Parallel Universes: Multiverse vs Many Worlds - Splits?

[DarMM]

Thanks, I shall dig out my copy and judge context, but in the meantime, saying it courts circulatory is not the same as saying it is circular.

It's just a poetic way of saying it. Here is the full context, he clearly rejects his old proof, see the last line:

Decoherence done ‘in the usual way’ (which, by the way, is a step in the right
direction, in the understanding of the practical and even many of the fundamental
aspects of the quantum–classical transition!) is not a good starting point for
addressing the more fundamental aspects of the origins of the classical. In particular,
decoherence is not a good starting point for the derivation of Born’s rule. As
the saying goes, there is no preacher like a reformed sinner. I previously proposed
a derivation of Born’s rule based on the symmetries—invariance of a state of the
system under permutations of pointer states, ‘events’ obtained in the usual way
from decoherence (Zurek [1998]). We have already noted the problem with this
strategy: it courts circularity. It employs Born’s rule to arrive at the pointer states
by using reduced density matrix which is obtained through trace—i.e., averaging,
which is where Born’s rule is implicitly invoked (see e.g. Nielsen and Chuang
[2000]). Therefore, using decoherence to derive Born’s rule is at best a consistency
check. While the above is a mea culpa, this circularity would also afflict other
approaches, including proposals based on decision theory (Deutsch [1999], Wallace
[2003], Saunders [2004]), as noted also by Forrester [2007] among others.
So one has to start the task from a different end.

 

[Michael Price]

It's just a poetic way of saying it. Here is the full context, he clearly rejects his old proof, see the last line:

Okay, well that seems clear, thanks. When I locate my copy I'll see just what Zurek is proposing, if anything.

 

[caspiansea3]

Another thing to consider for deriving the Born Rule in MWI is the work of Hsu and Hanson. Hsu postulates a discreteness of the quantum state space and Hanson postulates a cutoff where small amplitude worlds are 'mangled' by larger ones.

https://arxiv.org/abs/quant-ph/0108070 When Worlds Collide: Quantum Probability From Observer Selection?
In Everett's many worlds interpretation, quantum measurements are considered to be decoherence events. If so, then inexact decoherence may allow large worlds to mangle the memory of observers in small worlds, creating a cutoff in observable world size. Smaller world are mangled and so not observed. If this cutoff is much closer to the median measure size than to the median world size, the distribution of outcomes seen in unmangled worlds follows the Born rule. Thus deviations from exact decoherence may allow the Born rule to be derived via world counting, with a finite number of worlds and no new fundamental physics.

https://arxiv.org/abs/hep-th/0606062 Discreteness and the origin of probability in quantum mechanics
Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal is to account for apparent collapse phenomena, including the Born rule for probabilities, assuming only unitary evolution of the wavefunction. For finite number of degrees of freedom, observers on the vast majority of branches would not deduce the Born rule. However, discreteness of the quantum state space, even if extremely tiny, may restore the validity of the usual arguments.

 

[Michael Price]

Okay, well that seems clear, thanks. When I locate my copy I'll see just what Zurek is proposing, if anything.

Okay, well that seems clear, thanks. When I locate my copy I'll see just what Zurek is proposing, if anything.

Since there is another 18 pages after the "last line" it is a bit misleading to imply Zurek hasn't got a solution. He is criticizing earlier "solutions" (including his own), which start from decoherence, and then proceeds to present an alternative approach he is happier with. Please note that my recapitulation (link previously posted) of Zurek's derivation did not involve decoherence.
On page 417 he states Here we present the ideas behind a circularity-free approach.

 

[DarMM]

Since there is another 18 pages after the "last line" it is a bit misleading to imply Zurek hasn't got a solution

My point was that the derivation in your Quora post is circular. No implications about other work by Zurek. Your quora post doesn't deal with his later Quantum Darwinism work and it's a very different proof. From a mathematical perspective it would be equally valid to discuss Wallace's proof. I've no need to discuss it as you weren't talking about it. I know that he presents what he claims is a "circularity-free approach", but the essay was quoted to show you Zurek (and the rest of the community) thinks his 2005 work (the one you use in your quora post) is circular (and thus you shouldn't be using it as a definitive proof), not to say that Zurek has had no further alternative ideas.
The "last line" simply meant it was the last line of my quote of the article, not the last line of the article.

Please note that my recapitulation (link previously posted) of Zurek's derivation did not involve decoherence.

You are claiming to have modified Zurek's 2005 argument, but removed the dependence on decoherence? The envariance argument requires decoherence (his later Quantum Darwinism argument does not, but it is a separate argument with other weaknesses), as Zurek himself says in the essay I referenced.

 

[akvadrako]

Here we present the ideas behind a circularity-free approach.

It's fair to say all these derivations of Born's rule are not completely circular, but they do require some additional assumptions. One of the most innocuous ones I know of is: if you have a perfectly symmetrical state you can assume it represents two worlds of equal Born weights. That's what your quora derivation assumes and it's the most controversial part.

Using only the axioms of unitary QM, can you show why a symmetric state should give rise to equal probabilities?

To steel man the arguments of critics: if you are given two separate worlds it seems like their weights are completely irrelevant and can be scaled arbitrarily with no effect (except to zero). For the occupants of worlds with unequal weights, a safe assumption is they will both have equally real experiences.

