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All of aotell's Comments + Replies

Welcome to Less Wrong! (July 2012)
aotell00

You keep ignoring the fact that the dominant eigenstate is derived from nothing but the unitary evolution and the limitations of the observer. This is not a "new theory" or an interpretation of any kind. Since you are not willing to discuss that part your comments regarding the validity of my approach are entirely meaningless. You criticize my work based on the results which are not to your liking, and not with respect to the methods used to obtain these results. So I beg you one last time, let us rationally discuss my arguments, and not what you... (read more)

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Welcome to Less Wrong! (July 2012)
aotell10

This would be a lot simpler if you weren't avoiding my questions. I have asked you whether you have understood and accept the derivation of the dominant eigenstate as the best possible description of the state of a system that the observer is part of. I have also asked if you have read my blog from the beginning, because I need to know where your confusion about what I am saying comes from.

The Stern Gerlach experiment goes like this in my theory: The superposition of the spins of the silver atoms must be collapsed already at the moment the beam splits up, ... (read more)

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2Mitchell_Porter
Earlier, I should have referred to the calculation as being in part IV, not part V. I've read part V only now - including the stuff about "branch switching" and how "The observer can switch between realities without even noticing, because all records will agree with the newly formed reality." When I said these ideas led towards "stochastic, piecewise-linear Bohmian mechanics", I was more right than I knew! Bohmian mechanics is rightly criticised for supposedly being just a single-world theory, yet having all those other world-branches in the pilot wave. If your account of reality includes wavefunctions with seriously macroscopic superpositions, then you either need to revise the theory so it doesn't contain such wavefunctions, or you need to embrace some form of many-world-ism. Supposing that "hidden reality branches" exist, but don't get experienced until your personal stream-of-consciousness switches into them, is juvenile solipsism. If that is where your theory leads, then I have little interest in continuing this discussion. I was suspicious from the beginning about the role that the "subjectively reconstructed state of the universe" was playing in your theory, but I didn't know exactly what was going on. I had hoped that by discussing a particular physical setup (Stern-Gerlach), we would get to see your ideas in action, and learn how they work by demonstration. But now it seems that your outlook boils down to quantum dualism in a virtual multiverse. There is a subjective history which is a series of these "dominant eigenstates", plucked from a superposition whose other branches are there in the wavefunction, but which aren't considered fully real unless the subjective history happens to jump to them. There is some slim possibility that your basic idea could play a role in the local microscopic dynamics of a new theory, distinct from quantum mechanics but which produces quantum mechanics in a certain limit. Or maybe it could be the basis of a new type of many
Welcome to Less Wrong! (July 2012)
aotell00

There must be something that you have fundamentally misunderstood. I will try to clear up some aspects that I think may cause this confusion.

First of all, the scattering processes presented in the paper are very generic to demonstrate the range of possible processes. The blog contains a specific realization which you may find closer to known physical processes.

Let me explain in detail again what this section is about, maybe this will help to overcome our misunderstanding. A photon scatters on a single qubit. The photon and the qubit each bring in a two dim... (read more)

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1Mitchell_Porter
I understand that you have an algebraic derivation of Born probabilities, but what I'm saying is that I don't see how to make that derivation physically meaningful. I don't see how it applies to an actual experiment. Consider a Stern-Gerlach experiment. A state is prepared, sent through the apparatus, and the electron is observed coming out one way or the other. Repeat the procedure with identical state preparation, and you can get a different outcome. For Copenhagen, this is just a routine application of the Born rule. Suppose we try to explain this outcome using decoherence. Well, now we are writing a wavefunction for the overall system, measuring device as well as measured object, and we can show that the joint wavefunction splits into two parts which are entirely decohered for all practical purposes, corresponding to the two different outcomes. But you still have to apply the Born rule to "obtain" a specific outcome. Now how does your idea explain the facts? I really don't see it. At the level of wavefunctions, each run of the experiment is the same, whether you look at just the wavefunction of the individual electron, or at the joint wavefunction of electron plus apparatus. How do we get physically different outcomes? Apparently it requires these random scattering events, that do not feature at all in the usual analysis of the experiment. Are you saying that the electron that has passed through the Stern-Gerlach apparatus is really in a superposition, but for some reason I only see it as being located in one place, because that's the "dominant eigenstate"? Does this apply to the whole apparatus as well - really in a superposition, but experienced as being in a definite state, not because of decoherence, but because of scattering + my epistemic limitations??
Welcome to Less Wrong! (July 2012)
aotell10

Your question is absolutely valid and also important. In fact, most of what I write in my paper and the blog is about answering precisely this.

