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Field theory approaches to understanding Quantum Theory

  1. Writing style

    2 vote(s)
    20.0%
  2. Measurement events ARE caused by particles

    0 vote(s)
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  3. Too complicated

    2 vote(s)
    20.0%
  4. Too different from quantum theory

    1 vote(s)
    10.0%
  5. Don't want to read citations to understand the paper

    2 vote(s)
    20.0%
  6. The format of the paper - not LATEX

    0 vote(s)
    0.0%
  7. It's nonlocal - coarse-grained equilibrium doesn't cut it

    1 vote(s)
    10.0%
  8. Too much holism

    0 vote(s)
    0.0%
  9. Too impractical to be useful

    2 vote(s)
    20.0%
  10. Let me sell you a different interpretation

    0 vote(s)
    0.0%
  11. OTHER

    4 vote(s)
    40.0%
Multiple votes are allowed.
  1. Oct 16, 2008 #1
    Why do people who think that quantum theory is great go on and on that classical particle models are impossible? Why do they never mention fields? There are endless articles in Nature on the latest experiment and why classical particle models won't do. Give or take the de Broglie-Bohm approach and various ad-hoc models that exploit the detection loophole, I grant that classical particle models are impossible. I also think quantum theory is great. Very pretty mathematics, very useful, sometimes wonderfully simple.

    If we want to think in terms of fields, but we want to model experiments, we had better also introduce probability. That means that we have to engage with the mathematics of continuous random fields. These exist in the mathematics literature, and are used in Physics. Classical continuous fields, such as an electromagnetic field that satisfies the Maxwell equations, won't do, sadly, because thermal or quantum fluctuations make the field rather badly defined.

    The whole argument is sadly long-winded, because it's enough of a different way of thinking that it needs to establish a lot of basics. For anyone who wants to understand quantum field theory, I offer the two page PDF attachment, "The straw man of quantum physics", as an outline of how to think about experiments in terms of continuous random fields and discrete thermodynamic transitions of finely tuned experimental apparatus, instead of in terms of particles and their properties (the PDF is also available as arXiv:0810.2545 [quant-ph]).

    My question for the thread is: why do you think this paper doesn't work? It's based on several papers that are published in good journals, but this effort has been rejected by a number of big journals, Nature, Nature Physics, Science, and Physics Today, so it's clear that I haven't achieved the leap to the next level. I hope for feedback before trying a new approach next year. Of course people on PF will have ideas that derive from their own theories, which I will be glad to hear, but I'm particularly interested in how people see this paper relative to conventional ideas about quantum theory.
     

    Attached Files:

  2. jcsd
  3. Oct 17, 2008 #2

    DrChinese

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    I like the paper, still studying it. :)

    From your paper:

    1. A continuous random field model is contextual just because the whole experimental apparatus must be modeled.
    2. If the unusual past that is required is thought unreasonable, then quantum field theory has the same problem.

    I think 1. is good, and it is time for everyone to acknowledge the obvious: any viable theory will need to be contextual. We need to abandon the realistic (a/k/a hidden variable) requirement altogether as clearly the Weihs experiment rules that out. Even in non-local theories such as dBB, a mechanism in which the final detector settings are factored in will be necessary. So I think your direction is great.

    The thing about 2. is that it is not really a criticism of QM, as it is silent on the underlying mechanics anyway. And I think that is the heart of the issue. Can QM remain neutral indefinitely? I interpret what you are advocating to be: what are the attributes of a suitable local contextual (non-realistic) theory? Of for that matter, what are the attributes of a any contextual (non-realistic) theory that fits with experiement? You are advocating a random field approach as a solution. I guess I will have to read your other papers to understand this approach in more depth.
     
  4. Oct 17, 2008 #3
    Thanks for the response! A pretty good choice of salient points.
    On your response to 1., absolutely! To me, however, contextuality is natural in a continuous random field approach, but I have never seen a classically natural way to do contextuality of particle properties. Another way to put it, contextuality becomes holism for fields, which is inconvenient, but contextuality becomes nonlocality for particles, which is conventionally anathema (as attested to by the conventional rejection of dBB). Or, the apparatus is always touching a field that's inside the apparatus (supposing there is a field), but it is not touching a particle that's inside the apparatus (supposing there is a particle).

