to be a distinction without a difference. We can hardly tell the difference in credence between an event that has a probability of 10-10 in a single trial and one with a probability 10-100. We stop making a difference long before "almost surely".

    There is still a possible/impossible distinction though. But is there, really? If "an event A is impossible" means for you that you should live your life as though A will never happen, then events with an extremely low probability are as good as impossible. You live your life assuming that the air will not suddenly evacuate the room through the window, leaving you choking on the floor, even though science says that such an event is possible (and even has a well-defined, finite probability!)
  • Marchesk
    1.6k
    There is still a possible/impossible distinction though. But is there, really? If "an event A is impossible" means for you that you should live your life as though A will never happen, then events with an extremely low probability are as good as impossible. You live your life assuming that the air will not suddenly evacuate the room through the window, leaving you choking on the floor, even though science says that such an event is possible (and even has a well-defined, finite probability!)SophistiCat

    Right, but if we're thinking about the universe at large, then all these low probability events could be happening elsewhere, assuming a large enough universe. There would even be worlds where the low probability events are common, and assuming anything intelligent can manage to survive long enough there, it might come to a different conclusion about how low those probabilities are.

    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.
  • SophistiCat
    253
    The case of a simple bound system, such as a hydrogen atom, is easier to analyze than a more general case: we can actually solve the quantum equations and enumerate every possible state. There is, however, a theorem for the general case in quantum mechanics, which puts a limit on the number of possible states, or degrees of freedom, given a volume and energy density within that volume.

    The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment. Even in a purely deterministic universe, as these systems transition from one state to another, they may end up in the same state at some point simply by chance. What that chance is - high, low, "almost surely" - will depend on a more detailed analysis.
  • tom
    1.1k
    Well, I cannot answer for Vilenkin or Tegmark, but I think they were speaking informally.SophistiCat

    I've quoted from Vilenkin's book. Nerither he not Tegmark were speaking informally.

    How we interpret these results depends on how we think about probability. If we interpret probability as a quantitative measure of credence, or degree of belief, then there isn't really a difference between "almost surely" and "surely": in either case, the credence is exactly zero. This failure to make a distinction between possibility and impossibility may be a deficiency of the epistemic interpretation of probability (not to mention the problems of formal probabilistic modeling that have been raised here).SophistiCat

    It's nothing to do with probability, or our interpretation of probability. All initial conditions are realised by inflation, deterministically.

    But if we further think about our concepts of probability and possibility, this might be argued to be a distinction without a difference. We can hardly tell the difference in credence between an event that has a probability of 10-10 in a single trial and one with a probability 10-100. We stop making a difference long before "almost surely".SophistiCat

    It's nothing to do with credences either.

    There is still a possible/impossible distinction though. But is there, really? If "an event A is impossible" means for you that you should live your life as though A will never happen, then events with an extremely low probability are as good as impossible. You live your life assuming that the air will not suddenly evacuate the room through the window, leaving you choking on the floor, even though science says that such an event is possible (and even has a well-defined, finite probability!)SophistiCat

    Impossible events are those forbidden by the laws of physics.
  • tom
    1.1k
    The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that momentSophistiCat

    And, this is also true for Hubble Volumes in the Level 2 Multiverse. Indistinguishable Hubble Volumes will have different histories due to different laws of physics operating.
  • noAxioms
    417
    The case of a simple bound system, such as a hydrogen atom, is easier to analyze than a more general case: we can actually solve the quantum equations and enumerate every possible state.SophistiCat
    Not sure which post brings on this reply. I brought up an insanely complex quantum equation in my prior post, but never suggested it was in need of being expressed or solved.
    There is, however, a theorem for the general case in quantum mechanics, which puts a limit on the number of possible states, or degrees of freedom, given a volume and energy density within that volume.
    We're talking a hubble-volume in this case, which has a finite but large degree of freedom. My wave function was based on that. Interestingly, I think it was a mistake to specify an inertial frame in my description. The full wave function of the one event is enough. If another event somewhere has the same wave function, it defines a clone Hubble sphere to ours.
    It is also a definition free from tom's concern about the two universes staying identical. The definition is of an event which doesn't become something else.
    My definition breaks down with Bill Clinton's oddly applicable statement: "It depends on what your definition of 'is' is". 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. The nearest Earth clone is massively closer than the figure Tegmark quotes where the number of finite states is computed and divided by distance, something that seems invalid without a measurement being taken, from here no less.
    The distance then becomes a function of the furthest historic matter that made a difference to our state now. That's further out that the Hubble-Volume, which is defined as the stuff that can make a future causal difference to here, not that which has made a past causal difference.

    The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment. Even in a purely deterministic universe, as these systems transition from one state to another, they may end up in the same state at some point simply by chance. What that chance is - high, low, "almost surely" - will depend on a more detailed analysis.
    Agree with this. Yes, I think I alluded to the opposite at first, but you're right. This was pointed out to me in a prior post.
  • andrewk
    907
    I've quoted from Vilenkin's book. Nerither he not Tegmark were speaking informally.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.
  • fishfry
    296
    I think I found the smoking multiverse.

    I went to the Wiki article on the multiverse. I searched for "ergodic," and found this:

    A prediction of chaotic inflation is the existence of an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

    Now we see a couple of things. First, here is the popularized explanation of the ergodic business. But note the imprecision and inaccuracy:

    ... which, being infinite, must contain Hubble volumes realizing all initial conditions.

