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Classical interacting random field models

  1. Dec 14, 2007 #1
    This is an announcement, in the Physics Forums context, of my "Lie fields revisited", arXiv:0704.3420, which has recently been accepted by J. Math. Phys., and an attempt to elaborate on why you might read it and to elicit critiques.

    For a little over ten years, I have been trying to understand and characterize in detail what differences there are between quantum fields and their closest classical equivalent, random fields. Random fields at finite temperature have nonlocal correlations, just as do quantum fields, so what is the difference?

    I showed in "A succinct presentation of the quantized Klein–Gordon field, and a similar quantum presentation of the classical Klein–Gordon random field", Phys. Lett. A 338 (2005) 8–12, arXiv:quant-ph/0411156, that in the random field context we can introduce "quantum fluctuations", which differ from thermal fluctuations only in that they are Lorentz invariant. Planck's constant on this view plays the role of a Lorentz invariant temperature. With the introduction of quantum fluctuations, there remains a difference between the quantum and classical models of measurement, but the distance is much less than for quantum particle properties/classical particle properties. A discussion of measurement theory is crucial, but would be too long-winded for a Physics Forums post (if this is not already), so if you are curious please see my web-page and papers.

    If you're wondering at this point what a classical random field IS, it's almost trivial, it's an indexed set of random variables (that's to say, if you know about random variables, a random field is easy, Wikipedia perhaps, but all we need here is that a Physical state and a random variable together give us an expected value associated with the random variable in that state). Two random variables, [tex]V_1[/tex] and [tex]V_2[/tex], say, are enough. A continuous random field effectively makes the index set be the points of space-time, so that we could talk about random variables [tex]\phi(x)[/tex] at every point of a (Minkowski) space-time, very similarly to a quantum field, but there are technical (and also notational) matters that make it mathematically much better to make the index set be a linear space of functions, which are called "test functions". It is possible to talk of a continuous random field [tex]\phi(x)[/tex] as a "random variable valued distribution", which is fairly directly comparable to the "operator valued distribution" way of talking about a quantum field. That continuous random fields are conceptually quite close to quantum fields, and can be presented in a Hilbert space and operator algebra formalism that is very close to quantum field theory, is a large part of why there is a small hope of casting some light on quantum mechanics. From here on, all the random fields are continuous.

    With honorable exceptions, almost all attempts to understand quantum mechanics have been through the nonrelativistic quantum theory and classical particles, quantum field theory has been felt to be too complicated for any understanding of it to be possible until quantum mechanics has already been understood. Big mistake, I believe.

    Of course, as classical models, random fields prima facie allow Bell inequalities to be derived, contradicting experiment, but in "Bell inequalities for random fields", J. Phys. A 39 (2006) 7441–7455, arXiv:cond-mat/0403692 v4 24 May 2006, I showed that Bell inequalities cannot be derived for random fields that have thermal or quantum fluctuations. Essentially, equilibrium states have non-local correlations at all times, and an absence of any pre-existing nonlocal correlations is required for Bell inequalities to be derived. Technically, this is usually called the conspiracy loophole. A lot of detail is required to get a paper on Bell inequalities into a good Physics journal; "Bell inequalities for random fields" takes several different approaches and gives a number of supporting arguments and references to papers that have previously argued that classical field theories allow the derivation of Bell inequalities. John Bell wrote the seminal paper, as so often, "The theory of local beables", which is in "Speakable and unspeakable in quantum mechanics", but it has a flaw, that it effectively works with particle properties and with random fields even-handedly, when the assumptions that are largely reasonable for one are not as reasonable for the other.

    Note that I'm claiming that the voluminous literature that proves that classical particle property models cannot be used as physical models is just taking on straw man theories, and is irrelevant to classical random fields that have non-zero fluctuations. Personally, I think that a classical particle property model that I like is not possible, despite the claims of the detection loophole, de Broglie-Bohm models, Nelson models, etc.

