In what sense does MWI fail to predict the Born Rule?

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Discussion Overview

The discussion centers on the Many-Worlds Interpretation (MWI) of quantum mechanics and its ability to derive the Born Rule. Participants explore criticisms of existing derivations of the Born Rule that are generally accepted by proponents of MWI, focusing on theoretical implications and the challenges faced in establishing a valid derivation strictly from MWI postulates.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that no derivation of the Born Rule has been produced using only the postulates accepted by MWI that is generally accepted as valid.
  • One participant questions how probabilities can be assigned to branches of a symmetric wavefunction without additional assumptions, suggesting that unitary quantum mechanics alone does not suffice.
  • Another participant discusses the limitations of Zurek's proof, noting that it relies on assumptions about state subspaces and begins with a notion of probability, which may not be justified within MWI.
  • Concerns are raised about the Oxford style decision theory proofs, which allow for the construction of a utility function that behaves as if the Born Rule is true, but do not establish its uniqueness or relevance to actual measurement outcomes.
  • Participants mention Gleason's Theorem as a potential reference point for deriving probabilities from quantum states, but its implications for MWI remain debated.
  • One participant describes a proposed modification to the splitting protocol in MWI to account for observed frequencies, but expresses skepticism about the non-randomness of outcomes and the necessity of quantum indeterminacy for accurate predictions.
  • There is a discussion about the rejection of wave function collapse in MWI and the implications this has for deriving the Born Rule solely from unitary evolution.

Areas of Agreement / Disagreement

Participants express differing views on the ability of MWI to derive the Born Rule, with some arguing that it cannot be done without additional assumptions, while others challenge the validity of existing derivations and the implications of decision theory approaches. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants highlight the dependence on definitions and assumptions in their arguments, particularly regarding the nature of probabilities and the role of wave function collapse in quantum mechanics. There are unresolved mathematical steps and conceptual challenges in establishing a clear derivation of the Born Rule within the framework of MWI.

  • #211
Stephen Tashi said:
Is the rational agent supposed to know the Born weights? For example, if he is an agent in a "maverick" world, do we assume he knows the correct values of the Born weights? - or would he believe some erroneous (from a global viewpoint) values for them?
I have been asking myself the same thing. Reading between the lines - and there are many of them - of what has been posted here, it seems that Wallace's scenario is of living in an MWI-universe but not necessarily realising it. And not necessarily knowing how to compute Born weights. Instead, the best expectation - as calculated by "us" on the rational agent's behalf - would be when the agent's decisions are based on estimates of probabilities which are numerically equal to the Born weights. So if he lives in a maverick world, his empirical estimates of the Born weights which he thinks of as probabilities, will simply be wrong. He will doubtless use them as they are presumably all he has but his strategy in life will be sub-optimum.
 
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  • #212
Stephen Tashi said:
Without digressing into metaphysics, we can look at the assumptions made about the sensation of self - namely that we think of ourselves (at time t) as being a unique physical phenomena. So, assuming our sensation of self is implemented by physical phenomena, we assume that we are not being implemented by two distinct phenomena. For example, if somehow an exact duplicate of our bodies was created we would assume that we would remain ourself. The duplicate would think it was us, but, from our point of view, be mistaken. It seems to me that in mathematical discussions about a rational agent "the agent" (at time t) denotes a unique physical phenomena and the agent makes decisions thinking of itself as a unique physical phenomena. Is that correct? Or do the technicalities of macroscopic vs microscopic phenomena undermine the uniqueness of an agent as a unique physical phenomena?
A probabilistic argument won't get very far if it postulates the existence of an entity without defining a measure on the entity. Which is why it is best to decouple who or what an observer is from the phenomena that she observes. I.e. for MWI to stop at the sense organs, thus allowing "what she sees" to be defined in terms of Everettian relative states. Anything else is metaphysics. Whilst it is entirely reasonable to say that an improper mixture, such as Schroedinger's Cat, is a superposition of einselected states, it is complete gibberish to talk about the observer's mind being a superposition of experiences. To mine of the same anyway.
 
