- TL;DR Summary
- I decided to finally "find out" what Dieter Zeh had in mind, when he wrote that a little more than just a universal Schrödinger equation is required for explaining the stochastic nature of measurements
All the universe needs is the wave function and the Hamilton operator.
No, that is not enough, see Nothing happens in the Universe of the Everett Interpretation by Jan-Markus Schwindt. MWI proponents like Lev Vaidman agree with that assessment, and Dieter Zeh independently already remarked much earlier that "a little bit more" is needed, even so I never found out what "little addition" exactly he had in mind when he made that remark. (I read his remark in his "Physik ohne Realität: Tiefsinn oder Wahnsinn?")
Sorry for derailing that discussion even further. My reference to Dieter Zeh's German book was unlucky, not just because it is not a peer reviewed paper, but also because I did not remember the exact place with the remark.That is not even a peer reviewed paper and I'm not talking about the Everett interpretation in the first place.
Since this has bothered me since a long time anyway, I now searched the book until I found that exact place in chapter "13 Wurzeln des Dekohärenzkonzepts in der Kernphysik". That chapter is an abriged translation of Roots and Fruits of Decoherence (Talk given at the Seminaire Poincare (Paris, November 2005)), and the relevant paragraph occurs already on the first page:
I highlighted local basis, because sentences like "we rely on a single key principle: changes purely to the environment do not affect the probabilities one ought to assign to measurement outcomes in a local subsystem" from the abstract of arXiv:1405.7577 (a derivation of the Born rule by C. Sebens and S. Carroll) and Jan-Markus Schwindt's analysis both seem to hint that what is missing is a connection to a space-time structure. Or maybe a tensor product structure (for quantum computing), I guess the important part is just that talk about locality has to be meaningful. (Not so sure about talk of system and environment, probably less important, because it will remain somewhat arbitrary anyway.)So let me first emphasize that by decoherence I do neither just mean the disappearance of spatial interference fringes in the statistical distribution of measurement results, nor do I claim that decoherence without additional assumptions is able to solve the infamous measurement problem by explaining the stochastic nature of measurements on the basis of a universal Schrödinger equation. Rather, I mean no more (and no less) than the dynamical dislocalization of quantum mechanical superpositions, which are defined in an abstract Hilbert space with a local basis (given by particle positions and/or spatial fields, for example). The ultimate nature of this Hilbert space basis (the stage for a universal wave function) can only be found in a unifying TOE (theory of everything), but does not have to be known for the general arguments.
Another relevant paragraph mentioning assumptions occurs on page 5:
That sound like Zeh's Many Minds interpretation to me. I believe Zeh knew that it was not widely accepted, therefore I guess that this is not what he meant by "additional assumptions".However, what I had in mind went beyond what is now called decoherence, since it was inspired by the above mentioned picture of an observer inside a closed quantum system. An external observer, who is part of the environment of the observed object, becomes entangled, too, with the property he is observing – just as the observer within the deformed nucleus is entangled with its orientation. He is thus part of a much bigger “nucleus” (or closed system): the quantum universe. So he “feels”, or can be aware, only of a definite value of the property he has measured (or separately of different values in different “Everett worlds”). All you have to assume is that his various quantum states which may exist as factor states in these different components of the global wave function are the true carriers of awareness. This is even plausible from a quite conventional point of view, since these decohered component states, which are a consequence of the Schrödinger equation, possesses all properties required to define observers, such as complexity and dynamical stability (memory). Indeed, these states are the same ones that would arise in appropriate collapse theories if they were, according to von Neumann’s motivation, constructed in order to re-establish a psycho-physical parallelism. But I do not see why such a modification, that just eliminates all “other” components from reality, should be required.
I also found paragraphs relevant to Zeh's opinion on derivations of the Born rule and the role of the initial condition of the universe in chapter "5 Physik ohne Realität: Tiefsinn oder Wahnsinn?" and chapter "18 Warum Quantenkosmologie?". Those can be found here, but there is no English version, nor "the slightest trace of peer review". The places in the "WebEssays" are page 16 "Alle Interpretationen postulieren die bornschen statistischen ... Versuche, sie aus der everettschen Interpretation abzuleiten, muß man als fehlgeschlagen ansehen." and page 3 "It is the initial condition of the universe that ... explains the origin of quasiclassical domains within quantum theory itself." Those places helped me to remember, why it was so difficult for me to be sure what exactly Dieter Zeh had in mind when he mentioned those "additional assumptions". (But in the meantime, at least I learned that Dieter Zeh had always warned about misinterpreting what can be explained by decoherence alone, so maybe it was just a mistake from my side to interpret his warning as "a remark about a hypothetical completion of MWI".)