 

[DarMM]

if you have a perfectly symmetrical state you can assume it represents two worlds of equal Born weights...
Using only the axioms of unitary QM, can you show why a symmetric state should give rise to equal probabilities?

This is often a question posed to MWI, but the circularity goes deeper. One is starting here with a symmetric superposition of two worlds. There is the problem of showing that with just unitary QM one can demonstrate equal probabilities, as you said.

More fundamental however is using unitary QM to demonstrate that such stable non-interfering superpositions of classics worlds exist, even ignoring managing to get probabilities out of them.

Trying to answer this question is where the circularity originates. The worlds can only be shown to be stable and separated via decoherence, but decoherence requires the Born rule. For this reason the derivations are all somewhat circular, or so it seems to me.

 

[akvadrako]

More fundamental however is using unitary QM to demonstrate that such stable non-interfering superpositions of classics worlds exist, even ignoring managing to get probabilities out of them.

Why? Is it because there are always some interference terms (or maverick worlds) and you need the Born rule to neglect them? I have seen a few attempts to show exact decoherence, with no terms that need to be neglected. In the context of those models, would you say this circularity is avoided?

PS — In most cases exact classical worlds don't exist in unitary QM, but that's probably nitpicking.

 

[DarMM]

PS — In most cases exact classical worlds don't exist in unitary QM, but that's probably nitpicking.

You're right, I should be saying quasi-classical. I believe Wallace uses that phrase, i.e. classical down to a certain scale.

Why? Is it because there are always some interference terms (or maverick worlds) and you need the Born rule to neglect them?

That's one part, also the stability part. Without decoherence you don't have stable pointer states, so you don't have a stable basis defining the worlds.

I have seen a few attempts to show exact decoherence, with no terms that need to be neglected. In the context of those models, would you say this circularity is avoided?

Taking for example the paper referenced here earlier https://arxiv.org/abs/hep-th/0606062, something like that would seem to avoid circularity if it worked out. However it's not so much exact decoherence, but some kind of decoherence without the Born rule, i.e. being able to neglect certain terms in some Born independent way, even if it isn't exact.

Do you know of some references to non-Born or exact approaches to decoherence, I only know of Zurek's Quantum Darwinism in any depth.

 

[akvadrako]

Do you know of some references to non-Born or exact approaches to decoherence, I only know of Zurek's Quantum Darwinism in any depth.

I don't know it in any depth and I doubt it's general enough; my question was mostly trying to flesh out what would be needed for a satisfying derivation. For reference the paper I though of is: Exact Decoherence Brought by One Internal Degree of Freedom (https://arxiv.org/pdf/1808.02645.pdf). The main idea was published in 2016.

 

[Michael Price]

My point was that the derivation in your Quora post is circular. No implications about other work by Zurek. Your quora post doesn't deal with his later Quantum Darwinism work and it's a very different proof. From a mathematical perspective it would be equally valid to discuss Wallace's proof. I've no need to discuss it as you weren't talking about it. I know that he presents what he claims is a "circularity-free approach", but the essay was quoted to show you Zurek (and the rest of the community) thinks his 2005 work (the one you use in your quora post) is circular (and thus you shouldn't be using it as a definitive proof), not to say that Zurek has had no further alternative ideas.
The "last line" simply meant it was the last line of my quote of the article, not the last line of the article.You are claiming to have modified Zurek's 2005 argument, but removed the dependence on decoherence? The envariance argument requires decoherence (his later Quantum Darwinism argument does not, but it is a separate argument with other weaknesses), as Zurek himself says in the essay I referenced.

Okay, having studied Zurek's informal review in Many Worlds?, and the references therein, it is clear that all I need do to tidy up my quora answer is to reference Zureks's 2007 paper, rather than the 2005 paper. Zurek gives a detailed and non-circular explanation of why probabilities will be equal when the coefficients are all equal, and then proceeds to generalize this to the more interesting non-equal-coefficients case.

 

[Michael Price]

That's one part, also the stability part. Without decoherence you don't have stable pointer states, so you don't have a stable basis defining the worlds.

I think Zurek's quantum Darwinism is trying to show that you have stable pointer states even without decoherence. His point is that information about the stable pointers can be copied endlessly, without restriction, throughout the environment.

 

[DarMM]

it is clear that all I need do to tidy up my quora answer is to reference Zureks's 2007 paper, rather than the 2005 paper. Zurek gives a detailed and non-circular explanation of why probabilities will be equal when the coefficients are all equal

I think Zurek's quantum Darwinism is trying to show that you have stable pointer states even without decoherence. His point is that information about the stable pointers can be copied endlessly, without restriction, throughout the environment.

I'm well aware what Zurek's Quantum Darwinism tries to show, I've read all his papers. Why do you think it is noncircular or unproblematic?

It assumes that there is a universal preferred division of the universe into system+environment and that all the different components of the environment have relatively thermalised phases. What in a pure unitary approach justifies this?

 

[Michael Price]

I can't see where Zurek assumes thermalisation. The copying of information from the object system to the measuring apparatus and/or environment is an explicitly unitary process (as is all time evolution). I don't think Zurek writes very clearly, in places, so I may have missed something, but I don't see the circularity. The quantum Darwinism comes at the end, after he's constructed pointer states and derived the Born rule.