So, I took this class some time ago where we discussed Hugh Everett's approach to QM. The premise seemed very logical to me:

  • Isolated systems evolve according to the Schrödinger Equation.

Of course this would need the existence of at least one isolated system for it to make any sense. It could be argued that the universe as a whole is an isolated system.

What I really liked about this idea is that it doesn't need the artificial "collapse" of the wavefunction (which almost always is explained in terms of there being a classical object interacting with the quantum system... I find this idea ridiculous since if QM was true then there wouldn't be any "classical systems").

But whenever I read online about the Everett picture I find this "many worlds" interpretation attached to the idea of the universal wavefunction (which I personally find unappealing, since it wouldn't be possible to ineract with the other "worlds" making them unphysical). How are these two ideas related?

Thank you very much.

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    $\begingroup$ 'If QM was true then there wouldn't be any "classical systems"': this supposes that everything can be described by QM, but one could be open to the simple possibility that QM has a domain of validity (like all other theories in physics, so it is difficult to see why it has to be different here). At the moment the idea that classical systems can be reduced to quantum ones is just a conjecture, and since the measurement problem is not solved, the alterntaive idea that we still have to cope with a dual description of nature (quantum vs classical) is not so ridiculous. $\endgroup$ – Stéphane Rollandin Sep 26 '18 at 15:35
  • $\begingroup$ The thing here is that (I believe) QM should at least be self consistent. It would make no sense to argue that an object in Newtonian mechanics could quantum tunnel through a wall, because that's not acceptable within the classical theory. $\endgroup$ – S V Sep 26 '18 at 18:58
  • $\begingroup$ In the Lagrangian description of n classical particles in $R^3$ its configuration space is $R^3 x ... R^3$ n times; that rather looks like one particle in $n$ different worlds! MWI rather seems to put the mathematical cart before the physical horse... $\endgroup$ – Mozibur Ullah Sep 27 '18 at 2:33
  • $\begingroup$ @MoziburUllah My last comment on this: if it was really that trivial why would it have exercised the minds of some of the greatest physicists of 20th century: Hawking, Gell-Mann, Weinberg, .. but never mind at least MWI is a good learning tool. e.g. thinking about your example you see there is no entanglement then you appreciate how rich quantum theory is. $\endgroup$ – Bruce Greetham Sep 27 '18 at 4:44
  • $\begingroup$ @Bruce Greetham: Well the word Einstein used was 'cheap'; he was talking about Bohms theory but the same critique holds for MWI - that it 'tries to explain away the irreducible determinism of QM'; if you look into the book by Schlosshauer Enigma & Elegance which is a collection of interviews by physicists you'll find it on pg.44. I'd be curious what Feynman would have made of MWI. $\endgroup$ – Mozibur Ullah Sep 27 '18 at 5:38

If you treat the universe as an isolated system, then an outside observer will assign it a universal wavefunction which evolves under the Schrodinger equation and never collapses. The problem is that we -- by which mean the people who run experiments on quantum systems in the lab -- are not outside observers to the universe; we are definitely inside the universe. The universal wavefunction in principle contains the information about the quantum state of all the particles, including those which make up ourselves. But somehow you have to relate this to our subjective experience, and in particular, to the measurement outcomes that we observe when we run certain experiments in the lab. The Everett picture is one way to do this. I sometimes hear people say that Many-Worlds is a "logical consequence" of the universal wavefunction, but I strongly disagree; it is a proposal for how to assign physical meaning to the universal wavefunction.

Now, what is true mathematically (in any interpretation of quantum mechanics) is that if you start with a superposition of two macroscopically distinct quantum states, for example $$\frac{1}{\sqrt{2}} ( | \mbox{atom decayed} \rangle + | \mbox{atom not decayed} \rangle)$$ and allow the system to interact with its environment, then the combined wavefunction of the system and environment (which is a part of the universal wavefunction) will decohere. What this means is that by the time the influence of the superposition has reached macroscopic scales, for example $$ \frac{1}{\sqrt{2}} ( | \mbox{cat dead} \rangle + | \mbox{cat alive} \rangle)$$ or even $$ \frac{1}{\sqrt{2}} ( | \mbox{the experimenter has opened the box and seen a dead cat} \rangle + | \mbox{the experimenter has opened the box and seen a live cat} \rangle)$$ there is no feasible operation that will ever distinguish this state from a classical statistical ensemble of cat dead with probability 1/2 and cat alive with probability 1/2. Thus, "cat dead and "cat alive" effectively forms two completely non-interacting "branches" of the universal wavefunction. So far, this is simply a mathematical statement about the structure of the wavefunction.

What the Many-Worlds interpretation does is it assigns physical meaning to these branches within the universal wavefunction -- namely, each branch describes a physical universe which actually exists, and the two universes both split off from a single universe. In each universe, the experimenter sees the corresponding result (dead cat or live cat). Now this is really a huge interpretative leap. But it might well be the only way to extract anything meaningful out of the universal wavefunction.

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    $\begingroup$ It is not clear to me how two branches can decohere within an universal wavefunction, since as you rightly say decoherence implies an environment, so the environment itself should somehow decohere along with the branches. This is the preferred basis problem. $\endgroup$ – Stéphane Rollandin Sep 26 '18 at 15:48
  • $\begingroup$ @StéphaneRollandin Good link - I was looking for a good answer to the preferred basis problem on the site. A student of Zurek no less. My only comment: my reading of this link and elsewhere suggest the preferred basis problem is a complex issue, but can't you agree that broad outline progress has been made. e.g. (whatever interpretation) it is well understood that a position basis is a more naturally stable basis than some basis made up of superpositions of positions 10m away. I don't understand why this keeps getting shot down on this site. $\endgroup$ – Bruce Greetham Sep 26 '18 at 16:27
  • $\begingroup$ @BruceGreetham. I can only answer for myself, not for the whole site: no, I am not convinced. Actually my current position is exposed on this page, as a comment to the OP question. I do think that, at the time being, we cannot get rid of classicality and have to consider QM as a non-universal theory, although its domain of vailidity is not well understood (this being the multiform measurement problem, of which the preferred basis problem is an aspect IMO). $\endgroup$ – Stéphane Rollandin Sep 26 '18 at 17:36
  • $\begingroup$ As far as I remember from my class there was also a timescale for decoherence (I found it here) right? So that, for example Ψ=|cat alive⟩, is reached only asymptotically (with exponential decay). Couldn't one then argue that the universe doesn't branch off because the superposition still exists? $\endgroup$ – S V Sep 26 '18 at 19:14
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    $\begingroup$ @SalvadorVillarreal Yes, so a way to think of it, is the branches are an approximate emergent classical feature of the underlying one quantum world. Some here find that very naturally what QM is telling us, some find it incoherent nonsense - take you choice. $\endgroup$ – Bruce Greetham Sep 26 '18 at 19:54

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