    My earlier papers do some mathematics, but they are largely non-constructive, so they have not so far provoked comment or rebuttal. "Lie fields revisited", in contrast, constructs a new class of interacting random field models that are not available to quantum field theory. "Lie fields" were introduced in the 1960s, but it became apparent after a few years that they are incompatible with the Wightman axioms, so they became moribund. Once we admit classical random fields as a possibility, and adopt an algebraic approach to constructing them that exploits the mathematics of quantum field theory, it turns out that we can sidestep renormalization completely, and we discover a mathematically well-defined concept of interacting particles that is quite closely analogous to the free quantum field's Fock space structure (without having to work with asymptotic states).

    The approach I take attempts to be as empirical as possible, to the extent that it takes a view that is common in Physics, that correlations of "the field" are the observables for the purpose of theoretical physics. Renormalization, for example, takes as its empirical starting point that correlation functions must be finite. The class of models that I construct, however, generalizes the generalized free quantum field, with an arbitrary (complexification of a) Källén-Lehmann weight function required to specify a particular dynamics, so there is a "landscape" of possible models, as they say in string theory. From the point of view of empirical usefulness, this is good, but such a large class of models is essentially not very explanatory. Still, it seems good to have an intermediate explanation of the relationship between quantum (field) theory and classical modeling that I like better than anything I have seen elsewhere in the literature.

    The most discursive account of my approach (but which pre-dates the mathematical developments in "Lie fields revisited") is probably in a Växjö Conference Proceedings, "Models of measurement for quantum fields and for classical continuous random fields", also available as a preprint, arxiv:quant-ph/0607165.

    I will post separately a couple of responses that I have received from main-line physicists, and my responses to them, which hopefully will give some indication of the sorts of interpretational and mathematical objections that can be raised about my approach.
     
  2. jcsd
  3. Dec 14, 2007 #2
    Physicist A (whom I will not identify) wrote:
    My reply:
    As usual, I'm too long-winded. I haven't received a reply to this, nor did I expect to. Some of the readers of this post will be only too familiar with not getting replies from people whom they cold-call, so these few lines are gold-dust, to be carefully considered over the next year or two, but as usual I write in a way that guarantees no reply (actually, I have met this person, and he does remember me, but I'm pushing something conceptually new, which he doesn't think has much value. I have, of course, very sadly, made it just slightly more likely that he won't answer at all next time I venture to write to him).

    Hopefully I will change my approach enough over time to address the issues raised here. Note that A is right about everything. Although my approach is moderately mathematically sophisticated, more than most crank papers, still the paper has holes a mile wide in it, which mean that I will probably have to write another, more detailed paper, if I can, to persuade anyone of the interest of my approach. A has picked on what I think probably is the biggest hole in the paper, and expressed his feeling that the hole is currently too big for him to spend any more time on it. Being married to an academic, who is currently head of the classics department at Yale, makes it easier to understand how busy A is, and to cut him some slack.

    The request for experimental testability is of course harder to satisfy than the mathematical question. THAT has to wait, but I hope there's as much possibility of useful models for experiment being constructible within this approach as there is within the string theory approach. Reading between the lines, you may notice that A is not so robustly demanding of experimental testability as he might be. Cautiously, that makes me hopeful that he's recognized that this is not purely theoretical, although A wrote this e-mail in 42 seconds, so not too much should be taken from it. I reckon a thousand Physicists and Mathematicians working on this approach would have a fairly decent chance of getting first Physics in 10 years, but I haven't yet lined up the funding.

    I'm frankly expecting no responses to this topic. Still, any response you do come up with will be just as welcome as the above.
     
  4. Dec 14, 2007 #3

    marcus

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    Thanks for giving us this announcement of your work, and opening a thread where people can ask you about it. And welcome to PF's Beyond forum!

    I have the impression that you have published quite a lot (half dozen or so?) in peer-review physics journals, and that before joining the Yale physics department you were at Oxford (philosophy of science/foundations of physics, I think). I could be wrong about any or all all these details.

