Many Worlds proved inconsistent?

[Demystifier]

In a paper entitled
"Nothing happens in the Universe of the Everett Interpretation":
http://arxiv.org/abs/1210.8447
Jan-Markus Schwindt has presented an impressive argument against the many-world interpretation of quantum mechanics.

The argument he presents is not new, but, in my opinion, nobody ever presented this argument so clearly.

In a nutshell, the argument is this:
To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

As reasonable possibilities for the additional structure, he mentions observers of the Copenhagen interpretation, particles of the Bohmian interpretation, and the possibility that quantum mechanics is not fundamental at all.

 

[DrChinese]

Well, nothing much happened around here yesterday. So maybe his title gets it right.

 

[The_Duck]

Suppose I'm willing to postulate a preferred basis and the Born rule. Are there any further problems with MWI?

 

[DrClaude]

As this been published anywhere?

 

[bohm2]

The shortest pictorial presentation ("idiot's guide") of this type of argument I've come across is R. Kastner's:

Why the World Cannot Really Split in the Many-Worlds Interpretation
https://rekastner.files.wordpress.com/2014/07/decoherence-fail.pdf

 

[atyy]

Suppose I'm willing to postulate a preferred basis and the Born rule. Are there any further problems with MWI?

In which way are you postulating the Born rule?

 

[The_Duck]

In which way are you postulating the Born rule?

Once I have a preferred basis I should be able to decompose the universal wave function into branches or "worlds." Then instead of relying on some unconvincing decision-theoretic argument I simply postulate that the probability of ending up in a given branch is the square of the amplitude of the branch. Once I do this, do I have a consistent, complete, and defensible interpretation of QM?

My impression is that I do. So I see complaints about the preferred basis problem as sort of nitpicking: they don't seem to fundamentally undermine MWI if all I have to do to avoid the problem is give my Hilbert space a little more structure by picking a preferred basis.

 

[atyy]

Once I have a preferred basis I should be able to decompose the universal wave function into branches or "worlds." Then instead of relying on some unconvincing decision-theoretic argument I simply postulate that the probability of ending up in a given branch is the square of the amplitude of the branch. Once I do this, do I have a consistent, complete, and defensible interpretation of QM?

My impression is that I do. So I see complaints about the preferred basis problem as sort of nitpicking: they don't seem to fundamentally undermine MWI if all I have to do to avoid the problem is give my Hilbert space a little more structure by picking a preferred basis.

I don't understand how there can be any probability of "ending up in a given branch".

If the state is $\psi = \alpha A + \beta B$ in a given basis, then since there are two possibilities, the universe will branch into two branches A and B with certainty. So I will end up in branch A and branch B with certainty.

 

[The_Duck]

I don't understand how there can be any probability of "ending up in a given branch".

OK. Suppose I came up with a really convincing argument that resolved this issue decisively. Would you have any further complaints about this interpretation?

 

[atyy]

OK. Suppose I came up with a really convincing argument that resolved this issue decisively. Would you have any further complaints about this interpretation?

I think I would also like it to be shown that observers in most (all?) branches can recover the Copenhagen interpretation if they use the notion of probability as relative frequency.

 

[stevendaryl]

I don't understand how there can be any probability of "ending up in a given branch".

If the state is $\psi = \alpha A + \beta B$ in a given basis, then since there are two possibilities, the universe will branch into two branches A and B with certainty. So I will end up in branch A and branch B with certainty.

This is really a philosophical question about the meaning of probability. If you flip a coin (or do something equivalent, quantum mechanically, such as preparing an electron in a state that is spin-up in the z-direction, and then later measuring the spin in the x-direction), then in a many-worlds ontology, then after the coin flip, there will be a copy of you who remembers getting heads and a copy of you who remembers getting tails. For each of those copies, the history recorded in his brain seems nondeterministic: At some point, you had no knowledge of how the coin would land, and later, you found out it landed heads (or tails). So while the many-worlds as a whole is deterministic, each history as recorded in brains is a history of a nondeterministic world.

 

[stevendaryl]

I think I would also like it to be shown that observers in most (all?) branches can recover the Copenhagen interpretation if they use the notion of probability as relative frequency.

I think that's true, although in a sort-of circular way. For the whole many-worlds, you could show that the set of worlds for which relative frequencies are very different from the Born interpretation of the wave function will be a set that has very low probability--according to the Born interpretation of probability.

So it's all self-consistent, it seems to me, but slightly circular.

 

[atyy]

I think that's true, although in a sort-of circular way. For the whole many-worlds, you could show that the set of worlds for which relative frequencies are very different from the Born interpretation of the wave function will be a set that has very low probability--according to the Born interpretation of probability.

So it's all self-consistent, it seems to me, but slightly circular.

I think the problem is that it isn't circular. I'm not sure, but I think it can be shown that the relative frequency for an observer in a branch with large weight is close to that predicted by the Born rule. But we still have to give a probability interpretation to the weight of the branch, which seems to be a different probability than the relative frequency probability seen within a branch.

 

[stevendaryl]

I think the problem is that it isn't circular. I'm not sure, but I think it can be shown that the relative frequency for an observer in a branch with large weight is close to that predicted by the Born rule. But we still have to give a probability interpretation to the weight of the branch, which seems to be a different probability than the relative frequency probability seen within a branch.

Hmm. I would have thought that the Born rule would apply to both: the probability of a branch, and the relative frequency within a single branch.

 

[Fredrik]

In a paper entitled
"Nothing happens in the Universe of the Everett Interpretation":
http://arxiv.org/abs/1210.8447
Jan-Markus Schwindt has presented an impressive argument against the many-world interpretation of quantum mechanics.

The argument he presents is not new, but, in my opinion, nobody ever presented this argument so clearly.

In a nutshell, the argument is this:
To define separate worlds of MWI, one needs a preferred basis, which is an old well-known problem of MWI. In modern literature, one often finds the claim that the basis problem is solved by decoherence. What J-M Schwindt points out is that decoherence is not enough. Namely, decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique. Therefore, MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.

I'm getting a strong sense of deja vu. Didn't you post this a couple of years ago? Maybe it was a comment deep inside another thread.

I'm very reluctant to get into another discussion about interpretation, but I'll say what I think I said the last time this was brought up. I agree with this view:

decoherence solves the basis problem only if it is already known how to split the system into subsystems (typically, the measured system and the environment). But if the state in the Hilbert space is all what exists, then such a split is not unique​

I don't agree with this:

MWI claiming that state in the Hilbert space is all what exists cannot resolve the basis problem, and thus cannot define separate worlds. Period! One needs some additional structure not present in the states of the Hilbert space themselves.​

It has never made sense to me that we would need a "preferred basis" or some "additional structure" to tell us what the worlds are. The only MWI approach that makes sense to me is to postulate that every 1-dimensional subspace is a world. Then there isn't really any "preferred basis problem", and the basis selected by decoherence can at best tell us in what worlds it's the least wrong to describe the interaction in classical terms.

 

[Demystifier]

I'm getting a strong sense of deja vu. Didn't you post this a couple of years ago?

Yes, it was posted in my blog. As the blogs will soon be removed, many of my old blog entries have been (and will be) reposted here.