    The language here clearly shows that the author thinks that the mere fact that there are infinitely many Hubble volumes implies that all initial states must be instantiated. But of course we have seen that this is not true.

    I do realize that the fault here is not with Tegmark or with any other serious multiverse theorists, but rather with the Wiki author. But this is a good example of the type of loose thinking and careless use of infinity that seems to be a big part of this subject.

    Now two paragraphs later, we find this beautiful resolution to our entire problem.

    Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe. This follows directly from the cosmological principle, wherein it is assumed that our Hubble volume is not special or unique.

    AHA!!!! Mere infinity is not sufficient, we all agree on that. And as I've pointed out, ergodicity is not sufficient, because a distribution could be ergodic yet still behave badly on a set of measure zero.

    We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors!

    So ergodicity says that the large scale behavior is statistically well-behaved; and the cosmological principle says that there are no measure zero exceptions. Ergodicity allows that for all we know, our own earth is a statistical exception. The cosmological principle says that there are no statistical exceptions.

    None of us know (though some claim to know) how the world got started, if was really a big bang multiverse or whether it's just turtles all the way down.

    But as philosophers we can at least point out which arguments correctly follow from which assumptions.

    As far as I can determine, the fact that there must be a duplicate earth does not follow from ergodicity; but rather from the additional assumption of the cosmological principle. It's the cosmological principle that rules out measure zero exceptions. And of course the cosmological principle is an assumption not directly supported by evidence. It's simple an assumption whose purpose is to make the duplicate earth theory true. Without that extra assumption you haven't got certainty that there's a duplicate earth.
  • fishfry
    296
    No it doesn't. You can't count your clones. Physics tells us that the cardinality of your clones is Aleph_0.tom

    This is something that troubles me deeply. You are claiming that physicists assume that Zermelo-Fraenkel set theory applies to the physical universe.

    If that were true, wouldn't their be clever physics postdocs applying for grants to see if the axiom of choice or the continuum hypothesis or any of the large cardinal axioms are true?

    If you claim that the collection of clones may be placed into bijection with the set of positive integers, then how large does physics say is the collection of the set of subsets of the clones? Is it Aleph-1, as the continuum hypothesis would imply? Or do you think it might be Aleph-2, as ‎Gödel suspected? Or perhaps far larger than that, as Paul Cohen believed?

    It seems to me that these questions are utter nonsense. Nobody knows whether ZF applies to the real world. Perhaps category theory or homotopy type theory, two modern alternatives to set theory, better describe the mathematical foundations of the world.

    You have a reference for the claim that physicists believe there are countably many clones? Or that Zermelo-Fraenkel set theory has relevance to physics? This I would really like to see.

    Along the same lines, if you claim there are uncountably many indistinguishable Hubble volumes, what is the cardinality of this uncountable quantity? Is it one of the Alephs? Or perhaps the axiom of choice false and the uncountable cardinality is not an Aleph at all. Could that be the case?

    I don't think physics has given any credence to these questions at all. In which case any claim about the cardinality of clones is nonsense.
  • noAxioms
    417
    We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors!fishfry
    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.

    As such, it is, as you say, an assumption, not some mathematical certainty that we're not unique.
  • fishfry
    296
    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

    Well the probability is zero. But that is not the same as guaranteeing with absolute certainty that there is another earth. That's the claim on the table. The difference between absolutely certain or almost certain. If someone wants to claim that the multiverse theory says that it's almost certain [in the technical sense] that there's a duplicate earth, I'll accept that this conclusion follows from the premises. But @Tom is claiming absolute certainty, and I don't see it.
  • andrewk
    907
    We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors!fishfry
    Well actually the author has misused the cosmological principle, which implies nothing of the sort. The cosmological principle states that each constant-time hypersurface of the universe ('this spacetime') is homogeneous and isotropic at the large scale. When formalised (which is quite tricky to do - see this discussion), this is a statement about observed average quantities as the size of the hypersurface subsets we average over approaches infinity.

    So the cosmological principle says absolutely nothing about microphenomena such as whether a particular teensy-weensy arrangement of molecules like the Earth recurs - even though the author of that article appears to think it does. I am confident that neither ergodicity nor the cosmological principle, either alone or together, can imply the conclusion that there is certainly a duplicate Earth in this spacetime.
  • fishfry
    296
    So the cosmological principle says absolutely nothing about microphenomena such as whether a particular teensy-weensy arrangement of molecules like the Earth recurs.andrewk

    I suspected that, but didn't want to complicate my point.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. But if there are two Hubble volumes that are identical, that must (might?) mean that those volumes are particle-by-particle identical, which would imply a duplicate earth. Is that true? If there are two identical Hubble volumes, what does identical mean? Are they quark-by-quark the same? Ih which case they have duplicate earths.

    I must say that I don't really believe there are duplicate earths, duplicate people, or for that matter an actual infinity of anything. I'm with Lee Smolin, who coined the phrase, "the trouble with physics." He was talking about string theory, but multiverse theory strikes me as suffering from the same type of problem. We are at the limit of our ability to do experiments, so the theorists are running amok and no longer doing science.

    https://www.amazon.com/Trouble-Physics-String-Theory-Science/dp/061891868X
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