June 24, 2015 at 9:52 pm #2389
Dear Dieter and Shan,
Thank you for running this workshop. In full compliance with Dieter’s ‘moderating remarks’, I want here to point out a deeper layer of the Everett [original] interpretation on the purely technical level. The details on what follows below can be found at http://link.springer.com/article/10.1007/s10773-013-1794-x as well as at http://arxiv.org/abs/1109.6424.
The argument reads: the concept of ‘world branching’ cannot be taken unconditional in the context of the universally valid and complete quantum theory. Where does this claim come from?
For the start, it comes from the fact that quantum entanglement is relative, [Entanglement Relativity (ER)], i.e. entanglement is not a characteristic of a quantum system or of any of the system’s state but is a matter of the system’s DIS. Simplified, the argument easily follows from ER: If one DIS branches then virtually no other DIS of the system in the same instant in time has branched. Hence ‘world branching’ is allowed practically exclusively for one and only one Universe DIS. Existence of such DIS is an additional  condition for the universally valid and complete quantum theory.
The fact that decoherence is not exact and that ‘branching’ may regard certain emergent  DISs of the Universe does not help. For the standard quantum Brownian motion (QBM) model, one can show existence of at least two, mutually irreducible, DISs which simultaneously ‘host’ the QBM dynamics for a pair of mutually irreducible Brownian particles, for which an ‘emergent’ Brownian particle cannot be defined . Bearing in mind that QBM is perhaps the most elaborated and the most ‘macroscopic’ decoherence model of paramount importance for the modern Everett theory, the above distinguished argument seems to be inescapable.
In conclusion, the very basic interpretational rule of the Everett MWI—the world branching–implies at least one additional condition, such as the existence of the preferred structure of the Universe or an elaboration of ‘decoherence process’ in the context of the Everett interpretation.
 E.g. “Without further physical assumption, no partition [of the Universe] has an ontologically superior status with respect to any other”, from http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.87.077901.
 Non-exactness of decoherence and ‘emergent branching’ are extensively discussed in http://ukcatalogue.oup.com/product/9780199546961.do#.T-yOyxcePzg .
 Technical details on the analysis of the QBM model [so-called parallel occurrence of decoherence] can be found at http://link.springer.com/article/10.1007/s12043-012-0296-3 as well as at http://arxiv.org/abs/1011.5919.
June 25, 2015 at 5:01 pm #2392
- This topic was modified 2 years, 8 months ago by Miroljub Dugic. Reason: A misprint
you are certainly right that concepts like entanglement or decoherence depend on an arbitrary definition of
(subsystems of the universe). Therefore, branches cannot (and need not) be exactly defined; these branches are merely a matter of convenience.
What IS important is a concept of local observers that is compatible with the assumed global unitarity. If observers are assumed to be organized and strongly coupled subsystems of the universe, they must be pretty local (assuming local dynamics), but as a consequence of unitarity, and in a universe of growing entanglement between its local parts (an important cosmic initial condition!), they must then permanently
into dynamically separate components states (
) – just like Schrödinger’s cat together with its environment. However, each component is coupled only to its own
branch, and so he observes only one outcome of a quantum measurement.
Clearly, we do not know very much about the precise (conscious?) observer states in the brain. (There is much decoherence still going on within the brain.) Nonetheless, we can estimate what superpositions in the world can have coherent effects on such local observers. If they can not any more, their components must separately affect separate components of the observer. Precisely such a coherent effect on potential observers is eliminated by an irreversible decoherence process. Therefore, it is CONVENIENT to consider components separated by decoherence as forming an incoherent ensemble thereafter (an apparent collapse), regardless of whether an observer will ever enter the scene.
I may have missed your essential point. Did I also overlook the definition of your letters DIS?
Regards, Dieter ZehJune 25, 2015 at 7:47 pm #2393
Dear Dieter [if I may]
Thanks a lot for your comments, which I fully agree and helped me to realize that my first post hadn’t been clear. Let me briefly draw the ‘DIS’ to your attention.
For the sake of the argument, let me illustrate DIS (decomposition into subsystems) via the standard [non-relativistic] treatment of the hydrogen atom (HA). HA is defined as a pair “electron+proton”, e+p, which is a pair of ‘elementary’ (structureless) particles. The pair e+p is one DIS for HA. However, as we all know very well, the standard quantum theory of HA regards the alternative DIS of the atomic “center of mass + internal (relative)” virtual systems that can be presented as CM+R. This CM+R is another DIS for the hydrogen atom and for this DIS, the CM and the R systems represent the ‘elementary particles’.
If the atom were an isolated system—a model Universe—then our main argument starts with Entanglement Relativity (ER) for the atom. Actually, if (as it is typically the case) we assume a tensor-product pure state for the CM+R, the pair e+p *must* be entangled; please notice: this ER argument is kinematical and no interaction (such as the realistic Coulomb interaction) is required for the e+p pair. Already at this point (i.e. even without any regard of decoherence), I can illustrate a challenge posed for the original Everett world branching: Let me assume that the tensor-product state for the CM+R structure (DIS) is a result of ‘world branching’. Then, and this is the point, due to ER, the e+p atomic structure has not branched. As long as we consider the two atomic structures (DISs), e+p and CM+R, on the equal footing, the Everett world branching cannot be physically justified—only one of these structures, either e+p or CM+R, is allowed to branch. Therefore a need to choose one and only one fundamental DIS (atomic structure) that may be allowed to branch.
Is there any realistic, sufficiently ‘macroscopic’ decoherence model in support of this argument? Yes, there is, the QBM model mentioned in my previous post.
I should better stop here with the hope that this time I have better performed.
