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I am not really familiar with the metaphysics of the "worlds" from the Many Worlds Interpretation of QM. How do these worlds relate to possible worlds in the Lewisian sense?

Lewis wrote a short piece (I believe his last published piece?) on MWI, "How Many Lives Has Schrödinger's Cat?", but he doesn't really say anything about the metaphysics of the QM worlds and seems to shy away from calling them worlds.

The SEP article on MWI says some things which suggest that the QM worlds are centered worlds, or what are sometimes called epistemic worlds. But that begs the question of which centered worlds? Presumably not all of them, since the worlds compatible with the experience of a hallucinating madman who experiences a world inconsistent with QM are presumably not among the QM worlds.

So, how do QM worlds relate to possible worlds?

Joseph Weissman
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Dennis
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  • Madman has no other worlds. Nobody ever thought yet of any **other** worlds. What hallucinating man has is also **our** world. If you refuse to call hallucination our world then you have no ground to call imagination as a part of our world. Same about thoughts. Simple. If by **other** you mean your/his/her **simplistic** **naive** modification of our **small** and **tiny** personal experiences then it is useless by definition. Or you assume there is somebody here with a non **vanishing** personal experience, compared to the scale of universe? – Asphir Dom Jun 10 '14 at 23:32

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Christopher Norris, in his book Quantum Theory and the Flight from Realism, draws some parallels between the 'many worlds' QM theory as presented by David Deutsch, and the possible worlds theory of David Lewis:

Lewis himself arrives at this conclusion by way of the modal logic and the argument that necessary truths are those that hold across all possible worlds rather than obtaining only in a certain limited subset of worlds which happen to resemble our own in respect of various contingent features... In this form the theory goes back to Leibniz and involves the essentially rationalist belief that thinking can indeed deliver such real-world applicable truths through a priori reflection...

My point is that Deutsch's argument in support of the many-world hypothesis shares certain features of Leibniz's doctrine of logical necessity and also with the recent revival of that doctrine by metaphysically minded modal logicians such as Lewis. That is to say, it works on the strong rationalist principle that one can derive certain necessary truths about the quantum 'multiverse'-truths that hold good across all possible worlds or universes-by a process of purely deductive reasoning from self-evident premises. (p. 107-108)

The key difference in the eyes of Deutsch between himself and philosophers from Leibniz to Lewis is that he claims to derive his theory from the a posteriori evidence of Quantum Mechanics. Norris argues (convincingly in my view) that nevertheless, Deutsch does rely on a priori arguments and hence his theory has an essentially metaphysical component.

So it comes down to the question of how we distinguish conceptual from evidential arguments that determines whether the multiverse belongs to science or metaphysics/philosophy.

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adrianos
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    This is a good lead--- thanks for that. But it doesn't really go quite deep enough for what I'm looking for. For instance, Lewis countenances worlds with physically impossible spacetimes--- obviously these can't be QM worlds. I'm interested in how you would translate QM multiverse talk into Lewisian modal realist talk (for one example). Alternatively, a presentation of the metaphysics of QM worlds that departs from Lewisian possible worlds but presents a more concrete picture than I'm used to seeing (no more than a mention of "worlds"). – Dennis Jun 11 '14 at 04:56
  • Deutsch doesn't rely on a priori arguments. He argues that single universe theories are ruled out by single particle interference experiments and other quantum mechanical experiments, such as the EPR experiment. – alanf Jun 11 '14 at 08:52
  • @alanf That requires a rebuttal of a Bohm-style theory. The question is whether the decision to go with a multiverse theory or a theory that gives up locality is one that can be made with reference to the evidence alone. Deutsch argues yes but see Norris for an alternate view. – adrianos Jun 11 '14 at 12:29
  • That's not the relevant issue. The problem with the Bohm theory runs as follows. (1) If the Bohm theory admits that the wavefunction is real, in which case the structures it describes, which include parallel universes are real. (2) The Bohm theory does not make this concession, in which case it doesn't explain why the outcome of an interference experiment depends on what happens in regions that the photon doesn't interact with. For more see http://arxiv.org/abs/0901.1278 http://arxiv.org/abs/quant-ph/0403094 – alanf Jun 11 '14 at 14:15
  • @alanf Thanks for the interesting link. We are off topic from the OP. However I note that the authors do on occasion refer to metaphysics and at one point reference functionalism. Everett admitted 'no observer will ever be aware of any "splitting" process' (1957, p.147 n). If the multiverse theory is free of metaphysics, it is an empirical theory. What observable difference does its truth then make to the empirical world of the observer? If none at all, can you still say it is not metaphysical? – adrianos Jun 11 '14 at 19:40
  • @Dennis Good point, got me thinking. One interesting difference is that the possible worlds of Lewis are logical possibilities. The multiple worlds of QM are determined not by logic, but by the wave function, which circumscribe a set possibilities with no obvious relation to modal logic. – adrianos Jun 11 '14 at 19:45
  • It is impossible to cleanly separate the predictions of a theory from the explanation it gives. The explanation is vital for doing experiments because if the experiment goes wrong what do you change to make it go right or interpret the results properly? You have to look at what the theory claims is happening in the experiment to work that out. Now, if the Bohmians want to use some way of working out the implications of the equations that is different from the one used for the MWI, they should explain it not just state that they disagree. – alanf Jun 12 '14 at 09:25
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You may find it interesting that Tegmark's Level III multiverse is the one implied by Everett/MWI, whereas his Level IV multiverse comes closer to Lewis' modal realism, although it is limited to all mathematical structures (and therefore does not include all imaginable universes).

