Decoherence in the Everettian Picture: Why It Fails

 

[Note: this is an adapted excerpt from the introductory chapter to a collected volume, Quantum Structural Studies, forthcoming from World Scientific (eds. R.E. Kastner, J. Jeknic-Dugic, and G. Jaroszkiewicz.]

The idea that unitary-only dynamics can lead naturally to preferred observables, such that decoherence suffices to explain emergence of classical phenomena (e.g., Zurek 2003) has been shown in the peer-reviewed literature to be problematic. However, claims continue to be made that this approach, also known as ‘Quantum Darwinism,’ is the correct way to understand classical emergence.

The problem of basis ambiguity in the unitary-only theory is laid out particularly clearly by Bub, Clifton and Monton (1996), and the difficulty highlighted by them is not resolved through decoherence arguments alone. This is because decoherence is  relational rather than absolute (Dugic and Jeknic-Dugic 2012; Zanardi et al 2004). In order to get off the ground with a particular structure, “Quantum Darwinism”-type arguments depend on assuming special initial conditions of separable, localizable degrees of freedom, along with suitable interaction Hamiltonians, which amount to “seeds” of classicality from the outset.

Under these circumstances, the purported explanation of classical emergence becomes
circular (Kastner, 2014a, 2015). But circularity is not the only problem with the decoherence-based attempt to explain the emergence of classicality. In what follows we examine the logical structure of the argument and find a further, serious flaw: affirming the consequent.

2. The logical flaws of “Quantum Darwinism”

The structure of the Quantum Darwinism argument is as follows:
If
1. the quantum dynamics is unitary-only, and
if
2. the universe has initially separable, localizable degrees of freedom such as distinguishable atoms, and
if
3. those degrees of freedom interact by Hamiltonians that do not re-entangle them,
then
4. classicality emerges.

For decoherence to account for the emergence of classicality under the assumption of unitary-only (U-O) evolution (approximately and only in a “FAPP” sense, see below), all three premises must hold. However, classicality is implicitly contained in 2 and 3 through the partitioning of the universal degrees of freedom into separable, localized substructures interacting via Hamiltonians that do not re-entangle them, so (given U-O) one has to put in classicality to get classicality out. Premises 2 and 3 are special initial conditions on the early universe that may not hold–certainly they are not the most general case for an initially quantum universe. Yet it seems common for researchers assuming U-O to assert that 2 and 3 also must hold without question. This actually amounts to the fallacy of affirming the consequent, as follows: one observes that we have an apparently classical world (affirm 4), and then one asserts that 1, 2 and 3 therefore must hold.

The insistence on 2 appears, for example, in Wallace’s invocation of “additional structure on the Hilbert Space” as ostensibly part of the basic formalism (Wallace 2012, p. 14-15). Such additional structure–preferred sets of basis vectors and/or a particular decomposition of the Hilbert space–is imposed when quantum theory is applied to specific situations in the laboratory. However, what we observe in the laboratory is the already-emergent classical world, in which classical physics describes our macroscopic measuring instruments and quantum physics is applied only to prepared quantum systems that are not already entangled with other (environmental) degrees of freedom.

If the task is to explain how we got to this empirical situation from an initially quantum-only universe, then clearly we cannot assume what we are trying to explain; i.e., that the universe began with quasi-localized quantum systems distinguishable from each other and their environment, as it appears to us today. Yet Wallace includes this auxiliary condition imposing structural separability under a section entitled “The Bare Formalism” (by which he means U-O), despite noting that we assign the relevant Hilbert space structures “in practice” to empirical laboratory situations. The inclusion of this sort of auxiliary condition in the “bare formalism” cannot be legitimate, since such imposed structures are part of the application of the theory to a particular empirical situation. They thus constitute contingent information, and are therefore not aspects of the “bare formalism,” any more than, for example, field boundary conditions are part of the bare theory of electromagnetism.

These separability conditions are auxiliary hypotheses to which we cannot help ourselves, especially since the most general state of an early quantum universe is not one that comes with preferred basis vectors and/or distinguishable degrees of freedom. Thus, the addition of this condition amounts to asserting (2), and becomes (at best) circular reasoning, or (at worst) outright affirming of the consequent, illicitly propping up the claim that quasi-classical world “branches” naturally appear in an Everettian (unitary-only) picture.

