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My paper on the Born rule

  1. Oct 19, 2005 #1

    vanesch

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    Hi,
    A while ago I discussed here about a paper I wrote, which you can find on the arxiv: quant-ph/0505059
    I submitted it to the Royal Society, and I received a notification of rejection, with the following comments from the referees, might be of interest for those who participated in the discussion. The emphasis is mine.
    First referee:
    The second referee:
    On a personal note, although this paper was a bit outside of my field and thus "for fun", in my field too, I had several rejections of similar kind, which always make me think that the referee has missed the point I was trying to make (which must be due to the way I wrote it up, somehow).
    The only point I tried to make was a logical one, as seems to be recognized by the first referee only, but then he seems to miss the point that in the end of the day, we want a theory that spits out results that are given by the PP, whether or not we take that "as primitive". So I don't see why considering the PP "as primitive" makes the reasoning "not relevant". The second referee seems to have understood this (that we have to rely on empirical data to endorse the PP), but he seems to have missed the point I was making a logical claim, and seems to concentrate on the minor remark when I said that "this APP seems to be the most natural probability rule going with MWI".
    The very argument that some have tried to MODIFY QM introducing non-linear decoherence is *exactly what I claim*: that you need an extra hypothesis with unitary QM if you want to derive the PP. Finally, the proposition of revision, namely to limit myself to the consequences of the APP, take away the essential point of the paper which simply stated: since two different probability rules, the APP, and the PP, are both compatible with unitary QM, you cannot derive the PP logically from unitary QM without introducing an extra hypothesis.
    The only truely valid critique I find here, is the one of the first referee who finds that my paper is not sufficiently different from Barnum's paper (something I ignored) - which is of course a valid reason of rejection (which I emphasised in red).
    Most other points seem to miss the issue of the paper, I have the impression, and focus on details which are not relevant to the main point made. This often happens to me when I receive referee reports. Do others also have this impression, or am I such a terrible author ?
     
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  3. Oct 19, 2005 #2
    All attempt to derive the PP from unitary theory is condemed to failure.

    It is a simple mathematical (and physical) question. The information contained into a nonunitary evolutor is more rich that informaiton contained into a unitary evolutor. 'More' cannot be derived from 'less'.

    It took near 100 years that physicists understood that measurement problem CANNOT be solved via QM of closed systems. During 50 years or so had an intensive research in open systems and decoherence. Finally decoherence is in a dead way.

    I wait that in some 100 or 200 years physicists will understand that the old unitary Schrödinger equation is an approximation to realistic nonunitary evolutions.

    In fact, in some other fields this is known for decades...

    See page 17 of

    Nobel Lecture, 8 December, 1977

    http://nobelprize.org/chemistry/laureates/1977/prigogine-lecture.pdf

    The measurement process is an irreversible process generating entropy. QM conserves entropy and is reversible, therefore QM cannot explain the PP without invoking it adittionally. But then one is invoking a postulate that violates others postulates of the axiomatic structure, doing QM both incomplete and internally inconsistent.
     
  4. Oct 19, 2005 #3

    ZapperZ

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    I always find that I have to ask an "outsider" to read my manuscript before I submit it. This is because what I find to be rather obvious, is really isn't. Authors have a clear idea in their heads what they're writing. Other people don't. So we tend to write things as if the reader already has an insight into our punch line. If you find that most people seem to miss the main point you're trying to make, chances are that you are not emphasizing it in the clearest fashion. This has happened even to the best of us.

    I find that the most effective means to emphasize the main points I'm trying to get across is by clearly numbering them. I've been known on here to list the points one at a time:

    (i) Point 1

    (ii) Point 2

    .. etc. Unfortunately, if you're writing to PRL, or trying to save publication costs, those take a lot of valuable spaces, so I also have listed them in line. As a referee, I also find them to be easier to focus on. I can easily go back and look at them again while I'm reading the rest of the paper to keep reminding myself that these are the points the authors are trying to make. It is no secret that most of us start a paper by reading the abstract, intro, and conclusion first (well, I certainly do). So you have to keep in mind that you literally have to reveal to the reader in the most direct way the message you are trying to get across in those sections of the paper.

    Zz.
     