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  • #213
bhobba said:
That is the big problem with Wallace - it took me about 6 months to fully study it. It is very mathematical and I could not break any of it's theorem's - but its just that - very mathematical. In fact it helped me understand decoherent histories a lot better. I have said its mathematically very beautiful - but math is not physics. The big issue is can the assumptions it makes ie can you use decision theory to deduce the Born Rule. If you accept yes its fine - if not its challengeable. But if you have a deterministic theory that does not give the version of you that in a particular world then what can you do? If you reject it then the whole thing goes down the gurgler in the sense in MW all you have is a wave-function and that's it.
My biggest problem with Wallace comes early on in the book and is number one on my list above. Currently there is only the standard way of deriving decoherence, via use of the tracing rule. Wallace and many other proponents of MWI can't do this, they basically need to reverse the usual proof order, derive a branching structure first and then the Born rule.

The problem is, they haven't done this, outside of having vague arguments that it could be done by coarse-graining Hilbert space. So Wallace's proof is fine provided you accept the assumptions that a branching structure will derived via other methods at some point. I certainly don't accept the arguments in his book, they're not a calculation proving the emergence of robust quasi-classical branches. And at times the arguments are a little self-contradictory as Mandolesi discusses (others point this out as well).

So my main contention would indeed be with the use of decision theory, but more so in the assumption of a stable background for it to take place in.
 
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  • #214
DarMM said:
My biggest problem with Wallace comes early on in the book and is number one on my list above. Currently there is only the standard way of deriving decoherence, via use of the tracing rule. Wallace and many other proponents of MWI can't do this, they basically need to reverse the usual proof order, derive a branching structure first and then the Born rule.
Regardless of Wallace, where does Zurek's proof assume the tracing rule? Or will you be showing it sneaking in somewhere when you post the "issues"?
 
  • #215
bhobba said:
but math is not physics

Even more importantly can it postdict or predict anything new. Or give some real testable understanding of things like what are particles, what is exactly charge ..etc. Any theory that is of a fundamental nature should contain many of these things as aspects of a coherent concept/theory.
 
  • #216
From a paper of Kent about the MWI:

After fifty years, there is no well-defined, generally agreed set of assumptions and postulates that together constitute “the Everett interpretation of quantum theory”. Far from it: Everett[1, 2], DeWitt[7], Graham[8], Hartle[6], Geroch[10], Deutsch[11], Deutsch[12], Saunders[13], Barbour[14] (partly inspired by Bell[15], though Bell’s aim was not to inspire), Albert-Loewer[16], Coleman[17], Lockwood[18], Wallace[19], Wallace[20], Vaidman[21], Papineau[22], Greaves[23], Greaves-Myrvold[24], Gell-Mann and Hartle[25], Zurek[26] and Tegmark[27], among many others, have offered distinctive and often fundamentally conflicting views on what precisely one needs to assume in order to get the Everett programme off the ground, and what precisely an Everettian (or, some say, post-Everettian) version of quantum theory entails.
​
 
  • #217
DarMM said:
Zurek has four axioms
But you stated only three. Please correct the post.
 
  • #218
A. Neumaier said:
But you stated only three. Please correct the post.
I think all four are listed. Axioms A1-A3 and then anyone of B1-B3.

EDIT: I see I had said there were four versions of the fourth axiom, there are only three versions of it, so I've corrected that.
 
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  • #219
DarMM said:
I think all four are listed. Axioms A1-A3 and then anyone of B1-B3.
Ah yes.
DarMM said:
the environment can always be enlarged by adding an extra system to reduce the unequal amplitude case to the equal amplitude case.
This is only true in a formal sense that an environment exists with this property. But to apply to the real world, it wold have been necessary to show that enlarging the actual environment to a bigger actual environment is possible, such that his property holds. This is unlikely to hold.
 
