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Does the difficulty of making sense of quantum mechanical phenomena, (i.e. arriving at a nice philosophical interpretation of QM) taken together with Everett's many-worlds interpretation, constitute real evidence for accepting modal realism? I understand that Everett's worlds are just nomologically possible worlds, not possible worlds in general.

Has this already been discussed somewhere philosophically?

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    Lewis's possible worlds are classically separated and do not interact with each other at all. So there is no room for coherence and decoherence, and modal realism can do nothing useful for many worlds interpretation. It services classical modal intuitions. – Conifold Jul 10 '15 at 22:34
  • So, all of the the worlds posited by MWI are part of the actual world only? – user132181 Jul 11 '15 at 18:42
  • " the difficulty of making sense of quantum mechanical phenomena" what do you mean by that? which difficulty exactly? – Alexander S King Jul 12 '15 at 3:45
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What today is named many-world interpretation of quantum mechanics goes back to Everett's doctoral thesis 'Relative State' Formulation of Quantum Mechanics, Reviews of Modern Physics. Vol. 29, 1957, p. 454–462

Quoting from this paper:

We thus arrive at the following picture: Throughout all of a sequence of observation processes there is only one physical system representing the observer, yet there is no single unique state of the observer (...). Nevertheless, there is a representation in terms of a superposition, each element of which contains a definite observer state and a corresponding system state. Thus with each succeeding observation (or interaction), the observer state "branches" into a number of different states. Each branch represents a different outcome of the measurement and the corresponding eigenstate for the object-system state. All branches exist simultaneously in the superposition after any given sequence of observations.

In a footnote added in proof Everett clearifies:

In reply to a preprint of this article some correspondents have raised the question of the "transition from possible to actual" arguing that in "reality" there is - as our experience testifies - no such splitting of observer states, so that only one branch can ever actually exist. Since this point may occur to other readers the following is offered in explanation.

The whole issue of the transition from "possible" to "actual" is taken care of in the theory in a very simple way - there is no such transition nor is such a transition necessary for the theory to be in accord with our experience. Form the viewpoint of the theory all elements of a superposition (all "branches") are "actual", none any more "real" then the rest. It is unnecessary to suppose that all but one are somehow destroyed, since all the separate elements of a superposition individually obey the wave equation with complete indifference to the presence or absence ("actuality" or not) of any other elements. This total lack of effect of one branch on another also implies that no observer will ever be aware of any "splitting" process.

On the other hand, the theses of Dawid Lewis on modal realism are summarized in http://users.ox.ac.uk/~worc0337/modal.realism.html as follows:

  1. Possible worlds exist -- they are just as real as our world;
  2. Possible worlds are the same sort of things as our world -- they differ in content, not in kind;
  3. Possible worlds cannot be reduced to something more basic -- they are irreducible entities in their own right.
  4. 'Actual' is indexical. When we distinguish our world from others by claiming that it alone is actual, we mean only that it is ours -- we live here.
  5. Possible worlds are unified by the spatiotemporal interrelations of their parts; possible worlds are spatiotemporally isolated from each other.
  6. Possible worlds are causally isolated from each other.

Apparently, the similarities between Everett and Lewis are overwhelming. Only Lewis no. 4 probably would have been repudiated by Everett. In general, Everett seems to be more consequent in his terms: He even refuses to employ the concept of a transition from possible to actual.

Leibniz was the first to state a clear difference between possible and actual worlds. And Leibniz proposed a criterion to single out the real world from the set of all possible worlds: The actual world is the best possible.

The most important fact seems to me that Everett argues on the basis of a mathematical formulation of quantum theory. I do not know on which ground Lewis built his theses.

For a similar question concerning the whole topic see also in this blog How do quantum-mechanical worlds relate to possible worlds?

  • +1: great answer! I'd wondered about the connection myself; can one say that the branching is instantaneous? This doesn't seem right as it appears to involve the concept of time; so perhaps atemporal? – Mozibur Ullah Jul 12 '15 at 9:46
  • Similarities between Everett and Lewis are not overwhelming, they are superficial. All Everett's branches have a common past and they can in principle recohere (this may be unlikely for reasons external to Everett's model), so by 5. and 6. they belong to the same "possible world" of Lewis. Lewis's 3. does not hold for branches either, they are all reducible to a single "wave function of the universe", in fact they are just relative reductions of it. – Conifold Jul 13 '15 at 19:35
  • @Conifold: Do you know: Is there a formal theory behind the theses of Lewis? – Jo Wehler Jul 14 '15 at 6:32
  • He formalized the counterpart theory of modal semantics, which is part of modal realism en.wikipedia.org/wiki/Counterpart_theory#The_formal_theory – Conifold Jul 16 '15 at 23:51

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