Now, to be charitable: perhaps unitary-only theorists are tacitly assuming that (1) is not subject to question; i.e. they  take it as a “given.” If one presumes the truth of (1) in this way, then (2) and (3) seem required in order to arrive at our current apparently classical world. If (1) were really known to be true, the logical structure of the argument would be: “2 and 3 if and only if 4”. So, rather than reject the argument based on its circularity, such researchers seem to assume that the consequent is evidence for the truth of premises 2 and 3 (i.e., 2 and 3 together are seen as the only way that we could have arrived at the classical macro-phenomena we now experience). The possibility that the dynamics may not be wholly unitary–the falsity of the unitary-only premise (1)–does not seem to be considered. However, the need to use a circular argument in order to preserve the claims of Quantum Darwinism should prudently be taken as an indication that the U-O assumption (1) may well be false, and that non-unitary collapse is worth exploring for a non-circular account of how classically well-defined structures arise in a world described fundamentally by quantum theory. (Such an account is proposed in Kastner (2012) and (2014b). In that account (‘possibilist transactional interpretation’ or PTI), decoherence can of course occur under circumstances discussed in Zurek (2003), as a deductive consequence of quantum theory under certain specified conditions; but decoherence alone is neither necessary nor sufficient as an explanation for everyday classical phenomena such as the observed determinacy of macroscopic objects. Decoherence is not necessary because classical emergence can arise through a specific collapse process in PTI, and decoherence is not sufficient because it does not solve the measurement problem (cf. Bub 1997, p. 231).)

3. Conclusion.

Everettian unitary-only quantum theory seems to have become so “mainstream” that in many quarters it now appears to be considered the “standard” theory, replacing the theory consisting of Schrodinger unitary evolution plus von Neumann non-unitary measurement transition. Yet the only way to arrive at the world of classical phenomena we experience in the unitary-only theory is to assume classicality at the outset–and even this is only approximate and “FAPP,” since it fails to solve the measurement problem, as noted in Bub 1997, Section 8.2. The “decoherence” process as invoked in service of “Quantum Darwinism” is at best circular and at worst amounts to the logical fallacy of affirming the consequent. The alleged utility of decoherence is greatly overstated and illusory. It is time to consider the possibility that Everett might have been wrong.

References

Bub J, Clifton R, Monton B, 1998, The Bare Theory Has No Clothes.

In {\bf Quantum Measurement: Beyond Paradox}, eds. Healey R A, Hellman
G, {\bf Minnesota Studies in the Philosophy of Science 17}, 32-51.
Dugi\’ c M., Jekni\’ c-Dugi\’ c J., 2012, Parallel decoherence in composite quantum
systems, Pramana {\bf 79}, 199

Dugi\’ c M., Arsenijevi\’ c M., Jekni\’ c-Dugi\’ c J., 2013,
Quantum correlations relativity, {\bf Sci. China Phys., Mech. Astron.
56}, 732
Jekni\’ c-Dugi\’ c J.. Dugi\’ c M., Francom A., 2014, Quantum
Structures of a Model-Universe: Questioning the Everett
Interpretation of Quantum Mechanics, {\bf Int. J. Theor. Phys.
53}, 169

Kastner, R.E., 2012. {\bf The Transactional Interpretation of Quantum Mechanics: The Reality of Possibillty}.
Cambridge: Cambridge University Press.

Kastner R. E., 2014a, Einselection of pointer observables: The new
H-theorem?, {\bf Stud. Hist. Phil. Mod. Phys. 48}, 56

Kastner R. E., 2014b, The Emergence of Spacetime: Transactions and Causal Sets,
forthcoming in {\bf Beyond Peaceful Coexistence}, I, Licata, ed.; Preprint version http://arxiv.org/pdf/1411.2072v1.pdf.

