The repeated problem for many worlds is that if the quantum state is 1⁄2 |dead cat> + sqrt(3)/2 |live cat>, then (squaring the coefficients) the probability of dead cat is 1⁄4, the probability of live cat is 3⁄4, and so there should be three times as many live cats compared to dead cats (for such a wavefunction); but the decomposition into wavefunction components just produces one dead-cat world and one live-cat world, which naively suggests equal probabilities. The problem is, how do you interpret a superposition like that, in terms of coexisting, equally real worlds, so as to give the right probabilities.
It looks like part of what Zurek does is to pick a basis (Schmidt decomposition) where the components all have the same amplitude—which means they all have the same probability, so the naive branch-counting method works! A potential problem with this way of proceeding is that, expressed in the position basis, the branches end up being complicated superpositions of spatial configurations. (The space of quantum states, the Hilbert space, is a large abstract vector space with a coordinate basis formally labeled by spatial configurations, so the basis vectors of a different basis will be sums of those position-basis vectors.) Explaining complicated superpositions which don’t look like reality by positing the existence of many worlds, each of which is itself a complicated superposition that doesn’t look like reality, is not very promising. It’s sort of okay to do this for microscopic entities because we don’t have apriori knowledge about what their reality is like, and we might suppose that the abstract Hilbert-space vector is the actual reality; but somewhere between microscopic and macroscopic, you have to produce an actual live cat, and not just a live cat summed with an epsilon-amplitude dead cat. I have no idea how Zurek deals with this.
Actually, Zurek has a lot of background assumptions which make his reasoning obscure to me and I really don’t expect it to make sense in the end, though it’s impossible to be sure until you have decoded his outlook. His philosophy is a weird mixture of Bohr’s antirealism and Everett’s multirealism, and in other papers he says things like
Quantum states acquire objective existence when reproduced in many copies. Individual states—one might say with Bohr—are mostly information, too fragile for objective existence.
(thanks to DZS for the quote). And of course it’s nonsense to say that something doesn’t exist until there are multiple copies of it (how many is the magic number? how can you make an existing copy of a nonexistent original?). Zurek is using the words “objective existence” in some twisted way. I’m sure the reason is that he doesn’t have the answer to QM, but he wants to believe he does; that is how smart people end up writing nonsense. But I would have to understand his system to offer a more precise diagnosis.
Schroedinger Cat is dead. Maybe it’s time to update plausibility of classic many worlds interpretation is spite of “Einselection, Envariance, Quantum Darwinism”.
I am not sufficiently competent to analyze work of W.H. Zurek, but I think that work can be a great source of insights.
Edit: Abstract. Zurek derived Born’s rule.
The “derivation” is on page 12.
The repeated problem for many worlds is that if the quantum state is 1⁄2 |dead cat> + sqrt(3)/2 |live cat>, then (squaring the coefficients) the probability of dead cat is 1⁄4, the probability of live cat is 3⁄4, and so there should be three times as many live cats compared to dead cats (for such a wavefunction); but the decomposition into wavefunction components just produces one dead-cat world and one live-cat world, which naively suggests equal probabilities. The problem is, how do you interpret a superposition like that, in terms of coexisting, equally real worlds, so as to give the right probabilities.
It looks like part of what Zurek does is to pick a basis (Schmidt decomposition) where the components all have the same amplitude—which means they all have the same probability, so the naive branch-counting method works! A potential problem with this way of proceeding is that, expressed in the position basis, the branches end up being complicated superpositions of spatial configurations. (The space of quantum states, the Hilbert space, is a large abstract vector space with a coordinate basis formally labeled by spatial configurations, so the basis vectors of a different basis will be sums of those position-basis vectors.) Explaining complicated superpositions which don’t look like reality by positing the existence of many worlds, each of which is itself a complicated superposition that doesn’t look like reality, is not very promising. It’s sort of okay to do this for microscopic entities because we don’t have apriori knowledge about what their reality is like, and we might suppose that the abstract Hilbert-space vector is the actual reality; but somewhere between microscopic and macroscopic, you have to produce an actual live cat, and not just a live cat summed with an epsilon-amplitude dead cat. I have no idea how Zurek deals with this.
Actually, Zurek has a lot of background assumptions which make his reasoning obscure to me and I really don’t expect it to make sense in the end, though it’s impossible to be sure until you have decoded his outlook. His philosophy is a weird mixture of Bohr’s antirealism and Everett’s multirealism, and in other papers he says things like
(thanks to DZS for the quote). And of course it’s nonsense to say that something doesn’t exist until there are multiple copies of it (how many is the magic number? how can you make an existing copy of a nonexistent original?). Zurek is using the words “objective existence” in some twisted way. I’m sure the reason is that he doesn’t have the answer to QM, but he wants to believe he does; that is how smart people end up writing nonsense. But I would have to understand his system to offer a more precise diagnosis.