    On 2., I think it's OK for QFT to be probabilistically superdeterministic, and I think it's just as OK for a random field to be so. It's perhaps important to note that a continuous random field is as agnostic about causality as is a quantum field. A random field describes correlations, and there can be various symmetries amongst those correlations, but it doesn't tell us anything about the dynamics. In the sense that a random field has resources for describing correlations but no explicit resources for describing causal relationships, a random field gives up questions about causality. Establishing causal links when we have observed only correlations is a delicate matter in general. Indeed, taking correlations amongst isolated events to be caused by particles could be thought to be at the heart of our misunderstandings of QT. This doesn't mean that another formalism couldn't include explicit resources to describe causal relationships, or that causal relationships cannot be derived from a given random field structure, but I'm not in a position to do those things. I think this rather evades your question, "Can QM remain neutral indefinitely?", in the context of random fields, but at this time I'm content to do so; one defining intention is to be as empiricist as I can, another is that I am nonetheless engaged in a model-building enterprise.

    Needless to say, I'm partisan for a random field approach. It gives up something of classical physics, but perhaps not too much. Holism is a kind of nonlocality, of course, but, again, it's less against the spirit of classical Physics. I like to think that Bohm would give up trajectories for something like this holistic approach, given some of his writings. Interestingly, Stochastic Electrodynamics (SED), has produced a lot of successful work that takes the electromagnetic field to be a field that has Lorentz invariant zero-point fluctuations, effectively a continuous random field, but I part company with SED on its insistence that fermions should be modeled as particles.
     
  5. Oct 20, 2008 #4

    Fra

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    Hello Peter, I think I skimmed some of your random field paper long time ago, but doesn't remember the points (I probably need to read it again), I remember that the last time I asked for the "physics of the indexing process". FWIW, here are my personal impressions, which may not be very representative.

    1) a somewhat unclear benefit in adaoting the supposed solution (random fields) of the question posed. I would want a stronger motivation to read the paper more carefully. Ie. Why is the desired to have some kind of "classical style model" (fields or particles) such an important question?

    To me this is not very clear, thereby does my motivation to analyze a supposed solution to that drop.

    I am not saying there are no issues with QM, I am just thinking that perhaps this original concern of loss of classical logic and old style realism isn't the main problem? Or if it is, perhaps your paper should try to explain why, as to increase the motivation to study your solution.

    Ie. to describe and argue for your choice of question, before trying to argue in favour of the solution. I've got some feeling that implicitly it's assume that the logic of classical physics is the ideal one? I don't share that view, so I think I (as a reader of your paper) need to get this motiation to your questioning?

    2) I think one may need to read up on your other papers to appreciate this paper more.

    Other than that, I tried to think about this and there might be elements that I like. I also think the general trait of contextuality is plausible. But my personal view of contextuality is the evolutionary one that the logic of interactions are best understood conditional to the evolved present (which is dependent on the past).

    Also general idea of indexing observables is something I feel needs a physical explanation. Ie. from the point of view of "black box physics", how is the index on which the field is defined emergent?

    I guess one of the classical logic things is that these things "just are", but from the point of view of information process that I find more plausible than the ontologies of classical physics, I see these as emergent. Isn't the index structure itself an ontology? How do you "measure" the index? or don't you?

    From my perspective I don't clearly see from that two page paper what fundamental problem you are addressing. To me the loss of some "classical features" is not a fundamental problem, because the classical logic wasn't satisfactory to start with.