    It is interesting to see the correspondence---showing the effort involved in calling attention to ideas off the beaten track. I'll stop answering so i can get back and read your last post more carefully.
    ============

    You know it is quite possible that you will get some reaction to your ideas here. I was struck by the coincidence that the mathematician John Baez who has sometimes visited here, and posted pedagogical notes on things that interest him, is also married to a classicist. I forget his wife's name, Lisa Raphals, I think. Her specialty is comparing classical Greek social and literary themes with their classical Chinese counterparts. Maybe that comes under the heading of Comp Lit, but at least it isn't modern Comp Lit.:wink:

    ============
    I will isolate a few lines to look at more carefully (although other people here are specifically more expert.)

    *Dear Peter,
    I looked at your paper but I could not find an answer that is of utmost importance for me. What is your proposal for the function xi in Eq.(5) for photons? I could not find an answer to this question in Section V where you discuss the electromagnetic field. Your proposal may become experimentally testable only if you propose a specific form of the deformation for the commutation relations and, of course, the photons are the best testing ground of your hypothesis.*

    It sounds like he is challenging you to propose a specific formulation, that could lead to testing.

    *"Lie fields" were introduced in the 1960s, but it became apparent after a few years that they are incompatible with the Wightman axioms, so they became moribund. Once we admit classical random fields as a possibility, and adopt an algebraic approach to constructing them that exploits the mathematics of quantum field theory, it turns out that we can sidestep renormalization completely, and we discover a mathematically well-defined concept of interacting particles...*

    This helps me understand your title "Lie fields revisited". I had never heard of Lie flelds. Just from the name I would assume it refers to a vector field taking values in a Lie algebra. that seems much too simple, what is it really? and what was the original motivation for studying Lie fields? (in basic entry-level terms please :smile:)
     
    Last edited: Dec 14, 2007
  5. Dec 14, 2007 #4
    Physicist B wrote:
    That's more of a downer! Physicist B doesn't get the paper. Still, I write a reply, knowing that there's no chance of getting anything else back, but I need to formulate a reply for my own good. I had no intention of posting this or the previous e-mail when I sent it, so I have to edit this one a little to keep it anonymous. You'll notice that I naturally take the role of supplicant-who-can-be-ignored, further ensuring that I don't get a reply.

    That's enough of a conceptual miss that I really may not get anyone interested at all, although B focuses on the fact that I conceived the mathematics of "Lie fields revisited" as particularly targeted for Mathematicians who work on what is known as "Local Quantum Physics" (which makes my mathematics look like 2+2=4 -- that is, I hope I'm not erroneously saying 2+2=3.7). Perhaps there's hope! You'll probably notice that's far too much to infer from B's reply. I also hope that B just read the paper very fast; I'm in no doubt that my approach is conceptually far enough from the ordinary that it can't be understood or any of the consequences appreciated in a moment.
    I have met B, and talked to him for about a minute about Bell inequalities, perhaps two years before my J.Phys.A paper was published. The joys of living in Oxford, where almost everyone seemed to come through. He's not someone who just dismisses the hidden variables question instantly, but if he remembers me then I'm in a Bell inequalities slot in his head, not a serious physicist slot, so it would probably be better not to be remembered.

    Note that I want my papers rejected. I'm not just puffing this guy. If my paper had been rejected by JMP, I would have had to try to find a way to improve it, perhaps even to rewrite it, for a submission to another good journal. It would have been better. "Bell inequalities for random fields" was accepted by the sixth journal I submitted it to, after six years of effort, by the skin of its teeth -- one referee thought it was OK, two thought it shouldn't be published, the editor, amazingly on that showing, sent the paper to a journal board member, who, it turned out, knows me and was willing to work on the paper enough with me to make it acceptable. It's really no wonder the paper has no citations yet, being published is absolutely only the first step, you've got to be read, and you've got to be understandable enough for someone to think that they can write a paper that cites your methods. I hope with this blitzkrieg that someone will read the paper, particularly in the context of "Lie fields revisited", and find it interesting.