  • #220
A. Neumaier said:
From a paper of Kent about the MWI:

After fifty years, there is no well-defined, generally agreed set of assumptions and postulates that together constitute “the Everett interpretation of quantum theory”. Far from it: Everett[1, 2], DeWitt[7], Graham[8], Hartle[6], Geroch[10], Deutsch[11], Deutsch[12], Saunders[13], Barbour[14] (partly inspired by Bell[15], though Bell’s aim was not to inspire), Albert-Loewer[16], Coleman[17], Lockwood[18], Wallace[19], Wallace[20], Vaidman[21], Papineau[22], Greaves[23], Greaves-Myrvold[24], Gell-Mann and Hartle[25], Zurek[26] and Tegmark[27], among many others, have offered distinctive and often fundamentally conflicting views on what precisely one needs to assume in order to get the Everett programme off the ground, and what precisely an Everettian (or, some say, post-Everettian) version of quantum theory entails.
​
Derek P said:
Please restrict your answers to criticisms of derivations of the Born Rule that are generally accepted by proponents of MWI. Please provide a verbal description of the issue where possible so that people like myself who are certainly graduate-plus* but rusty as hell have a chance of seeing what the point is.
*plus nearly half a century in my case :biggrin:
So then, in what sense does MWI fail to predict the Born Rule?
Someone else's list of other author's different treatments doesn't really answer the question.
 
  • #221
Derek P said:
Someone else's list of other author's different treatments doesn't really answer the question.
But it shows that the question is far too imprecise to be clearly answered. Talking about MWI without saying whose MWI is meant is very ambiguous.
 
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  • #222
A. Neumaier said:
This is unlikely to hold.
Why?
 
  • #223
Derek P said:
Why?
Because we can construct a particular environment artificially in mathematical terms, whereas in reality we must pick one from the environments encoded in the universal wave function.
 
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  • #224
A. Neumaier said:
Because we can construct a particular environment artificially in mathematical terms, whereas in reality we must pick one from the environments encoded in the universal wave function.
I assume you mean a sub-system of the total environment?
 
  • #225
Derek P said:
I assume you mean a sub-system of the total environment?
Of course since one cannot augment the total environment.
 
  • #226
A. Neumaier said:
Of course since one cannot augment the total environment.
And you feel that we cannot pick/specify a subsystem with enough degrees of freedom to obtain degeneracy? Sorry to sound like a stuck record, but why not?
 
  • #227
Well, I was reading a few papers around Zurek's proof to give more context and hadn't finished them yet, but roughly the problems are:
  1. Zurek assumes the existence of a pre-existing branching structure of the type usually proven via decoherence. This is the same problem Wallace has. Note that Zurek himself now says this is true and considers the proof not to hold for this reason. This is a major motivation for his Quantum Darwinism project.
  2. Of the B1-B3 axioms needed to complete the proof, B1 and B2 have little physical evidence in their favour and it is hard to imagine them holding for arbitrary states.
    B3 is a very general statement about entangled states having the interpretation of correlations between the systems. If you take as your four axioms A1-A3 and B3, then the entire proof is just concerned with the statistics of Schmidt states and doesn't take place in any particular interpretation.
    Basically B1 and B2 have MWI meanings, but are probably not valid on real physical systems. B3 turns the proof into a proof of the full Born rule from a weak Born rule in any interpretation and isn't about MWI per se anymore.
  3. The problems A. Neumaier mentioned about the environment extension.
I'd like to give more detail however, including a full discussion of a simple case of the proof, where it can be seen that it isn't really envariance that holds the proof together, but a certain noncontextuality assumption.
 
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  • #228
Thread closed for moderation, in order for the Mentors to consider whether allegations about whether the thread is acceptable or not are off topic.
 
  • #229
Thread reopened. Some off topic posts have been deleted.
 
  • #230
Derek P said:
why not?
An alleged proof is supposed to explain why, and not to öeave filling out the gap to the reader.
 
  • #231
A. Neumaier said:
But it shows that the question is far too imprecise to be clearly answered. Talking about MWI without saying whose MWI is meant is very ambiguous.

