# How does the “many worlds” interpretation follow from the “universal wavefunction” idea?

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.

• '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. – Stéphane Rollandin Sep 26 '18 at 15:35
• 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. – Salvador Villarreal Sep 26 '18 at 18:58
• 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... – Mozibur Ullah Sep 27 '18 at 2:33
• @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. – Bruce Greetham Sep 27 '18 at 4:44
• @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. – Mozibur Ullah Sep 27 '18 at 5:38

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.