My observer is well defined, as a mechanism that is part of a quantum system and who interacts with the quantum system to gather information about it. He is limited by the locality of interaction and the unitary nature of the evolution. I imagine the observer to be a physicist, who tries to describe the universe mathematically, based on what he sees. But that is only a trick in order to have a mathematical formulati... (read more)

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0Mitchell_Porter
I finally got as far as your main calculation (part IV in the paper). You have a two-state quantum system, a "qubit", and another two-state quantum system, a "photon". You make some assumptions about how the photon scatters from the qubit. Then you show that, given those assumptions, if the coefficients of the photon state are randomly distributed, then applying the Born rule to the eigenvalues of the old "objective state" (density operator) of the qubit, gives the probabilities for what the "dominant eigenstate" of the new objective state of the qubit will be (i.e. after the scattering). My initial thoughts are 1) it's still not clear that this has anything to do with real physical processes 2) it's not surprising that an algebraic combination of quantum coefficients with random variables is capable of yielding new random variables with a Born-rule distribution 3) if you try to make this work in detail, you will end up with a new modification of quantum mechanics - perhaps a stochastic, piecewise-linear Bohmian mechanics, or just a new form of "objective collapse" theory - and not a derivation of the Born rule from within quantum mechanics. Are you saying that actual physical systems contain populations of photons with randomly distributed coefficients such as you describe? edit Or perhaps just that this is a feature of electromagnetically mediated measurement interactions? It sounds like a thermal state, and I suppose it's plausible that localized thermal states are generically involved in measurement interactions, but these details have to be addressed if anyone is to understand how this is related to actual observation.
Welcome to Less Wrong! (July 2012)
aotell10

You really come up with tricky questions, good :-). I think there are several ways to understand your questions and I am not sure which one was intended, so I'll make a few assumptions about what you mean.

First, an event is a nonlinear jump in the time evolution of the subjectively perceived state. The objective global evolution is still unitary and linear however. In between the perceived nonlinear evolution events you have ordinary unitary evolution, even subjectively. So I assume you mean the subjective states psi1(t) and psi2(t). The answer is then t... (read more)

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-2Mitchell_Porter
I find your reference to "the subjectively perceived state" problematic, when the physical processes you describe don't contain a brain or even a measuring device. Freely employing the formal elements and the rhetoric of the usual quantum interpretation, when developing a new one supposedly free of special measurement axioms and so forth, is another way for the desired conclusion to enter the line of reasoning unnoticed. In an earlier comment you talk about the "objective observer state", which you describe as the usual density operator minus the usual statistical interpretation. Then you talk about "reality for the observer" as "the eigenstate of the density operator with the greatest eigenvalue", and apparently time evolution "for the observer" consists of this dominant eigenstate remaining unchanged for a while (or perhaps evolving continuously if the spectrum of the operator is changing smoothly and without eigenvalue crossings?), and then changing discontinuously when there is a sharp change in the "objective state". Now I want to know: are we really talking about states of observers, or just of states of entities that are being observed? As I said, you're not describing the physics of observers, you're not even describing the physics of the measurement apparatus; you're describing simple processes like scattering. So what happens if we abolish references to the observer in your vocabulary? We have physical systems; they have an objective state which is the usual density operator; and then we can formally define the dominant eigenstate as you have done. But when does the dominant eigenstate assume ontological significance? For which physical systems, under which circumstances, is the dominant eigenstate meaningful - brains of observers? measuring devices? physical systems coupled to measuring devices?
Welcome to Less Wrong! (July 2012)
aotell10

I see it exactly like you. I too see the overwhelming number of theories that usually make more or less well hidden mistakes. I too know the usual confusions regarding the meaning of density matrices, the fallacies of circular arguments and all the back doors for the Born rule. And it is exactly what drives me to deliver something that is better and does not have to rely on almost esoteric concepts to explain the results of quantum measurements.

So I guarantee you that this is very well thought out. I have worked on this very publication for 4 years. I flip... (read more)

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0Mitchell_Porter
Here's another question. Suppose that the evolving wavefunction psi1(t), according to your scheme, corresponds to a sequence of events a, b, c,... and that the evolving wavefunction psi2(t) corresponds to another sequence of events A, B, C... What about the wavefunction psi1(t)+psi2(t)?
Welcome to Less Wrong! (July 2012)
aotell00

I think it will be helpful if I briefly describe what my approach to understanding quantum theory is, so that you can put my statements in the correct context. I assume a minimal set of postulates, namely that the universe has a quantum state and that this state evolves unitarity, generated by the strictly local interactions. The usual state space is assumed. Specifically, there is no measurement postulate or any other postulates about probability measures or anything like that. Then I go on to define an observer as a mechanism within the quantum universe... (read more)

