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Derivation of the Born rule

  1. Sep 24, 2006 #1
    Hello all,

    Attached is the draft of a paper entitled, Derivation of the Born rule from outcome counting and a solution to the quantitative problem of the MWI, (MWI = multiple worlds interpretation), which I am considering for submission to Les Annales de la Fondation Louis de Broglie. I would welcome any input that any of you may have.

    Here is the abstract to my paper:

    This paper has undergone many drafts, and the current version is quite a bit shorter than previous versions. This is primarily because of the space limitations (6000 words) imposed by the journal; although I should say that the process of boiling it down to its essentials has proven to be a fruitful exercise in and of itself. One consequence, however, is that there are several arguments that I present only in skeleton form, and some that I have skipped entirely. So I would be especially interested in critiques of my presentation itself -- i.e., whether I have presented my arguments in a way that is understandable. Of course, I am also interested in critiques of the arguments themselves!

    There are a number of PF threads that I have been involved in that directly or indirectly pertain to my paper -- in particular, to philosophical issues surrounding "outcome counting." See, eg:

    "My paper on the Born rule ..." ("my" = Patrick Van Esch's :-) )

    "Are world counts incoherent?"

    Attempts to make the Born rule emerge explicitly from
    outcome counting

    Outcome counting, the action principle, and GR

    QM and action principles

    A democracy of spacetimes?

    GR and analytic continuation

    Many of my ideas have taken shape during some very interesting discussions in zapper's group undernetphysics -- see especially message #1382.

    What is the significance of my paper? Twofold.

    1. Philosophical. My theory was initially motivated by the conviction that the concept of probability must be based, in one way or another, on outcome counting. To me, it deserves the status of a symmetry principle, on a par with, say, the principle of relativity. Of course, I realize that not everyone shares this conviction; it's really a matter of taste more than anything else. But at the very least, the fact that it may be feasible to devise a theory based on outcome counting should, I think, have an impact on philosophical discussions of "what probability really is."

    I might add that the question: "whence the Born rule?" has received renewed attention of late. There have been a number of attempts to derive the Born rule over the years, two notable attempts being Gleason’s theorem and -- more recently -- Deutsch-Wallace decision theory. Deutsch-Wallace decision theory and related issues regarding the interpretation of probability in the MWI will be the focus of a conference in 2007, slated to coincide with the 50th anniversary of the publication of Everett's relative state formulation paper that formed the basis of the MWI:


    A very good argument can be put forward that these so-called “derivations” of the Born rule are not in fact derivations, because they contain hidden assumptions that assume the Born rule, so that their arguments are inherently based on circular reasoning. I argue that my theory does NOT contain such hidden assumptions, and is therefore a genuine derivation.

    2. Physical. I argue that my theory could -- potentially -- shed some light on what a theory of quantum gravity (QG) might look like. Now, it would be way too bold for me to say that my theory is itself a theory of QG. Rather, my theory starts with the assumption that “a theory of QG exists,” and I assume that this theory has certain characteristics. In particular, I assume a basic framework that looks a lot like (my understanding of) a loop quantum gravity (LQG) theory of QG, including the notion of an emergent spacetime that we can use as an approximation to the underlying theory. I then postulate certain features of this emergent spacetime, and use these features to derive quantum statistics in the form of the Born rule.

    Again, it is important that my postulates do not "sneak in" the Born rule. So what are these features of emergent spacetime that I postulate? A central assumption is that each of the "all possible paths" of the Feynman path integral (FPI) (which "live" in the emergent spacetime) has its counterpart in each of the quantum spacetimes of the underlying theory. Probably the next most significant assumption that I make has to do with how particle trajectories are modeled in each of the quantum spacetimes of the underlying theory. How do these work ... well, it's all in my paper.

    Let me address the terms of the guidelines:

    See the abstract above.

    My proposal fits into the latter category. The great majority of the paper is concerned with demonstrating empirical equivalence to standard quantum mechanics, at least in the approximation. As it now stands, I cannot suggest experiments to distinguish between my theory and standard QM; some new ingredient would need to be added for that to happen. That doesn't make me feel too bad though; string theory has about a zillion people working on it, and still no testable predictions. I'm just one lone guy doing this in my spare time :rolleyes:.

    As for the potential insights -- see the discussion above.

    I should point out that I know of two independent proposals that, like mine, assume outcome counting as the fundamental probability rule within an MWI context. These are the “mangled worlds” theory of Robin Hanson, and an independent proposal by Mike Weissman. Robin and Mike have each participated in some of the PF threads listed above.

    Robin Hanson's mangled worlds proposal, published in Foundations of Physics:
    Robin, btw, has presented his work at the Perimeter Institute ;-).

    Mike's paper, published in Foundations of Physics Letters:

    The primary focus of my paper is a derivation of the Born rule. As I said earlier, some parts of the derivation are presented in outline format only, due to space limitations. I would be interested in whether you think I should be more explicit for this introductory paper of mine (versus, say, being more explicit in a followup paper).

    (Oh yea -- I use LaTeX, with figures drawn in Powerpoint.)

    I make no such claims.

    Well I hope not … but that’s why I’m here!

