For any well-controlled isolated system, if it starts in a state |Ψ⟩, then at a later time it will be in state U|Ψ⟩ where U is a certain deterministic unitary operator. So far this is indisputable—you can do quantum state tomography, you can measure the interference effects, etc. Right?
It will certainly be mathematically well-described by an expression like that. But when you flip a coin without looking at it, it will also be well-described by a probability distribution 0.5 H + 0.5 T, and this doesn’t mean that we insist that after the flip, the coin is Really In That Distribution.
Now it’s true that in quantum systems, you can measure a bunch of additional properties that allow you to rule out alternative models. But my OP is more claiming that the wavefunction is a model of the universe, and the actual universe is presumably the disquotation of this, so by construction the wavefunction acts identically to how I’m claiming the universe acts, and therefore these measurements wouldn’t be ruling out that the universe works that way.
Or as a thought experiment: say you’re considering a simple quantum system with a handful of qubits. It can be described with a wavefunction that assigns each combination of qubit values a complex number. Now say you code up a classical computer to run a quantum simulator, which you do by using a hash map to connect the qubit combos to their amplitudes. The quantum simulator runs in our quantum universe.
Now here’s the question: what happens if you have a superposition in the original quantum system? It turns into a tensor product in the universe the quantum computer runs in, because the quantum simulator represents each branch of the wavefunction separately.
This phenomenon, where a superposition within the system gets represented by a product outside of the system, is basically a consequence of modelling the system using wavefunctions. Contrast this to if you were just running a quantum computer with a bunch of qubits, so the superposition in the internal system would map to a superposition in the external system.
I claim that this extra product comes from modelling the system as a wavefunction, and that much of the “many worlds” aspect of the many-worlds interpretation arises from this (since products represent things that both occur, whereas things in superposition are represented with just sums).
OK, so then you say: “Well, a very big well-controlled isolated system could be a box with my friend Harry and his cat in it, and if the same principle holds, then there will be deterministic unitary evolution from |Ψ⟩ into U|Ψ⟩, and hey, I just did the math and it turns out that U|Ψ⟩ will have a 50⁄50 mix of ‘Harry sees his cat alive’ and ‘Harry sees his cat dead and is sad’.” This is beyond what’s possible to directly experimentally verify, but I think it should be a very strong presumption by extrapolating from the first paragraph. (As you say, “quantum computers prove larger and larger superpositions to be stable”.)
Yes, if you assume the wavefunction is the actual state of the system, rather than a deterministic model of the system, then it automatically follows that something-like-many-worlds must be true.
…And then there’s an indexicality issue, and you need another axiom to resolve it. For example: “as quantum amplitude of a piece of the wavefunction goes to zero, the probability that I will ‘find myself’ in that piece also goes to zero” is one such axiom, and equivalent (it turns out) to the Born rule. It’s another axiom for sure; I just like that particular formulation because it “feels more natural” or something.
Huh, I didn’t know this was equivalent to the born rule. It does feel pretty natural, do you have a reference to the proof?
I’m really unsympathetic to the second bullet-point attitude, but I don’t think I’ve ever successfully talked somebody out of it, so evidently it’s a pretty deep gap, or at any rate I for one am apparently unable to communicate past it.
I agree with the former bullet point rather than the latter.
FWIW last I heard, nobody has constructed a pilot-wave theory that agrees with quantum field theory (QFT) in general and the standard model of particle physics in particular. The tricky part is that in QFT there’s observable interference between states that have different numbers of particles in them, e.g. a virtual electron can appear then disappear in one branch but not appear at all in another, and those branches have easily-observable interference in collision cross-sections etc. That messes with the pilot-wave formalism, I think.
It will certainly be mathematically well-described by an expression like that. But when you flip a coin without looking at it, it will also be well-described by a probability distribution 0.5 H + 0.5 T, and this doesn’t mean that we insist that after the flip, the coin is Really In That Distribution.
Now it’s true that in quantum systems, you can measure a bunch of additional properties that allow you to rule out alternative models. But my OP is more claiming that the wavefunction is a model of the universe, and the actual universe is presumably the disquotation of this, so by construction the wavefunction acts identically to how I’m claiming the universe acts, and therefore these measurements wouldn’t be ruling out that the universe works that way.
Or as a thought experiment: say you’re considering a simple quantum system with a handful of qubits. It can be described with a wavefunction that assigns each combination of qubit values a complex number. Now say you code up a classical computer to run a quantum simulator, which you do by using a hash map to connect the qubit combos to their amplitudes. The quantum simulator runs in our quantum universe.
Now here’s the question: what happens if you have a superposition in the original quantum system? It turns into a tensor product in the universe the quantum computer runs in, because the quantum simulator represents each branch of the wavefunction separately.
This phenomenon, where a superposition within the system gets represented by a product outside of the system, is basically a consequence of modelling the system using wavefunctions. Contrast this to if you were just running a quantum computer with a bunch of qubits, so the superposition in the internal system would map to a superposition in the external system.
I claim that this extra product comes from modelling the system as a wavefunction, and that much of the “many worlds” aspect of the many-worlds interpretation arises from this (since products represent things that both occur, whereas things in superposition are represented with just sums).
Yes, if you assume the wavefunction is the actual state of the system, rather than a deterministic model of the system, then it automatically follows that something-like-many-worlds must be true.
Huh, I didn’t know this was equivalent to the born rule. It does feel pretty natural, do you have a reference to the proof?
I agree with the former bullet point rather than the latter.
Someone in the comments of the last thread claimed maybe some people found out how to generalize pilot-wave to QFT. But I’m not overly attached to that claim; pilot-wave theory is obviously directionally incorrect with respect to the ontology of the universe, and even if it can be forced to work with QFT, I can definitely see how it is in tension with it.
Wasn’t this the assumption originally used by Everret to recover Born statistics in his paper on MWI?