So, from this perspective, MWI's and Lewis' are distinct ideas of worlds. (Even more so than Levels III and IV are.)

See Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, p. 350 (or search inside for "Lewis").

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The quantum mechanical worlds obey some restrictions, as you have noted. Universes are structures within the multiverse within which information can flow:

http://arxiv.org/abs/quant-ph/0104033.

There is a version of me sitting one centimetre to my right, but he can't interact with me directly and he also can't convey information to me indirectly by typing something on the keyboard that is different from what I am typing now. The reason is that I can't interact with the version of the keyboard on which he is typing, nor can he interact with my version of the keyboard. Me and my version of the keyboard is in one universe "one centimetre to the right" me and his version of the keyboard is in another universe.

The quantities that carry information that can be copied are described by Heisenberg picture observables: Hermitian operators. No quantity that is described by something other than such an observable can be realised in any quantum mechanical world:

http://arxiv.org/abs/1212.3245.

alanf
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  • "So, how do [Everettian] QM worlds relate to [Lewisian] possible worlds?" –  Jun 11 '14 at 09:29
  • Everett worlds are a set of worlds that people can experience and so they are a set of counterfactual worlds that actually exist. They have that in common with Lewis worlds. My understanding is that Lewis worlds are supposed to be causally isolated from one another, which is not quite true of Everett worlds. However, it is true that you can't send a message from one specific Everettian world to another specific Everettian world. (See "The Beginning of Infinity" by David Deutsch for discussion of this issue.) It is unclear to me how that would affect whatever problem Lewis is trying to solve. – alanf Jun 11 '14 at 13:37
  • "Everett worlds are a set of worlds that people can experience[.]" I don't remember Everett being concerned with anthropic-like arguments. And I don't think that MWI denies the existence of (all) worlds not containing observers. –  Jun 11 '14 at 20:42
  • You're right. All of the worlds that people can experience are Everett worlds, but not all of the Everett worlds are worlds that people can experience. – alanf Jun 12 '14 at 08:53
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It's important to note that David Lewis doesn't have a monopoly on the use of the term possible world and I think some of the answers above are confusing modal logic itself with some much more controversial metaphysical views.

As far as the standard Kripke semantics for modal logic are concerned, a possible world is a just a set of assignments of truth-values (T or F) to a set of atomic formulae. Therefore, as far as the semantic theory of modal logic is concerned, possible worlds are abstract objects like a numbers or sets.

Call the thing that we live in, right now, in which Barack Obama is the current U.S. president and so on the universe. Now, you might think that the actual world must be one of the possible worlds, and so at least the actual world must be one concrete possible world. Again, this would be wrong. The actual world is just an abstract object too--it is the world which assigns all the atomic formulae the truth values that obtain in the universe. So the universe =/= the actual world.

Now, Lewis's modal realism involves the claim that each of the possible worlds (not just the actual world) has some universe that makes it true. These other universes are supposed to be the concrete things. Lewis has interesting metaphysical argument for why this must be the case, but it is clear that this is a strictly metaphysical argument. The claim doesn't follow from the semantics of modal logic itself.

Now Lewis might be right about modal realism or he might be wrong. Perhaps it is the case that possible worlds interpretations of QM give some evidence in favor of Lewis's modal realism or it might not. But it is very important to note that what possible worlds are supposed to be in this interpretation of QM are what we were calling above "other universes", that is, they are concrete objects, not just abstract sets of assignments of truth values. I don't have the expertise to weigh in on the evidence for or against this view of QM: I just want to make clear exactly what role such evidence would play in the philosophical dispute at issue here.

  • Thanks for the input, but unfortunately this touches mostly on the side of the question I know well--- possible worlds semantics and modal realism. My question is really looking for input from the other side, how do the things that a defender of MWI call worlds compare to the things Lewis calls worlds? Now, since asking this question one difference has come out. Lewis had a mostly Newtonian conception of physics in mind and he doesn't explicitly allow for a fundamental relation/properties to correspond to the QM wave function. So, in a sense, none of the Lewisian worlds are QM worlds. – Dennis Sep 22 '14 at 00:32
  • But I think that is uncharitable to Lewis, since when he was writing he considered QM to be too young and poorly understood to start drawing philosophical conclusions from. He likely could/would have amended this portion of his view. Besides, I'm not sure how much this actually infiltrates the rest of his theory. – Dennis Sep 22 '14 at 00:35
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If the possible world in a philosophical sense can be constituted out of particles of matter and exchanges of energy, it is almost assuredly one of the multiple worlds of Quantum Mechanics.

When you do the prediction integration over all possible Quantum worlds it is (theoretically) over every possible configuration of particles the universe could be in. Since the possibility curve for every particle extends through all of space, and the movement of particles could conceivably reshape space in pretty much any geometry humans have described, most alternative versions of the material world qualify. Given string theory and M-theory so do worlds with different physical constants, arbitrary numbers of dimensions and different characteristic particles. They may be incredibly unlikely, but none are ruled out. The computations are going to write them off, but they are in the range officially considered.

Of course, in reality, such a computation is always staged over a very small area and a very short time limit with very few outside influences (like Feynman's examples), or is estimated over a huge area and time where a lot of other factors are assumed to cancel one another out (like Hawking's explanation of the lifespan of black holes), because anything else is pretty much beyond human scope. And very few people consider realms where the physical constants would be different, unless they are concerned about an entire abstract universe with almost no detail (like the stuff Green discusses at the end of 'The Elegant Universe').

But theoretically, there is a huge overlap.