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3Mitchell_Porter
As you would know, the arxiv sees several papers every month claiming to have finally explained quantum theory. I would have seen yours in the daily listings and not even read it, expecting that it is based on some sort of fallacy, or on a "smuggled premise" - I mean that the usual interpretation of QM will be implicitly reintroduced (smuggled into the argument) in how the author talks about the mathematical objects, even while claiming to be doing without the Born rule. For example, it is very easy for this to happen when talking about density matrices. It is a tedious thing to go through a paper full of mathematics and locate the place where the author makes a conceptual mistake. It means you have to do their thinking for them. I have had another look at your paper, and seen a little more of how it works. Since you are here and wanting to promote your idea, I hope you will engage with me even if I am somewhat "lazy", in the sense that I haven't gone through the whole thing and understood it. So first of all, a very simple issue that you could comment on, not just for my benefit but for the benefit of anyone who wants to know what you're saying. An "observer" is a physical being who is part of the universe. The universe is described by a quantum state vector. The evolution of the state vector is deterministic. How do you get nondeterministic evolution of the observer's state, which ought to be just a part of the overall state of the universe? How do you get nondeterminism of the part, from determinism of the whole? We know how this works in the many-worlds interpretation: the observer splits into several copies that exist in parallel, and the "nondeterminism" is just an individual copy wondering why it sees one eigenvalue rather than another. The copy in the universe next door is thinking the same thing but with a different eigenvalue, and the determinism applies at the multiverse level, where both copies were deterministically produced at the same time. That's
Welcome to Less Wrong! (July 2012)
aotell00

Thank you for your feedback Mitchell,

I'm afraid you have not understood the paper correctly. First, if a system is in a superposition depends on the basis you use to expand it, it's not a physical property but one of description. The mechanism of branching is actually derived, and it doesn't come from superpositions but from eigenstates of the tensor factor space description that an observer is unable to reconstruct. The branching is also perfectly deterministic. I think your best option to understand how the dominance of one branch and the non-reality of... (read more)

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0aotell
I think it will be helpful if I briefly describe what my approach to understanding quantum theory is, so that you can put my statements in the correct context. I assume a minimal set of postulates, namely that the universe has a quantum state and that this state evolves unitarity, generated by the strictly local interactions. The usual state space is assumed. Specifically, there is no measurement postulate or any other postulates about probability measures or anything like that. Then I go on to define an observer as a mechanism within the quantum universe that is realized locally and gathers information about the universe by interacting with it. With this setup I am able to show that an observer is unable to reconstruct the (objective) density operator of a subsystem that he is part of himself. Instead he is limited to finding the eigenvector belonging to the greatest eigenvalue of this density operator. It is then shown that the measurement postulate follows as the observer's description of the universe, specifically for certain processes that evolve the density operator in a way that changes the order of the eigensubspaces sorted by their corresponding eigenvalues. That is really all. There are no extra assumptions whatsoever. So if the derivation is correct then the measurement postulate is already contained in the unitary structure (and the light cone structure) of quantum theory.
Welcome to Less Wrong! (July 2012)
aotell00

Thanks Nancy!

Have you checked out the posts at my blog? I don't know about your background, but maybe you will find them helpful. If you would like to have a more accessible break down then I can write something here too. In any case, thank you for your interest, highly appreciated!

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0Mitchell_Porter
From your blog and your paper, your idea seems to be that the quantum state of the universe is a superposition, but only one branch at a time is ever real, and the selection of which branch will become real at a branching is nondeterministic. Well, Bohmian mechanics gets criticised for having ghost wavepackets in its pilot wave - why are they less real than the wavepackets which happen to be guiding the classical system - and you must be vulnerable to the same criticism. Why aren't the non-dominant branches (page 11) just as real as the dominant branch?
Welcome to Less Wrong! (July 2012)
aotell70

Hi everyone!

I'm a theoretical physicist from Germany. My work is mostly about the foundations of quantum theory, but also information theory and non-commutative geometry. Currently I'm working as head of research in a private company.

As a physicist I have been confronted with all sorts of (semi-) esoteric views about quantum theory and its interpretation, and my own lack of a better understanding got me started to explore the fundamental questions related to understanding quantum theory on a rational basis. I believe that all mainstream interpretations h... (read more)

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0Shmi
Have fun :) I'll see if I can make sense of your blog.
2NancyLebovitz
Welcome to Less Wrong! I'm interested in your idea that quantum theory doesn't have to be interpreted.