Kastner R. E., 2015, Classical selection and quantum Darwinism,
{\bf Phys. Today 68}, 8
Wallace, D., 2012, {\bf The Emergent Multiverse: Quantum Theory
according to the Everett Interpretation}. Oxford University Press,
Oxford
Zanardi P., Lidar D. A., Lloyd S., 2004, Quantum Tensor Product
Structures are Observable Induced, {\bf Phys. Rev. Lett. 92},
060402

Zurek W. H., 2003, Decoherence, einselection, and the quantum
origins of the classical, {\bf Rev. Mod. Phys. 73}, 715

19 thoughts on “Decoherence in the Everettian Picture: Why It Fails

  1. Hi, Ruth–you said comments welcome, so I thought I’d leave one. I’ve always thought the idea that decoherence produces ‘parallel worlds’ is also an added assumption. If it were true, it would seem more consistent with a reality where any measurement renders the quantum involved thereafter incapable of producing an interference pattern; yet self-interference persists, or after all these billions of years we probably wouldn’t know about QM. So why assume decoherence results in parallel worlds that never interact? It may be a mathematical and logical possibility, but it doesn’t seem very inevitable. I’ve also thought that, even if they can someday resolve all the difficulties, there are probably still fatal philosophical problems. I don’t see how you can avoid a universe without probability, even if it all works on paper. But then, if all outcomes are equally likely, how can ANYTHING be impossible? Or coming from the other direction, why does this whole range of possibilities exist if it’s not part of a probability distribution? Most importantly, what does it say about the laws of physics if all outcomes are equally likely? Finally, the whole idea of the self splitting–it seems heavily dependent on the ‘consciousness as meaningless epiphenomenon’ view, which is almost certainly wrong. But then you and I have talked A LOT about that! :)
    Have a great week!
    Eric.

  2. Of course, I should’ve added that, while loss of ‘quantumness’ upon any measurement would seem more philosophically consistent with the idea of worlds irrevocably splitting, it would swiftly render any future world-splitting impossible. But that’s hardly a reason to assume the world splits!

    1. Yes–the splitting comes about because decoherence does not eliminate the superposition, it just suppresses the interference. Decoherentists were forced into a many-world picture because of this. And of course, as you noted, it makes the quantum probabilities questionable. This problem has been tackled by Everettians with reference to decision theory heavily dependent on a vague notion of the ‘observer’ as a counterpart of some single identity. But in any case they have the circularity and the affirming the consequent as part of their program too (and ignoring of the published literature pointing out these problems).

  3. Thanks, Ruth. I didn’t mean to imply MWI was not SELF-consistent. I was just thinking, not all the decoherence people believe in a multiverse–some of the Consistent Histories people, etc.; and some collapse interpretations claim to make use of it. That’s why I was thinking the idea of the world split is an added assumption. As for what I was saying about interference, it might not have been the best analogy–but I was also thinking the idea that decoherence PERMANENTLY suppresses interference is not so inevitable–why should the ‘multiverse’ not be a big mush with separate branches interfering all the time? Just because we don’t see it and QM wouldn’t work if that were true (two electrons don’t blend into one interference pattern, they measure each other) isn’t good enough–because we don’t see the other universes, either. You have to assume decoherence works in a specific way to get an arbitrarily large number of worlds superimposed on each other to no effect. And what’s more elaborate: a whole wavefunction self-interferes all the time, then stops at a measurement, then the whole things starts self-interfering again–or, a wavefunction always self-interferes, except for when it splits into other wavefunctions that never re-interfere, even while they continue to self-interfere (independent of measurement)? I’m not arguing with you, of course–this is just something I’ve thought about before, because MWI people are always claiming elegance and inevitability.

    1. Yes of course there are a lot of assumptions that go into it. (And the ‘decoherent histories’ idea is wishful thinking since the decoherence is only approximate, and requires special initial conditions.) That’s why it’s hardly ‘inevitable’. It’s only ‘inevitable’ if one commits a logical fallacy of assuming what they claim to explain or affirming the consequent.