    /Fredrik
     
  6. Oct 20, 2008 #5
    Yes, I posted in January, just after a paper was accepted by J. Math. Phys. It's here.
    I think I didn't answer your query about the index set back then. I think it's problematic, but I'll give it a try again now. The usual index function is a pure frequency. Thus, when we say in quantum optics that waves of a particular frequency are being measured, that's what the equipment is sensitive to, so we use creation and annihilation operators associated with pure frequency index functions, perhaps exp(-i\omega t+ikx). This is problematic in QFT: mathematically, because it has infinite norm, because it's spread over all space-time; operationally, because the experimental apparatus doesn't really resonate with a signal over all of space-time. The experimental apparatus does resonate with the signal over some of space-time, at least where the measurement device is placed, so the appropriate index function is one that is centered on a given frequency in Fourier space-time and centered on a given place in real space-time. Test functions that represent a measurement device well, in great detail, have to be established by characterizing the device with standard sources of various kinds (of course it's a succession of approximations, standard sources become standard by being measured with standard measurements, which became standard by ...).
    I'm not a modernist Physicist. I'm post-positivist. Classical Physics is not a better conceptual system than quantum Physics. They are different. There is a straightforward Occam's razor reason for preferring to use classical models throughout, instead of using classical models at macroscopic scales and quantum models at small scales when necessary, IF we can do so without introducing even greater complexities. All existing classical models either appear ad-hoc or introduce non-locality in some way that Physicists, on balance, think unacceptable. I think continuous random fields might be acceptable to Physicists. The history of Physics is strewn with people who've failed to convince anyone of a myriad of similar claims, of course.

    Additionally, since quantum theory cannot give a detailed account for Physical processes without introducing quantum fields, but there is, so far, no mathematically valid interacting quantum field in Minkowski space, and the mathematical procedures and our conceptual understanding of both perturbative and non-perturbative QFT are somewhat problematic, the fact that there are mathematically elementary models for continuous random fields is enough to justify more attention. It may be that people will decide against this approach, but I believe it now justifies more attention that just from me.
    You surely have better things to do.
    I think I can agree with your sentiment about contextuality, or at least my reading of it makes sense to me, but how are you going to represent that web of multiple interactions? Also, does the past superdetermine the present? Perhaps deterministically or perhaps only probabilistically (the latter is enough that Bell inequalities cannot be derived, for a random field)? How will you represent, mathematically, the exact, detailed ways in which your physical model of dependencies is not deterministic, or does not determine evolving probabilities?

    If you stay with quantum theory, you are essentially staying with an effective way to talk about the contextuality of measurements, in which measurements change the possibility of carrying out other experiments. Alternatively, in a classical approach, measurements can change the system that is measured, changing the context in which the other measurement is made. The irony is, perhaps, that before the EPR paper Bohr and Heisenberg both talked about quantum mechanics in terms of measurements changing the system that was measured, a position they dropped when they realized that it required nonlocality for particle properties. For continuous random field models, holism is required, but not nonlocality.
    I tried to answer this above, but I'll try again. The world is what it is. We are in it. We construct various experiments, frequently reusing parts from other experiments, attempting to construct parts that we understand well so that we can extend our understanding and control incrementally. To do so, we try one mathematical system or another, which have various degrees of freedom that we try to fix with the experimental results. Our measurements of the lengths, geometry, and approximate symmetries of an apparatus are part of those experimental results. Quantum theory, on this view, is not a linear theory, because we know neither what the state is not what the measurement is Tr[\rho_i,\M_j]=R_{ij} is bilinear in the unknowns, constrained by the experimental results R_{ij}. To solve this bilinear system, we guess what measurements we've constructed, then iterate. There are all sorts of subtleties, since we have only a finite number of finite accuracy data points, but we presume to fix a state in an infinite-dimensional space of density operators, but we work to obtain a system that is conceptually pleasing, self-consistent, and practical for engineering purposes --- hence we obtain quantum optics, for example.
    I agree, certainly, that classical logic, mechanics, continuous random fields, etc., are not satisfactory. But that doesn't mean we can't use them from time to time. There are conceptual problems with quantum mechanics, too, but I will certainly continue using them.

    This two page paper was my current attempt to reiterate the argument that I made in my published papers at a more accessible level. I don't think I succeeded very well, but, for what it's worth, I put a lot of work into it. I've valued comments made at PF on my earlier papers; here I am again, doing pretty well again. Most obviously, you've led me to mention Occam's razor in a way that I think I like and might possibly use again.

    Thanks, Fredrik! Best wishes.
     
  7. Oct 21, 2008 #6

    Fra

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    I, like you, doesn't think quantum theory is satisfactory as a fundamental model. But I suspect my objections to it, are different from yours. This is where the choice of question comes in.