    That's it, at least for now. No-one else has replied. I'm sitting on my hands worrying that I won't get enough feedback to take a worthwhile next step. I might have to provide feedback myself! After 10 years, I'd almost welcome someone showing me an easy proof that it's all nonsense. I said almost, right? Where did outrageous over-self-confidence go for a second? A half-dozen Physicists have been kind enough to reply, saying that they will look at my paper, to my e-mails bringing "Lie fields revisited" to their attention, but none of them may reply substantively, of course. It may also be that Physics Forums will ask me to cease and desist from this form of posting, fair enough if they do.
     
  6. Dec 14, 2007 #5
    Marcus, thanks for your reply. Very much. But I have to pick up my daughter from school now. She may want to play on her Webkinz account, or we may go out in the snow. So probably no reply to yours until later. I'm looking forward to trying to reply to the particular way you have phrased your questions, which looks productive.
     
  7. Dec 14, 2007 #6

    Haelfix

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    This is best put in the quantum mechanics forum. Moreover, you really want to talk in person with constructive field theorists and measurement theorists about this. I am not aware of a significant presence of them on PF though.. This is sufficiently advanced and esoteric that you probably won't find much help here other than explaining confusion. Perhaps alt.sci.physics or something like that if you absolutely have to scrounge the internet wasteland.
     
  8. Dec 14, 2007 #7
    Maybe. If BYSM decides they want it elsewhere, they'll let me know or just move it.
    That may well be true. I have e-mails to a few of them that are as yet unreplied to. The paper is posted on the LQP archive at Goettingen.
    If I can explain confusion, I guess that will reduce it from the esoteric. Einstein tells me I must teach my Grandmother, right? If what I'm doing comes across as advanced, I haven't explained properly. A random field is no harder in concept than a quantum field, which is easy enough. Isn't string theory harder? The only difference between random fields and quantum fields is that they commute at time-like as well as at space-like separation. Indeed, the presentation of random fields that "Lie fields revisited" proposes to make random fields a particular type of quantum field.

    What I'm doing is beyond the standard model, but perhaps as yet too far, or else beyond in the sense of wrong.
     
  9. Dec 14, 2007 #8
    I think that's right. I believe it may be a novel mathematical problem, however, so if that is what it takes it will take a while.

    I hadn't heard of Lie fields before a year ago either. I came across them while reading through a review paper (which is cited in "Lie fields revisited") by Streater, who was a mover and shaker in axiomatic quantum field theory. Coincidentally, Streater has a fairly well-known web-page on "Lost Causes in Theoretical Physics" that makes good cautionary reading.

    The creation and annihilation operators of a free quantum field satisfy a commutation relation
    [tex][a_f,a_g^\dagger]=(g,f)[/tex],
    where [tex](g,f)[/tex] is a Lorentz invariant inner product on the test functions [tex]g[/tex] and [tex]f[/tex]. The field itself is [tex]\hat\phi_f=a_f+a^\dagger_{f^*}[/tex], and the vacuum state is a zero eigenstate of the annihilation operators, [tex]a_f\left|0\right>=0[/tex]. This may not be familiar to people used to the long-winded descriptions of quantum fields in Physics textbooks, but there it is.

    A Lie field satisfies a commutation relation
    [tex][a_f,a_g^\dagger]=(g,f)+a_{\xi(g,f)}+a_{\xi(f,g)}^\dagger[/tex],
    where [tex]\xi(g,f)[/tex] is a linear Lorentz covariant functional of [tex]g[/tex] and [tex]f[/tex]. This equation is similar enough to the commutation relations satisfied by a Lie algebra to have earned the name. The inner product and [tex]\xi(g,f)[/tex] are effectively structure functions.