  4. BTW–the reason I didn’t comment directly on your criticism of Zurek is because you’ve actually shown me the above argument before, on your free will page–and I thought it was good. I even understood it, as an English major! :)
    As for what I was saying about the assumptions re the world split–I think there’s a weakness in logic there but I’m not sure what to call it. Technically, their assumptions, if you disregard preferred basis and probabilities, are possible–but this is what I was thinking. They assume the split happens because interference vanishes–weird and unverifiable, but logically okay. Then they say, ‘Parallel worlds don’t re-interfere,’ because that would break physics and it obviously doesn’t happen. But does it follow specifically from THEIR theory, or from the observations we’re all making within a single reality? Because the thing is, every other interpretation poses a very inevitable reason for why parallel worlds don’t re-interfere: they don’t exist!!! But MWI assumes the world-split happens without observing it, then uses observations to deduce that the worlds don’t re-interfere–they’re departing from observation, then turning back to it to complete the theory. But when they depart from observation (by assuming the split), they’re tossing out the ‘apparent’ rules and playing by new ones; to be credible, shouldn’t those ‘new rules’, have to explain why re-interference doesn’t happen, even though we know it doesn’t? They shouldn’t just be able to say, ‘The parallel worlds happen under our new rules; they don’t re-interfere because the old rules (every observation we’ve ever made) obviously forbid it.
    Isn’t this yet another example of ‘affirming the consequent’?
    Better get back to my book now–let me know whenever you’d like to see new pages! :)

    1. Actually I think that the assumptions they use to ‘derive’ decoherence (are contrived to) ensure that the chances of re-interference are negligible. If you start with suitably distinguishable degrees of freedom and Hamiltonians that don’t re-entangle those degrees of freedom, then you get essentially irreversible decoherence.
      I’m still swamped with stuff I have to write up, so I’ll hold off for now on reading more of the novel…but I look forward to it!

  5. Thanks, Ruth. You might have implied what I’m talking about when you said “(are contrived to)” about decoherence–it has to be contrived ‘just so’ to obtain the results they want. Now for one more question–one I’ve always had about MWI–even if its supporters can someday make everything work out internally regarding preferred basis and Born Rule–isn’t it STILL a gigantic leap to assume that reality really works this way? For instance, I could be sharing space with an interstate right now as I write this in my living room, yet the traffic doesn’t trouble me because my world and the interstate’s are not coherent. Would mere internal consistency force this conclusion? Beyond that, doesn’t one have to assume reality really works that way?
    Oh–one other thing; I thought I might leave a comment sometime at your “open letter to Dr. Sam Harris”. I’ve always liked that piece of yours and have a couple thoughts as a (hopefully moderate & open-minded) religious person.
    Didn’t mean to pester you–I know you’re busy!
    Eric.

    1. Well they are forced into that by the unitary-only assumption, because they can’t otherwise explain why we experience only one outcome. This is why collapse really needs to be brought back into the picture, but so far the only ‘mainstream’ collapse interpretation is the GRW mechanism which is thoroughly ad hoc. Hopefully people might start considering TI, which explains the Born Rule and solves these problems.

  6. Actually, the thing that I was thinking was that, if MWI addresses both your objection and somehow explains the appearance of the Born Rule in its own context (both of which scenarios seem extremely unlikely), that would make it a legitimate interpretation…but it STILL wouldn’t necessarily make it true. Of course the idea that there are many worlds would be forced by MWI’s explanation (by accepting it, I mean), but whether or not the explanation itself is actually correct would still be undecided. I guess I’m thinking of String Theory, here–the fact that it’s supposedly an internally consistent mathematical structure doesn’t make it right; I could also be thinking of inflationary bubble universes. Now, there’s probably no way of directly proving bubble universes, even if they exist; yet the idea of their existence isn’t as troubling as MWI because it doesn’t fly in the face of everything we’ve ever experienced. I’m thinking that, with MWI, probabilities will always be a severe philosophical problem, even with an ‘apparent’ Born Rule, and also that the idea that worlds are constantly splitting and also sharing space, and that consciousness is constantly splitting, seems so inconsistent with everything we know that MWI’s ability to explain ITSELF in a way that isn’t fatally flawed would not be enough to convince me of its correctness!
    BTW–you might find this interesting. I have thought before about how consciousness and the self might be reconciled with MWI. It might work like this: Brahman (universal wavefunction); Atman’s Brahman; Atman’s Many Atmans. There might even be real free will in this scenario–not for the Atman’s Brahman, but for the Many Atmans. All of this notwithstanding, I think the self as we know it is still a major argument against MWI, even if the other objections could be addressed.
    I’d say Happy St. Patrick’s Day–but it’s a day early, and you’re German, aren’t you? ;)
    Eric.