    If my paper exhibits any gross misunderstandings of basic science, it probably involves LQG, with which I am less familiar than, say, the FPI (Feynman path integral).

    Well I might add that for anyone interested, some of the older (and much much much longer!) drafts of my theory are archived for public viewing in my yahoo! briefcase. But I do not offer them as a formal part of the current submission.

    David Strayhorn

    Attached Files:

  2. jcsd
  3. Apr 17, 2007 #2
    journal submission: slow review process

    On 5 Oct 06 I submitted my paper, along with a short companion, to The Annales de la Fondation Louis de Broglie http://www.ensmp.fr/aflb/AFLB-Web/en-annales-index.htm, at about the same time that I originally posted this thread - more than seven months ago. Having heard nothing from the journal, I emailed to ask the status of my submission, and received the reply:

    Seven months, and still haven't found a referree. Has anyone ever heard of such a thing happening?

    I know that my papers are dense (as evidenced by the lack of response I've gotten on this forum! :grumpy: :blushing: :cry: ) -- so should I conclude that is the reason why AFLB cannot find a referree? OTOH, the journal website lists the current issue as 2006. Should I conclude the journal is about to go belly-up? Or that the journal is simply slow to do things in general?

  4. Apr 17, 2007 #3
    oops -- should have said 6, not 7.:uhh:
  5. Apr 18, 2007 #4
    I should have posted this a long time ago: there is an online version of my paper, posted at philica:

    "Derivation of the Born rule from outcome counting and a solution to the quantitative problem of the multiple worlds interpretation"

    I have a second paper archived at philica as well:

    "An illustration of the quantitative problem of the multiple worlds interpretation of quantum mechanics and the motivation for outcome counting"

    I would suggest to anyone trying to wade through my ideas :shy: to start with the latter (id=27) paper. Its purpose really is to provide the justification for launching into the longer and more complex paper (id=28).

    On a different note: the Perimeter Institute will be hosting a conference this september on the Everett interpretation, ie the multiple worlds interpretation:

    I'm going to see if I can go to that!
  6. May 15, 2008 #5
    paper accepted!

    Good news! A revised version of my second paper, "An illustration of the quantitative problem of the multiple worlds interpretation of quantum mechanics and the motivation for outcome counting," has been accepted for publication in Annales de la Fondation Louis de Broglie.

    BTW I had the opportunity to attend the Perimeter Institute conference on the many-worlds interpretation last fall. I thought it was great that they allowed a non-professional like me (and one or two others) to attend. It gave me an opportunity to meet some of the leaders in this particular field of research and to place my thoughts and ideas in the context of the state of the field -- iow, to relate what I'm doing to what everyone else is doing. This is the sort of thing that physics outsiders often fail to do, and I am determined not to make the same mistake. Aided by what I learned at PI, I have done a complete overhaul of my above two manuscripts into a new one, "Egalitarianism offers a coherent alternative to decision theory as a solution to the problem of probability of the many worlds interpretation." It is currently under review at Studies in History and Philosophy of Modern Physics.

  7. Jun 18, 2008 #6


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    Congratulations! Ans many happy returns!
  8. Jun 21, 2008 #7
    Thanks Carl! Here is the referee's original report. I sent a revised draft that was accepted.

    "A Referee report on D. Strayhorn's paper: "An Illustration of..."

    The paper discusses a variation of the "Many World Interpretation"
    (MWI) of quantum mechanics. As such, the paper does not belong to
    the narrow definition of physics but to its (philosophical)
    interpretation. In my opinion, this kind of papers should be welcome
    in a physical journal, provided it is restricted to a small percentage
    of the entire publication. Thus, I think that the paper can be accepted.
    However, I have some remarks and I wish that the Author consider them.
    Maybe he will decide to revise some points of his paper.

    1. By its definition, the Author's idea of "Outcome Counting" has no
    theoretical value in the sense of making a reliable prediction. At
    most, it can be regarded as a tool depending on phenomenological
    results of earlier experiments. As such, this idea cannot be
    incorporated in theoretical physics. Thus, it may only be considered
    as just one interpretation of physics. In particular, the Author's
    suggestion that Outcome Counting be elevated "to the level of a
    symmetry principle" like the principle of relativity (see the middle
    of p. 7) cannot be accepted.

    2. The Author discusses a hypothetical spin-1/2 experiment and claims
    that the Born probability interpretation is inconsistent with the
    idea "that each possible experimental outcome should be equally
    likely" (see the middle of p. 2). He also remarks that "from an
    empirical perspective, the success of the Born rule is undisputed"
    (see p. 2, end of the first paragraph).

    Referring to this matter, I wish to show a case where the Born
    statistical approach agrees with the "equally likely" idea of
    all possible experimental results. The example discusses a continuous

    Consider a double slit experiment and examine the results on a film.
    Looking not very closely at the film, one sees an interference
    pattern of a continuously varying gray level. The gray level
    represents the Born statistical interpretation. On the other hand,
    a close observation of the film reveals many isolated black points
    obtained from the collision of each photon with the film. This is
    the "equally likely" approach.

    Therefore, in a case of an experiment measuring a continuous
    variable, the two approaches are consistent with each other. Hence, the
    discrete spin results may deserve an appropriate treatment of infinities
    related to a Dirac delta function."
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