    I was trying to construct just this structure on my own, because linearity of the quantum field as a functional of the test functions -- so that [tex]a_{\lambda f+\mu g}=\lambda a_f+\mu a_g[/tex] -- is almost enough to require only this structure, so I was primed to recognize the reference in Streater's paper when I saw it. The Lie field structure was tried with some enthusiasm in the early 60s because it was seen to be mathematically very simple and beautiful -- which it is -- but being incompatible with the Wightman axioms was seen as too much. It's only the developments across the whole literature since then that make it possible to think of classical random fields; I think it would have been unthinkable 10 years ago for JMP to publish a paper that relies on such a delicate discussion of the relationship between quantum and classical measurement theories.
     
  10. Dec 14, 2007 #9

    marcus

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    Thanks for a brief clear explanation!

    Maybe the editor just happened to like your prose style :smile:
     
  11. Dec 15, 2007 #10
    The first time I heard of Lie fields was recently in http://arxiv.org/abs/0711.0627 . The following quote from p 2 may be relevant:

    "After the first attempts to construct (4D) Poincar´e invariant Lie fields led to examples violating energy positivity, it was proven, that scalar Lie fields do not exist in three or more dimensions."

    My own interest in that paper has to do with the immediately preceding lines

    "The spectacular development of 2-dimensional (2D) conformal field theory in the 1980’s is based on the preceding study of infinite dimensional (Kac–Moody and Virasoro) Lie algebras and their representations. A straightforward generalization of this tool did not seem to apply in higher dimensions."

    with which I completely disagree. :smile:
     
  12. Dec 15, 2007 #11

    Fra

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    I just skimmed this and something makes me curious. I'm no matematician but I'm interested in the foundations of QM. As I understand it you are trying to communicate ideas on new perspective to a physical problem?

    Every problems has to be analysed from some starting points, and I'm not matematician to mind and my starting points are different and to most I think philosophical.

    I'm not sure if the questions make sense to you but...

    1) When you consider random fields, which you say are basically indexed random variables. Then my first question is how do you _establish the indexing_ from an operational point when the variables are random? I've got a feeling that the indexing is implementing as a background structure? I see this related to the choice of microstructure to apply and ergodic hypothesis? Does this make sense?

    2) Did you try to connect your thinking in a new way in the context of GR? Does your idea offer a supposed (yet to be seen of course) competitive advantage in your opinion? Or are you considerations considered in isolation from the problem of unifiying QM and GR?

    /Fredrik
     
  13. Dec 15, 2007 #12
    Properly, what I have called Lie fields should be called Lie random fields; then we could say that Lie quantum fields do not exist in three or more dimensions.

    http://arxiv.org/abs/0711.0627 is not an easy read. I can't say I agree or disagree with much of it at all.

    I attempted to correspond a year ago with Seiler, Rehren (one of the authors of the above), and Fredenhagen over an aspect of the paper "Quantum Field Theory: Where We Are": I sought to point out that the principles they adopt there for quantum fields are remarkably weak:
    • the superposition principle for quantum states, and the probabilistic interpretation of expectation values. These two principles together are implemented by the requirement that the state space is a Hilbert space, equipped with a positive definite inner product.
    • the locality (or causality) principle. This principle expresses the absence of acausal influences. It requires the commutativity of quantum observables localized at acausal separation (and is expected to be warranted in the perturbative approach if the action functional is a local function of the fields).
    • In addition, one may (and usually does) require
      covariance under spacetime symmetries (in particular, Lorentz invariance of the dynamics), and
    • stability properties, such as the existence of a ground state (vacuum) or of thermal equilibrium states.
    As written, but as it emerged not as intended, these principles admit certain kinds of classical models. They didn't like my point of view, which is that these principles are weak, and hence perhaps an interesting new departure; they preferred to see them as a non-binding summary of existing axiomatic systems. "Quantum Field Theory: Where We Are" has started to be cited in the literature.
     