    1. Well, it’s very hypothetical that MWI could address the objections I’ve raised–because I think it’s fatally flawed in exactly those respects and that it has no way to address them. Of course they could surprise me, but then we’d still have a picture of uncountably infinite new ‘worlds’ arising at every uncountable infinitesimal unit of time, which as you say just sounds beyond absurd.
      My family background is Eastern European, but last year I spent St. Patty’s Day at our neighborhood Irish Inn drinking Guinness and wearing my green shamrock headband! Always happy to help the Irish celebrate! ;)

  7. Does it make sense to claim that “handshake” is just another name for strange loops from Douglas Hofstadter’s books “Gödel, Escher, Bach” and “I Am Strange Loop”, i.e. the many worlds interpretation and consciousness cannot share the same reality? It seems that even Hofstadter wouldn’t agree. Also, I totally fail to understand how the Born rule, Heisenberg’s uncertainty principle, and wave-particle complementarity could be explained by many worlds, i.e. how come that anyone supports that interpretation. If we didn’t already know about quantum mechanics, there would be absolutely nothing about how the many worlds folks see reality to assume its existence. On the other hand, strange loops and discussions about free will…

    “There’s no such thing as a free will.” – Douglas Hofstadter (http://www.scaruffi.com/mind/hofstadt.html)

    1. Thanks—I haven’t heard of ‘strange loops’ and would have to look into this. But I do agree that MWI is just an attempt to deal with the measurement problem of QM, and there is nothing else to suggest it. MWI certainly does not explain those aspects of QM that you cite. If anything, it is incompatible with them. My impression is that people support MWI because they can’t see any other way of addressing the problem of measurement. A while ago, Cramer and I wrote a paper entitled “Why Everettians Should Appreciate the Transactional Interpretation,” but apparently they were not interested. (http://arxiv.org/abs/1001.2867)

      1. There is a recent paper by David Deutsch: http://constructortheory.org/portfolio/logic-experimental-tests
        He writes for instance: “So, how is it that stochastic theories can be useful in practice? I shall show in Section 7 how ‘collapse’ variants of quantum theory can, even though they are ruled out as descriptions of nature by the above argument.” Either those who agree with him see something obviously and totally fail to share their insights with other people or they don’t rule out anything. He also says that “since quantum theory and general relativity are inconsistent with each other, we know that at least one of them is false, presumably both” and: “Traditional ‘collapse’ theories are also inherently far worse explanations than Everettian quantum theory, by criterion (i), since they neither explain what happens physically between measurements, nor what happens during a ‘collapse’.” In a way he says that his theory is terrible, but other theories are even worse (note the words “between” and “during”).

      2. Thanks. Deutsch’s comment “since quantum theory and general relativity are inconsistent with each other, we know that at least one of them is false, presumably both”, is a prime example of ‘inside-the-box’ thinking. Apparently it hasn’t occurred to him that the two theories describe different physical domains. If two theories describe different domains, of course they are going to ‘disagree’. It’s a shame when people dismiss fruitful new avenues of research because they have their heads in a box. Even worse when they castigate those who are willing to leave the box. But this goes on all the time and Boltzmann had to deal with it as well.

  8. It might be just me, but my understanding of what your work is that it’s about systems all the way down and why there are systems all the way down, von Bertalanffy applied to physics. A similar approach from a different angle seems to be Ladyman (someone you are familiar with) et al, “Every Thing Must Go”.

    1. Thanks. Certainly, at the spacetime level, PTI sees everything as events connected by a web of relationships, and ‘things’ are cohesive, semi-permanent patterns emergent from that web of relationships.

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