  5. Oct 19, 2005 #4

    vanesch

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    This reminds me of a simple paper I wrote once with a student, about how the signal generating process should be included in a reliable simulation of the behaviour of the front end electronics of a neutron detector, because assuming that the detector just "sent out a delta-pulse" was giving results which deviated by a factor of 2 from observations, while including the signal formation did predict this factor 2. I found this maybe worth publishing - even though not big news - because other papers omitted exactly that: they only took into account the electronics, and supposed a deltafunction for the signal coming from the detector (which might have been justified in their application, no matter - but it was not mentioned in their papers).
    So I carefully described the setup, and gave an explicit calculation of how the signal was generated in the detector, to show that this was the relevant part which allowed us to explain the discrepancy of a factor of 2. My point being that it was necessary to include this part in the description.
    I got a rather nasty referee report, in which he explained me that I must be pretty naive to think that I was the first one explaining how signals were generated in radiation detectors :bugeye:
     
  6. Oct 19, 2005 #5

    ZapperZ

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    I think it highly depends on WHERE you sent that in. If you sent it to, let's say, PRL, then I'd say you might get something like that. However, journals like EJP, or AJP, routinely publish pedagogy and techniques, especially when it is something relevant in physics education, be it at the undergraduate or graduate level.

    I don't know what you submitted that paper to, but honestly, where you send your manuscript is almost as important as what you wrote.

    Zz.
     
  7. Oct 19, 2005 #6

    vanesch

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    It was Nuclear Instruments and Methods, quite appropriate, I'd think :smile:
     
  8. Oct 19, 2005 #7

    ZapperZ

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    Well, I'm not sure about that.

    NIM is supposed to be a journal on new techniques, or an improvement of a technique. Your paper, from your description, is simply clarifying the missing piece that isn't commonly mentioned. In other words, there's nothing new or a new extension on an existing technique. If this is the case, then the referee is correct in asking you if you think that what you're describing is not known.

    I still think AJP or EJP might have been more suitable. You could emphasize the point that what you're describing is important and often omitted in the details of the experiment being reported in many papers that use the same technique. Such a paper would have been appropriate for those two journals.

    Zz.
     
  9. Oct 19, 2005 #8

    vanesch

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    This is an interesting comment ! Nobody ever made that, and it explains several other problems I had with NIM ; indeed, each time I erred more on the explanatory part than the "here's a new method" part, I got rebiffed (or one asked me to remove or reduce the explanatory part and to emphasize the practical application). It is true that amongst my collegues, I'm by far the most "explanation" oriented.
     
  10. Oct 19, 2005 #9

    ZapperZ

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    I tend to be quite verbose too in some of the things I write. But as a referee, when I pick up a paper that I'm reviewing, I would like to be hit right off the bat with the punch line. Tell me in no uncertain terms what you are trying to say here, and why it is important. I tend to pay attention to statements such as these:

    "To be best of our knowledge, this is the first report on.... "

    "This results contradicts an earlier report...."

    "This is the most accurate result so far on.... "

    "This is a new result..... "

    etc. These should be either in the abstract, or somewhere in the intro or the 1st 2 paragraph. If not, I will lose track of what you're trying to say, or why it is important. (Ironically, I've just finished reposting in my Journal an article I wrote a while back titled "It may be interesting, but is it important?") :)

    If you write a paper in such a way that the referee has to put an effort to find the point you are making, or why it is important, then you are just making it more difficult for that referee to recommend your paper to be published. It is that simple.

    Zz.
     
  11. Oct 20, 2005 #10
    Drat! I have my follow-up to your paper nearly ready for submission. Every weekend for the past several weeks now, I've told myself I'm going to make the final revisions and send it out, and then I run across something else that I need to incorporate. Like the Weissman paper, for instance ... In fact, I should probably make it at least evident that I'm aware of Weissman, Deutsch, Barnum, Hanson, and all the other authors mentioned in the reviews.

    So Patrick, do you think you're going to resubmit? I hope you do - I think (obviously) that it is a very important topic. I'll try to throw out my comments on the reviewers' comments on this thread, as I go through the literature (may be a slow process ...)

    BTW, does it normally take that long for review? Hasn't it been, what, 5 months?

    David
     
  12. Oct 20, 2005 #11

    vanesch

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    First I'll check out the Barnum paper. If (according to referee 1) my paper contains the same argument as his, well I conclude that 1) I'm in not a bad company (just 5 years late :grumpy:) and 2) I won't resubmit.

    If not, well, I wouldn't really know where to submit. Maybe foundations of physics.

    It's usually a bad sign when it takes that long :grumpy: But it is strongly dependent on the journal. Some journals first as one referee, and if that one doesn't give positive returns, they ask a second one for a second opinion. Others do it in parallel.
     
  13. Oct 21, 2005 #12
    A review article might not be such a bad idea. You could review the motivation behind the APP, review the various attempts to implement it, and perhaps include your own contribution in a separate section.

    What exactly is the reputation of FoP? Is it a lesser tier than the Royal Society?