  14. Dec 15, 2007 #13
    Yes.
    In answer to 1), there is a pre-existing background space-time in all my work. That's how QFT also proceeds. High Theory often takes correlation functions as the ground empirical input. Renormalization is conditioned, for example, by the requirement that correlation functions are finite at the end of the calculation. This is not what all theorists would take as ground empirical input, and I presume that experimentalists would never do so. Whether taking correlation functions to be a general enough empirical input to describe everything is OK from a Philosophy of Physics point of view is certainly open to discussion, but I have taken it as my unquestioned ground for now. Insofar as I want my audience to be Physicists, I don't want to have this discussion at this point in my research.

    In answer to 2), Oh Yes. Most attempts at QG try to quantize GR, with all the difficulties that results in, whereas my approach, by classicizing quantum field theory, opens up a very different perspective. Loosely, variation of Planck's constant from place to place would look like curved space. From Appendix B of "Lie fields revisited" (which is quite verbose, and hopefully more generally readable):
    Whether this is competitive with other approaches to QG is of course yet to be seen -- I really mean the "nontrivial" -- but it certainly opens up a new front. In fact, this is a front that is already open, in the book of G. E. Volovik: The universe in a helium droplet (final draft, 3.5MB PDF), for example, and the literature on "dumb holes" in general [I believe that literature somewhat needs the concept of quantum entropy, which I allude to in section 2 of "Lie fields revisited", as thermodynamic dual to Planck's constant, in analogy to entropy as the thermodynamic dual to temperature -- both Planck's constant and ordinary temperature being measures of fluctuations in a classical random field approach, but distinguished by different symmetry properties].
     
  15. Dec 15, 2007 #14

    Fra

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    Thanks Peter for your clear and honest answers.

    What you say motivates me to read and think about all this at least a second round.

    I was hoping for another answer on the background thing because I saw a possibility that you considered random fields in the sense of not random state microstructure, but random state random microstructures, so as to also "randomize" the space of possibly microtructures (spacetime included). Of course that is probably horribly complicated mathematically but also conceptually. Or would you say this relates to your landscape note?

    The other things you mention makes me curious. Maybe I'll get back with more questions when I've given it a second round of thinking.

    /Fredrik
     
  16. Dec 15, 2007 #15
    To move this to a dynamic space-time may require completely new thinking and mathematical structure, because everything currently depends on Fourier transforms, which are globally defined on the space-time. Deformation of Fourier transforms is possible, with what I find to be a significantly higher level of mathematical difficulty, to QFTs on a non-dynamic curved space-time, but if there's no background space-time then the Fourier transform has to be replaced by something else. There is also explicit use of the metric tensor at almost all points of my current approach.

    The "landscape" note is purely about methodology of research: what are we looking for when we try to construct new models? Something that we think "explains" how things are is more highly prized than something that just describes. My approach, I'm pretty sure, is essentially descriptive (it may be useful as an effective model at some scales as a fairly general deformation of free field theories even if it turns out to be wrong as a model below scales of 10^9 meters, say). An alternative description opens up new ways to look for more explanatory theories, which may well be conceptually and mathematically very different from my approach, as is indicated by my note on dynamic space-time above.
     
  17. Dec 18, 2007 #16

    Fra

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    Peter, I don't want to take focus of your thread. I hope others will give you the targeted feedback you wanted rather than the philosophical aspects you don't want to focus on, but here are some more comments on your last comment.

    Relating to my own thinking - what if from the space of possible transforms, the fourier transform will be emergent, and perhaps there is a logic as to why it is emergent. Start with random transformations of random fields, and the question is what is most likely to be observed, by most observers living in this "random world"?

    It may seems like as soon as we are starting to talk about the space of possible transformations and so on, we immediately run into the well known problems of convergence issues because the options just grow fields of fields of fields etc.*But* if you add the constraint of limited information capacity of an observer, this puts a bound on the complexity on all relatable structures which means that even in the continuum limit the sets should as far as I see at least be countable. The more complex and iterated the structures get, the less "weight" do they get - given an obsever.

    And if you see it from the view of self-organisation, the most random scenario seems to be when also the observers, clocks and rods are random. And if you start by considering low weight observers, the contraints of what is observable by an observable is very tight simply because there are only simple observers around.

