Hi Marcus et al. > On Apr 30, 2019, at 10:41 PM, Marcus Daniels <[email protected]> wrote: > > Eric writes: > > < The important consequence of this understanding is that we have > mathematical formalizations of the concept of state and of observable, and > they are two different kinds of concept. It is precisely that both can be > defined, that the theory needs both to function in its complete form, and > that the definitions are different, that expands our understanding of > concepts of state and observable. > > > It seems to me that it is kicking the can down the road. It enables > communication but it is not clear it drives toward a resolution of what is > going on. I have heard other (computational) physicists claim that "all > physics is local", which may or may not be true depending on what the > calculator chooses to believe. It seems to keep the two concepts clear one > cannot make that commitment.
I am not sure this is right, or that we can know whether locality is a problem until the quantum gravity situation is sorted out. Here I have to be careful, because I don’t work in this area professionally. Let me try a little, and stop when I know I can’t keep up with the topic. What I mean is this: 1. For now, classical gravity is all we have, which means that in our physics locations exist as definite indices, and on top of those we can write down a quantum theory in which states are defined in terms of those indices. Short of black hole unitarity problems, there isn’t any specific failure of that quantum theory that tells us what if anything would need to be changed. 2. In such a quantum theory, state vectors evolve under some Hamiltonian, and the Hamiltonian is written only in terms of local interactions in the spatial index. When I say something like “physics evolves locally”, that is all and everything I mean. We haven’t had to give any of that up, as far as I know. 3. There certainly can be superposition state vectors, with spin correlations that it has become popular to refer to as “entangled” since the quantum computing parlance took over the field. (I have nursed some vague discomfort that it is a double entendre with illegitimate romantic liaisons that is responsible for the popularity of that terminology; nobody would have got so excited over “correlated-spin superpositions”, which was the older language for the same thing). In those state vectors (say for an Einstein-Podolsky-Rosen pair allowed to evolve so the carriers of the spin are separated by a large distance), there can be zero values for some observables, such as “up-New-York-and-down-Los-Angeles”, or “left-New-York-and-right-Los-Angeles”, even though there are marginals “(up-New-York)-or-without-respect-to-(down-Los-Angeles)” etc. 4. The values of those microscopic observables can evolve jointly with values of more complicated large-actor observables that we describe as apparatus measuring spins etc., and the branches of the large-actor state vector can evolve to have no coherence; but that evolution is still all under the same local Hamiltonian. 5. A decoherent-histories formulation (Hartle, Gell-Mann for current versions, https://arxiv.org/abs/1807.04126 <https://arxiv.org/abs/1807.04126> is an index) seems to be fine with giving a descriptive language for, and to some extent tools to compute, which kinds of joint large-actor states exist as alternative histories. There will, in general, not be a unique basis in which such decoherent-histories can be shown to exist. Weinberg objects to this as a problem with DH renderings of quantum mechanics in the last section of Ch.3 of his textbook Lectures on Quantum Mechanics https://www.cambridge.org/core/books/lectures-on-quantum-mechanics/F739B9577D2473995024FA5E9ABA9B6C <https://www.cambridge.org/core/books/lectures-on-quantum-mechanics/F739B9577D2473995024FA5E9ABA9B6C>. I don’t see from what direction, however, other than comfort, one can argue that that objection has any weight.. Decoherent histories are defined; there may be more than one basis in which such histories split into branches (an up-down comparison branch or a left-right comparison branch for measurers set up in New York and LA), and that description is incompatible with referring to “a measurer” in NY or LA who is a projection of macro-variables in branches of two different and incompatible DH bases. There is no instantaneous dynamics that “creates” these correlations at the time of the measurement, the presence or absence of correlations was generated as a feature of the state vector, locally, when the EPR pair was produced, and they evolved locally with consequences for the possible correlations among macro-actors since. I guess whether this bothers you depends on whether you view the phases over which one averages to compute the coherence or decoherence as “properties” somehow of degrees of freedom at distinct locations. It is not clear to me that the math assigns them in that way, or that one is thus warranted to think of them that way. As quantum computers get clean enough to start to become large, it would be nice to start simulating “universe-in-a-box” decoherent histories states, so we can start to develop some familiarity and comfort with the very large numbers of branches that quantum systems can realize. Quantum computers already keep all these superposed branches in play; to make an internal decoherent-histories example would prune to a small subset of them, though still large relative to our classical habits of thinking. I think the exercises with superposed SQUID rings etc., from decades ago, already get at the main point, and have long advertised themselves as macroscopic Schroedinger’s cats that are in superposed states, so there isn’t necessarily new conceptual ground to be broken here. But quantum computers potentially allow a lot more design invention, and thus more fun examples. 6. I expect all this is going to be in the news fairly regularly now, as QC engineering builds up, so there won’t be any special event that is “the” time to talk about it. It came across my radar through other considerations a couple of months ago, because there were some “Wigner’s Friend” experiments done and published somehow recently, which claimed to get at Nick’s concerns with “I can’t know and not know” something. Many MANY writers of non-formal language (meaning, the physicists who publish the papers) LOVE to write in a way that uses exactly Nick’s formulation and posts it as a problem or paradox. But I don’t think that means we have to write that way. There is a nice blog post by Scott Aaronson https://www.scottaaronson.com/blog/?p=3975 <https://www.scottaaronson.com/blog/?p=3975> that shows where such languages make specific errors of attributing meaning to common-language words, when there is no referent for that meaning in the actual mathematical description. To Scott’s points, I would add that there is a further error (or at least gap): the authors of the Wigner’s Friend papers are using three correlated microscopic spins as models for a state and someone who “knows” something about it (the Friend role). I would argue that it doesn’t become the correct model until one is allowing one of the members in the correlated superposed state to become a large actor, because the state vector contributions from large actors are different from those of micro-spins with respect to decoherence. That is the thing I think a coming-generation quantum computer might allow someone to program. Aaronson’s analysis will still be exactly right, but there will be more detail that can be added to it to reflect the different roles of small and large subsystem contributions. Anyway, I will repeat that I have to be careful here. Penrose is smarter than I am, and he works in this area, and Smolin is smarter and works in this area. In the end one has to take appeals to authority seriously. But if I compare Smolin’s popular prose to Aaronson’s, I find them completely different. Smolin I do not trust to give the reader the best critical understanding; Aaronson I do (though he is usually in a hurry, which leads to limits). He also has a book out, Quantum Computing Since Democritus, which somebody has lent to me and of which I have read a little bit. He is consistently good in this way, though he is a logician, and that creates in me all the disquiet of logician’s proofs that are non-constructive. But that is a different topic. Don’t know if this is helpful or not. I probably don’t know enough to write anything beyond the above on this topic, and will just listen from here out, and accept if it turns out part of what I said here is wrong. Eric
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