    DS
     
  14. Nov 3, 2005 #13
    Hey Patrick,

    I've been trying to make sense of some of the comments made by your first referree:

    I looked at one of Greaves' papers, "Understanding Deutsch's probability in a deterministic multiverse" which is archived at the PhilSci archives at http://philsci-archive.pitt.edu/archive/00001742/ . Section 5.1 "Measurement neutrality" and section 5.2: "Measurement Neutrality versus Egalitarianism" really helped me to understand the above point. Basically, Greaves explains that one of the essential assumptions in Deutsch-Wallace decision theory is the postulate of "measurement neutrality," which is "the assumption that a rational agent should be indifferent between any two quantum games that agree on the state |phi> to be measured, measurement operator X and payoff function P, regardless of how X is to me measured on |phi>." afaict, this means that if we think of the measurement process as a "black box," then Deutsch assumes that a rational agent should in principle be indifferent to the details of the innards of this black box.

    In sec 5.2, Greaves very clearly argues that measurement neutrality automatically *excludes* the APP (where the APP = egalitarianism) as a possible probability rule. Therefore, measurement neutrality, as innocuous as it may appear at first glance, is not so innocuous at all.

    I've referenced Greaves (among others) in the revised introduction to my paper [1] on the probability interpretation of the MWI. I'm glad you posted your referree comments, Patrick -- they've helped me on my paper!

    -- David

    [1] To be submitted to Foundations of Physics Letters -- latest draft available at
    http://briefcase.yahoo.com/straycat_md
    Folder: Probability interpretation of the MWI
    archived (slightly older) versions also at:
    http://philsci-archive.pitt.edu/
    http://www.sciprint.org/
     
  15. Nov 3, 2005 #14

    vanesch

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    Yes, that's exactly the point. As I showed in my paper, that's NOT the case with the APP, (as I explicitly show with the example of X and Y where one is a refinement of the other) where the probabilities are dependent on context (on the other variables that are being measured).


    Ok, that's exactly my argument too. So I have some extra homework to make with this as reference.

    Thanks for pointing that out!
     
  16. Nov 4, 2005 #15
    Juan wrote:

    I cannot agree with that statement, altough I recognize a conceptual difficulty there.
    For me, this problem is similar to the problem of irreversibility seen from the classical mechanics point of view. Non-unitary evolution might be a good approximation (maybe even *exact*!) when an interaction with a huge system (huge freedom) is involved.

    My favorite example is the decay of atomic states: clearly the interaction of the discrete atomic system with the continuum system of electromagnetic radiation brings the decay. This decay is very conveniently represented by a "non hermitian" hamiltonian: this allows modeling of an atom (for the Stark effect e.g.) without including the whole field. This represents correctly the reality, altough the fundamental laws are unitary.

    For many people, the interaction with a 'classical' or 'macroscopic' system is all that is needed to derive the PP. I think this is the most probable explanation for the PP. Landau considered this so obvious that it comes in the first chapters in his QM book.
     
    Last edited: Nov 4, 2005
  17. Nov 4, 2005 #16

    vanesch

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    The irreversibility in classical statistical mechanics comes about from the very specific initial condition, which is highly improbable.

    I don't see how this can come about. The hamiltonian gives rise to a unitary operator, no matter how complicated the system. Especially the EM radiation field can always be considered as a discrete system with a huge number of degrees of freedom (it shouldn't make any difference if you put your system in a box with diameter one hundred billion lightyears or not, should it).

    No, it is a shortcut, where you *apply* already the PP in its derivation.

    This is the standard "explanation". But it is *postulated* and not *derived* from unitary QM. What qualifies a system as "macroscopic" and "classical" (without making circular reasoning ?) and why shouldn't it obey standard quantum theory ?
    Or is there an upper limit to the number product hilbert spaces (number of particles) before the exponentiation of a hermitean operator suddenly doesn't become unitary anymore ?
     
  18. Nov 6, 2005 #17
    The APP and extremum principles

    Hey Patrick et al,

    I'm posting an idea on this thread that has occurred to me on a potential consequence of the APP.

    Suppose that Alice is doing two Aspect-like experiments, one with Bob, and another simultaneously with Bert. Alice and Bob are 1 km apart, and Bert is 0.1 km farther away than Bob. Otherwise the experiments are the same, done at the same time. Bob and Bert flash the results of their measurements to Alice as soon as they get them. Before Alice receives these messages (which we suppose travel at the speed of light), Bob and Bert each exist in a superposition of the "B-- sees up"/"B-- sees down" state. Because of the general relativistic restriction on the speed of light, from the point of view of Alice, Bob's state will collapse prior to Bert's state. Pretty elementary.