    I think this makes alot of sense, but exactly what the choice of formalism will be is not so clear.

    I hope to find an answer to the uniqueness of the fourier transform in this emergent sense. But I don't know how to do it yet, but I'm trying to figure it out.

    /Fredrik
     
  18. Dec 18, 2007 #17
    Fredrik, what you're suggesting looks less like philosophy than it looks like mathematics to me, but I can't see a mathematization of your verbal presentation. Do you have a mathematical literature in mind when you speak of emergence in its relationship to Fourier transforms? Renormalization and effective field theory methods come to mind, but only weakly, since at the QFT level the mathematical methods very much depend on the metric and the Fourier transform.

    The concept of "limited information capacity of an observer" seems to me to be a very flimsy theoretical assumption to rest much weight on. I can do some mathematics, I can run this fast, I can understand and appreciate poetry only somewhat vaguely, I can't play a musical instrument, etc., etc. These are only a finite beginning to an infinite characterization of my information processing capacity, which I take to be infinitely multi-dimensional, so it cannot be characterized well by a single number. I think that you get into describing the psychology of the observer if you introduce "limited information capacity of an observer", which I'm not even sure is open to any comprehensive mathematical model.

    As far as my own approach is concerned, I think I believe, I expect, I hope, that there is no need to introduce anything except Fourier transforms or their non-dynamical space-time equivalents to achieve empirical adequacy for experiments that are characterized by length scales within, say, 10 orders of magnitude of human length scales. Claims that the observer is necessarily a part of physical models don't appeal to me, insofar as I haven't yet seen a good argument. Appeals to the quantum mechanical formalism certainly do not justify enthusiasm for the observer as a necessity.

    It does hi-jack the thread as I see it, Fredrik, and I'd rather not do it here, but apparently no-one else sees the thread, so perhaps it doesn't matter. Still, you should more respond here to the mathematical modeling aspect of things -- although I am also interested in the cultural issue of how I'm ever going to get anyone to read and vigorously critique these papers.
     
  19. Dec 18, 2007 #18

    Fra

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    > Fredrik, what you're suggesting looks less like philosophy than it looks like mathematics > to me, but I can't see a mathematization of your verbal presentation

    You just formulated the quest. To identify the representation and exact formalism is the task from my point of view at least, I'm working on it. Since the mathematical formalism is in progress, common language is actually the most accurate so far. But as progress is made I'd expect a transition from philosophy to mathematics. Needless to say I think the QM and QFT formalism on static backgrounds is not the answer.

    Since this is your thread I'll refrain from further expanding on my comments too much. It's not my intention to contaminate it. I did wait a couple of days to respond to your last message because I didn't want to prevent others from jumping in...

    About the mathematical formalism applied to physical models that implements the fuzzy reasoning - this is exactly what I am looking for. Given that I'm no librarian, if there was a paper I was aware of that solved this to my satisfaction I would certainly have quoted it. That's is why I got curious on your work if there was a connection. You're right that information bounds are fuzzy, but I would say this is fuzzy simply because I'm still looking for the satisfactory formalism. Once it's nailed, it will not be fuzzy at all. To me the difference between philosophy and mathematics

    > Still, you should more respond here to the mathematical modeling aspect of things --
    > although I am also interested in the cultural issue of how I'm ever going to get anyone
    > to read and vigorously critique these papers.

    I can only speak for myself. The questions I asked where the first questions of choice that would determine my further motivation to analyse your paper ni more detail. If you had provided an model for the emergence of the indexing process I would have been excited! from the simple reason that I would be able to directly relate to it.

    Given my current impression I don't think I personally can add anything of value as feedback at this point, because I feel that your posed question is formlated relative too much baggage so to speak. But so does all of QFT, so this isn't a specific critique of your paper of course, it's just me.

    Edit:
    > These are only a finite beginning to an infinite characterization of my > information processing capacity, which I take to be infinitely multi-
    > dimensional, so it cannot be characterized well by a single number.