    Simply put, my objection to QM is that it tries to deal model measurements without trying to deal with the full contextuality of a measurement. "A measurement" is always define in the context of an observer in my view. The standard (I'd say almost non-existent) way of trivializing the observer into a "classical device" that monitors the quantum world is not good enough.

    When analyzing this in, my personal reasoning suggest that the only sensible solution is to consider an "evolving observer". All, from the obserevr, expected interactions are conditional in it's present evolved state. This state contains all information the observer has about it's universe. So in my view, the observer IS a living image of the environment, in which the very laws of physics are implicit in how the observer has been selected during evolution.

    There is no fundamental superdeterminism, although I can't rule out that there will be FAPP-type superdeterminism in that sense that a complex observer can see patterns that a simple observer can not.

    But it's not deterministically probabilistic either. The probability induced from the observer information, determines a sort of probabilistic action. And then the actual behaviour of the observer is like a random walk. So in the differential sense, the evolution is probabilistic in my view, BUT the probability does not evolve deterministically (like in QM). It would onlt evolve deterministically in a special case of equilibrium. Meaning that the deterministic evolution of probability we see in QM, is emergent, not fundamental.

    I like the expression of Zurek

    "What the observer knows is inseparable from what the observer is"

    To me this is really an expression of holographic vision, that the observer IS an mirror image of what the observer sees. This is why evolution of law, and evolution of observers and matter are really dual to each other.

    How to do this mathematically, I'm working on that. But in short I am reconstructing a discrete probability theory which is self-evolving. There is no notion of "random variables". This should also contain spontanous index-formation, and thus emergent topology. But there are many problems here I surely haven't solved.

    More later...

    /Fredrik
     
    Last edited: Oct 21, 2008
  8. Oct 21, 2008 #7
    By "classical particle models" do you only mean billiard balls (particle interacting only by direct collisions) or classical particles that interact through fields (electromagnetism, gravity)? If you mean the later type of model (because Bohm's theory has particle plus fields) then I disagree with you, such models are possible.

    Yes, but I don't see the need to introduce probability at a fundamental level, as in a random field. You can start with a deterministic model and then, based upon the properties of that model, statistical approximations could be made.

    Thermal fluctuations are just a way of speaking about the particles' motion. What's the problem here for a classical field? Quantum fluctuations are an artifact of the quantum theory. They need not be fundamental elements of reality.

    Sorry but I am not qualified to judge such a paper.
     
  9. Oct 21, 2008 #8
    Misspeaking on my part. Yes, Bohm's particles+fields are possible. However, dBB is not Lorentz covariant, despite considerable effort. There are other, stronger reasons why I don't like dBB, constraints on theory construction that I would prefer to be satisfied, but my focused attention on why I don't like it was over ten years ago, so I can't quickly list my reasons coherently. I have followed work on dBB, however, and I haven't yet seen anything new that would change my mind. It's this kind of closed mind applied to my own work that kills me, of course, or at least that makes the work of opening doors a tricky business.
    Agreed. At this point, however, it's partly about making the argument. A continuous random field is mathematically very close to a quantum field, indeed can be presented as a commutative quantum field (classical mechanics can be given a Koopman-von Neumann representation on a Hilbert space, too, but the mathematical "distance" is larger), which makes it possible to compare continuous random fields and quantum fields in what I find to be interesting ways.

    Once we get over the hurdle, people can surely work on statistics of deterministic models if they think it might be productive to do so. What you are suggesting might be better handled by a different mathematics, however, something that algebraically or otherwise expresses causal relations as well as correlations of the field. The discovery of causal relations from correlations alone (which are frequently all that are measured) has become notoriously delicate in Philosophy of Science in recent years.
    The problem for fluctuations of a field, thermal motions of the field, or however we describe them, is that the mathematics becomes improper in the multiple infinite limits that have to be taken. Infinite numbers are everywhere, and controlling them gets out of hand. One word, renormalization. There are ways of handling those infinities more-or-less consistently, and I regard a continuous random field formalism as a relatively good way of doing that.

    Now, I have no objection to a Lattice approach, but there's a cultural thing that the continuum is either 1) the real thing; or 2) easier to manipulate than discrete approaches; that I both feel somewhat and have to take seriously if I want to persuade Mathematicians and Physicists that my approach is interesting. More elementally, I always want to know what's in the gaps when I see a lattice model, so I guess I am engaged.