Yes I now realize MW has an (maybe more than one) issue - not with its math - it's tight - many other issues are the same as decoherent histories and answered the same way. But you just can't get around this idea - its deterministic - how do you introduce probabilities. I think the bet/wager idea is OK meaning decision theory is ok - but can I prove it -it just seems reasonable to me - but reasonable and true are two different things. BTW the reason I find it too weird to believe in is this exponentially increasing number of worlds - there is no end and it keeps increasing faster and faster - that just doesn't seem right.

Thanks
Bill
 
  • #232
That's funny, as a result of this thread and what I've read, I've come to round to a different point of view. I don't mind it too much conceptually, but I find it mathematically inconsistent/circular, due to the assumption of branches and macro structures without any proof that these arise. Although maybe you are including this in conceptual issues.

I think there are two MWIs.
  1. Pure unitary QM MWI, i.e. a "literally" interpreted QM with only Hilbert Spaces and unitary evolution
  2. MWIs with various extra features already assumed to be present. The latter is really a family, being different elements of Kent's list quoted by A. Neumaier. Wallace has the extra features of a fuzzy branch structure and clear macrostate partitioning of the Hilbert Space. Zurek has a precise branching structure and powerful assumptions about quantum subsystems.
The theory is often discussed and promoted as 1, but the proofs all take place in some form of 2.

EDIT: I hope to get to a longer post about Zurek's proof sometime this week.
 
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  • #233
DarMM said:
The latter is really a family, being different elements of Kent's list quoted by A. Neumaier. Wallace has the extra features of a fuzzy branch structure and clear macrostate partitioning of the Hilbert Space.

I find decoherent histories has that same issue and seems resolved there - however a discussion of that (mentors hat on) requires a new thread. Here is a book on consistent histories but I find it a bit basic:
http://quantum.phys.cmu.edu/CQT/index.html

But getting more advanced stuff on it I don't find easy - what I know of it at an advanced level I got mostly from Wallace.

Zurecks stuff is the same - interesting, and I don't think it has been discussed as much as MW here - a bit - but not much - also really needs its own thread.

Thanks
Bill
 
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  • #234
bhobba said:
I find decoherent histories has that same issue and seems resolved there - however a discussion of that (mentors hat on) requires a new thread.
I won't go into decoherent histories as you suggest, only to contrast. I think the difference is that the use of decoherence is valid there as they can use the Born rule, MWI cannot unless it proves it first. So you have to show a fuzzy branching structure and macrostate partition arises without Born's rule.
 
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  • #235
DarMM said:
I won't go into decoherent histories as you suggest, only to contrast. I think the difference is that the use of decoherence is valid there as they can use the Born rule, MWI cannot unless it proves it first. So you have to show a fuzzy branching structure and macrostate partition arises without Born's rule.

Why do you think WMI cannot just assume the Born rule, interpreted as a measure of existence?
 
  • #236
akvadrako said:
Why do you think WMI cannot just assume the Born rule, interpreted as a measure of existence?

It can just assume it, or equivalently non-contextuality. The trouble is it ruins the 'beauty' of the interpretation that attracts many to it - you just have the Schrödinger's equation and that's it - you derive the Born rule. But, as a number of posts have shown here, before anything significant can be derived such as say the emergence of a classical world you need the Born Rule to do it - eg see my post on decoherence and its math - the Born rule is inherent in it. You can, like Decoherent Histories define a history without the Born Rule - but using the concept you need to be able to assign a probability to a history - that requires the Born rule. Note - I am using trace (OP) where O is the observable and P the state as what I call the Born Rule.

Thanks
Bill
 
  • #237
bhobba said:
The trouble is it ruins the 'beauty' of the interpretation that attracts many to it - you just have the Schrödinger's equation and that's it - you derive the Born rule.

Maybe it ruins the beauty for you, but I don't think it's a popular opinion for those working on it. It also seems clear that it's impossible without making some additional assumptions. So, it basically comes down to what are you trying to show? Not that the Born rule is incompatible with WMI and not that it has to be derived for the theory to make sense. But that you would like it to be derived with no additional assumptions and it can't be.
 
  • #239

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