    I understand the objection and I've thought of that too. Your enumeration of new combinations is a process in my view, and processing I think it related to changes (and time) and "learning". And information vs access times. When do we know what we know? Like the distinction between having the answer, or to be able computer the answer, and how long is the computing time?

    I agree, there is no clear limit to what we can LEARN, and our information capacity can also change. Which I think is the key. What we know, and what we "could know" or will become to know, are different. But this is IMO similar to the problem of dynamical references.

    /Fredrik
     
    Last edited: Dec 18, 2007
  20. Dec 18, 2007 #19
    I do agree with your assessment of this: you'll see a coded acknowledgment that I'm specifically working within QFT's acceptance that statistics and correlations of field observables, set against a background space-time, are sufficient as an empirical ground at the end of the introduction to my "Lie fields revisited". However my acceptance is certainly not without reservations.

    When doing innovative research, it's important eventually to restrict to a context in which there can be a formulation that makes contact with other approaches well enough for people who use those approaches to be able to see the advantages of the new relative to the well-known (or at least for others to see the possibility of advantage). To make progress in Physics, that means you have to create and/or find mathematics that expresses and refines your conceptual ideas. There was a stage in my research when no-one could see that what I was doing could possibly come to anything mathematical, it's taken me ten years to get to the point of publishing one paper in J. Math. Phys. and a few other papers in other journals.
    Your approach, I don't know. It looks to me as if you have at least five years before you reformulate, for the tenth time, what it is you think you're doing well enough that you'll be able to recognize applicable mathematics when you see it in the literature. I don't know how long you've been doing your research, but unless your experience is very different from mine you had better settle in for the long haul. Note also that I had to have random fields pushed in my face twice by friendly Physicists before I realized this was exactly the mathematics I wanted, when I'd already been working on what were effectively random fields for at least 5 years and I was very lucky that I was well-enough prepared immediately to recognize Lie fields as exactly what I had been trying to do when I saw a reference to them in a 1970s review article. Without that recognition, I doubt I could ever have published my work in J. Math. Phys.
    I'm somewhat projecting my problems onto you, which may well not be appropriate, so you will have to decide how seriously to take my experience and the advice I'm sort of offering you here. Your posts look informed enough about the role of mathematics, however, that you may agree with much of what I'm saying, but you want a mathematical ground that's more the next thing after the sort of thing that mine is. Good Luck!
    I will be on PF probably only for a few months. I will return again, it's useful, but I could not do research while posting heavily. It's a little addictive, so that I haven't yet found a way of posting only a little. I find posting here intellectually and emotionally demanding, and rewarding, but once I settle into reading and writing for The Next Paper, I don't think I will be able to keep this up as well.
     
  21. Dec 18, 2007 #20

    Fra

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    Thanks for your responses Peter.

    Everything you just said makes great sense to me and thanks for your advice.

    I have no illusions (and even if I did, I fail to figure out how I could tell), and I'm fully aware of that this is a long process. I am not affiliated with anything or anyone, this is a sincere interest and hobby of time and my driver is curiousity. My impression is that the research politics and social constraints seemed like interfering too severly with creativity. I wouldn't stand it and I have the wrong type of personality to align.

    I'm 34 and I will take the time it needs because what's the alternative? The choice is easy. I want the answer and I will keep looking until I find it, and in the meantime this is about the most intellectually rewarding hobby I can imagine, I ask for no morem and I have no reason to take shortcuts.

    I mention my thinking in the connection to your thinking to relate, but I have no plans whatsoever to seriously "promote" my ideas at this stage. At minimum I have to blow myself off the chair before even trying to convince others and _this_ stage is at minimum a few years away I suspect, probably longer.

    > what it is you think you're doing well enough that you'll be able to recognize applicable mathematics when you see it in the literature

    Either I recognize it or I don't. Wether it's not there or I just can't see it - I don't see how I could ever distinguish between the options :wink:

    Good luck to you as well.

    /Fredrik
     
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