MiroljubJune 26, 2015 at 8:40 am #2422
my point was that your arguments regarding definitions are correct but irrelevant for the measurement problem in terms of Everett. Nothing ever “branches” objectively in any definition. Instead of repeating my arguments let me invite you to read pp. 14-15 and pp. 18-19 of my first reference.
We may simply be discussing different things.
DieterJune 26, 2015 at 11:36 am #2423
After rereading the reference emphasized in your posts, I can re-emphasize my impression that, at certain point, I do agree with you.
The argument of my previous posts can be re-stated as follows: ‘world branching’ cannot be physically objective [except perhaps in a sense completely strange to me]. In your words: “Nothing ever ‘branches’ objectively in any definition.”.
[To me, this means that the phrases as ‘[dynamically] autonomous worlds’ etc are just a matter of, say, narrative aesthetics—which, according to your ‘moderating remarks’, we have agreed to avoid.]
Then, what might be new/relevant in our cited references?
Two things. First, I think that your position [that I find consistent] is not typical for the Everett MWI community; for this reason we had to go toward ‘emergent worlds’. To this end, our paper addressed the majority of the Everettians  and non-Everettians. Second, even in the context of our common view of non-objectivity of ‘world branching’, the findings referenced in my first post imply some fresh and probably interesting observations. Let me briefly focus on the latter.
Consider two bipartitions, 1+2 and A+B, of a closed composite system (the Universe) C; 1+2=C=A+B. Those bipartitions (the DISs from my previous letters) determine the pair of tensor-product-structures (TPSs) of the C’s Hilbert space. Now a universal state (in an instant of the universal time), some Psi [which has never branched], can be decomposed according to these two TPSs (DISs). Our point is that the closed composite system C (the Universe) hosts the mutually independent and autonomous, simultaneously dynamically evolving quasiclassical Worlds pertaining to the 1+2 and A+B DISs; needless to say, those worlds have nothing to do with ‘Everett worlds’. That is, instead of “Appearance of a Classical World in Quantum Theory”, we learn about “Appearance of THE Classical WORLDS in Quantum Theory”. Those non-branching/non-branched, equally (non)objective worlds [as in our QBM-model-analysis] may be mutually irreducible, i.e. not capable of defining any effective, emergent single quasiclassical world in the single Universe C. To the extent the measurement problem has been solved for the 1+2 world, it must have been equally solved also for the alternative A+B world, and vice versa.
Now the Everett world branching should be assumed for the both quasiclassical worlds, 1+2 and A+B, separately, and on the equal footing. In other words: instead of one Everett Multiverse, there are (at least) two mutually independent and irreducible Everett Multiverses. Certainly, this is a new and not yet explored picture of the quantum Universe (though initiated in http://arxiv.org/abs/1004.0148 ).
 Many Worlds? Everett, Quantum Theory, and Reality,
Eds. S. Saunders, J. Barrett, A. Kent, and D. Wallace, Oxford 2010.
June 26, 2015 at 3:52 pm #2425
- This reply was modified 2 years, 8 months ago by Miroljub Dugic. Reason: A short amendment
I tried to emphasize that – similar to Everett – I am assuming the existence of fundamental “observer” systems, which need only be vaguely known to be localized somewhere in the brain for this purpose. (It would be great if you could find out more about them!) All other subsystems are a matter of convenience, and usually chosen as local systems, too, since causal relations propagate in space.
DieterJune 26, 2015 at 4:49 pm #2426
The assumption of “the existence of fundamental ‘observer’ systems” takes us out of the agreed purely technical discussion. Such systems are not implied by the universally valid and complete quantum theory.
Nevertheless, even if it were applied, my argument does not change: Bearing in mind that quantum theory equally applies to every possible decomposition of the Universe into subsystems, the ‘fundamental observer systems’ (FOSs) must exist for virtually all Universe decompositions.
Please notice that the decompositions I have in mind are such that no subsystem (and therefore the FOSs) appear in the alternative decomposition–otherwise the variation of decompositions lead merely to ‘emergent structures’. In the hydrogen atom mentioned in my previous post: if there is an FOS in electron+proton (e+p), then there should be some another for the center-of-mass+internal-degrees-of-freedom (CM+R); of course, there is no ‘electron’ in the CM+R atomic structure and hence an FOS in the e+p structure is not reducible to a FOS in the CM+R structure.
MiroljubJune 27, 2015 at 2:41 pm #2434
The irreversible “dislocalization of superpositions” over many degrees of freedom (decoherence) is an objective process that leads to dynamically automous “branches”. This does not require any bipartition. However, since this dislocalization does not eliminate the superposition globally, its importance for what we observe can only arise from the locality of observers (the bipartition between them and rest of the universe). Their “subjective individualization” in their locally defined component states is confirmed empirically, and thus avoids an objective collapse as a new dynamical law (which is conventionally located in the measurement apparatus). In the formalism of QT, this individualization (corresponding to a splitting observer in the formalism) can obviously not be explained as a mere increase of information.
There is neither any decoherence nor branching in your simplistic e+p example. So I don´t understand what it has to do with Everett’s branches. The observer’s component states are sufficiently defined in the decoherent branches. In particular, they cannot observe any Schrödinger cats.
Can we leave it that way (whatever else you may have in mind)?
Regards, DieterJune 27, 2015 at 4:26 pm #2435
Leaving the details aside [e.g. the hydrogen atom is a paradigmatic illustration, while the QBM model is practically the only elaborated sufficiently ‘macroscopic’ model], I am happy to learn that you agree with the non-objective character of the Everett world branching–which is the only objective of this Topic. With the due respect, while your position is interpretational, our paper brings a technically elaborated proof for the quantum Brownian motion model.
I am sure there are plenty of those who would not accept non-objective ‘branching’ which nevertheless, I agree, completes our discussion.
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