    The point I wish to make is that relativity imposes a restriction on the order with which collapse occurs, from the point of view of Alice. So let's take this point and extrapolate. Suppose now that we have an observer Amandra who observes some variable X characteristic of a particle. But imagine that the value of X is not communicated to Amandra all at once, but rather in little chunks. That is, suppose that X_min is the lowest allowable value of X, and that it is quantized, ie it takes values in [X_min, X_min +1, X_min + 2, ...]. Imagine furthermore that Amandra's observation of X comes in a series of steps, like this: she observes either X = X_min, or X \in [X_min+1, X_min +2, ...]; if the latter, she next observes either X = X_min + 1 or X \in [X_min+2, X_min +3, ...]; if the latter, she next observes either X = X_min + 2, or X \in [X_min+3, X_min +4, ...]; and so on. If you draw the MWI-style world-splitting diagram to characterize this process **and apply the APP**, then it is apparent that lower possible values of X are *more probable* than higher values. In effect, X is MINIMIZED. We could equally well suppose that X might be maximized, if the information regarding the value of X were propagated to Amanda in the reverse order.

    So here's the Big Idea: the APP, perhaps, offers a mechanism by which Nature enforces various extremum laws. If X is the action, for instance, then we have the principle of least action.

    What d'ya think?

    David
     
  19. Nov 7, 2005 #18

    vanesch

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    Yes, that is the lack of non-contextuality the APP suffers from, and which I tried to make clear in my paper...

    The problem I see with your approach is of course, that if we now get the information *in the other way* (she first gets the biggest intervals, not the lowest ones) we would make the HIGHER values of X more probable. And if we apply yet another order, we'd make *those* values more probable... It's hard to make sense of a measurement theory that is not non-contextual...
     
  20. Nov 7, 2005 #19
    Umm, so is the glass half full, or half empty? :confused:

    It is certainly true that if you play around with the "order" with which information regarding X is progagated to the observer, you can make the most probable value of X come out to be, well, *anything*. But I would argue that Nature would not be so fickle as to do it differently every time! There *must* be some rules that govern how any given variable type is propagated. And the reason that no one has figured out these rules is that over the last 80 years, the most brilliant minds in physics have spent a total of, I dunno, 10 seconds contemplating this problem. How many papers exist that even investigate the APP in the first place? Not many that I've found. And I've never seen any paper to suggest that a minimization principle could arise from it. It's fertile ground, uninvestigated, imho. (That's why I wrote my paper!)

    So here's how the glass is half full: by playing around with how the tree diagram (ie the MWI world-splitting diagram) is constructed, there must be a way to make quantum statistics pop out. The only extra postulates needed for this to work will be whatever is needed for the tree diagram to take whatever configuration produces the right statistics. Then we have to explain *why* the tree diagram is constructed the way it is. The point is that this ought to be doable without postulating any extra unphysical assumptions, or doing damage to some aspect of the essential ontology of the MWI, as is the problem imho with all other attempts so far that I have seen to make the APP work. (I discuss all of this in my paper.) So this should be seen as an *opportunity*, not a roadblock!

    Consider this. Suppose X represents some global property of an extended (not pointlike) object, like the total mass of a composite particle. At time t_0 (in Amanda's FoR), the particle is outside of Amanda's past light cone - she has not yet observed it. At time t_2, the entire particle is in the past light cone -- she has observed it. Sine the particle has spatial extension, there must be some intermediate time t_1 such that the particle is partially in Amanda's light cone -- ie, she has observed part of it, but not all of it. So she does not observe X all at once; she receives info regarding X over some small but nonzero amount of time. Her observation of the mass of the particle might be analogous to a person's observation of the size of a mountain, which rises slowly over the horizon as you are driving down a road. First you see the tip, and you know the size is at least so-big. Then you see some more, so you know the size is at least that much bigger. And so on, until you see the entire mountain. Applying the APP to this would amount to a "minimization" of the size of the mountain.

    Note that in the previous scenario, relativity plays a central role in figuring which pieces of information have or have not yet reached the observer. Thus, GR *must* play a central role in determining the configuration of the tree-diagram. So if the tree diagram configuration gives rise to quantum statistics, and relativity gives rise to the tree diagram, then voila! we have derived QM from GR.

    Now I would argue that the line of reasoning that brings us to this point is *inescapable*. First off, you have to decide whether you like the APP. And I know that deep down, Patrick, you *know* the APP is better than the Born rule. Search your feelings, young Jedi, you know it to be true. :devil: Next, it is impossible to discount the above relativity-based argument in the analysis of the observation of a variable that is not encoded in any single point of spacetime, but rather is a global property of a *spatially extended* object. (If you think a particle is truly poin-like, then just consider a composite particle in the above analysis.) The only questions that remain: what are the "rules" that govern the configuration of the tree diagram? We know that GR must be involved in establishing these rules. And: how does quantum statistics pop out? We know that they do, somehow, some way. So buried down deep here is a connection between GR and QM that no one has figured out, because smart people like Deutsch are wasting their time with things like decision theory that will get us all nowhere. :cry: But we can be smarter than that!:rofl:

    How can you *not* be seduced by this line of reasoning?

    David
     
  21. Nov 9, 2005 #20

    vanesch

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    I moved all posts related to the "arrow of time" from this thread into the "arrow of time" thread...
     
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