    If someone shows me a nice mathematical model, and can spell out enough of the bridge principles that relate the model to the real world, I'm interested. Discrete or continuous is OK.
    You don't have to judge it. PF is more about discussion. Anyway you've given me as good as some referees would give.
     
  10. Oct 21, 2008 #9
    Fredrik, that all sounds OK to me, but the mathematization of course has historically been problematic. That's only a weak argument, from me, given my own enterprise.

    I think the contextual effect of the experimenter on an apparatus is not of comparable order to the contextual effect of the measurement apparatus on the preparation apparatus and the prepared system (my holistic stance only allows the idea of the separation of the apparatus into three parts as a pragmatic matter, but with that proviso I am willing to join QM in making the distinction). Indeed, if we observe an effect that is due to the observer, say because of stray capacitances as we walk past, we would certainly aim to shield the apparatus from them. We only need to be able to read the experimental data long after the event, as for Gregor Weihs' experiment, for example, which was ten years ago but the raw data is still available. Shielding the measurement apparatus from the preparation apparatus, on the other hand, is rather against the point of the Physics enterprise.
     
  11. Oct 21, 2008 #10

    Fra

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    Are you referring to string theory? If so, I agree that is too much of a mathematical game.

    It's funny that this comes out as a "mathematization" as I consider myself pretty philosophically inclined and paying attention to the conceptual things, and construction of measurements in particular. I am not suggesting that theory replaces experiment, what this really means in the context of a scientific method if you take it that far (and I do), what I am suggesting is really an evolving scientific method, where, unlike in poppers ideal, the process of hypothesis generation is analyzed more deeply.

    With observer I don't refer to a human observer specifically. Usually the entire environment are part of observer complexes. I agree 100% with you that the preparation part of an actual experiment is certainly part of the overall measurement, or the emergence of the measurement and measures. This contextual idea is to my liking. My way of expressing that is that the history of the observer matters. Here any "preparation" is definitely part of such abstraction.

    /Fredrik
     
  12. Oct 21, 2008 #11
    No, I meant your own mathematical project. I took you to be trying to mathematically describe the significance of the observer in some Physically meaningful way. Your reference to string theory throws me a little. String theory is nothing to me.
    To make numerical predictions, you have to do some mathematics. There are people who manage to say interesting things without doing any mathematics, but it's hard to persuade Physicists to find it interesting. The interplay between the mathematics and the real world experiment is interesting.

    Since you mention the construction of measurements specifically, I would be interested to hear your opinion of my three paragraph riff on how to think about experiments in terms of fields, starting with "We should think of Feynman and Hibbs’ “amplifying apparatus” as sensitive apparatus, not as detection or measurement devices or apparatus". If we take a holistic approach to understanding contextuality in classical terms, instead of taking a nonlocal approach, I think something like this account is necessary. Mathematizing what I have to say in those three paragraphs from scratch would be an enormous task, except that I can derive what I need because there is such a close mathematical relationship with existing quantum models.
    Do you mean to invoke the "memory loophole" in thinking about Bell inequalities (PHYSICAL REVIEW A 66, 042111 (2002); pre-print Quantum nonlocality, Bell inequalities, and the memory loophole), then? I agree that constructing an ensemble of systems (that is, preparation contexts) requires something like the ergodic hypothesis in conventional classical thinking, but from my more empiricist/post-empiricist point of view, it's enough if we achieve a relatively good model for Physics experiments. Pragmatically, if consecutive events in a device are correlated with each other, make the events happen less frequently, or take some other approach to removing or living with the correlations.
     
  13. Oct 21, 2008 #12
    I voted "OTHER" because my preferred choice wasn't listed. It would have been "Because it requires too many emergent properties to be assumed innate". I may be biased myself as a result of model building efforts and have my own list of reasons. I haven't gone over your reference list yet but some look interesting. I remedy that sometime.

    I liked the paper and am going over "Models of measurement for quantum fields and for classical continuous random fields" now to get a better notion of the indexing of variables. Wrt the above paper about the only general criticism, other than opinion, is that without a fully workable model it remains unknown what notions of realism, locality, etc. can be maintained. I think the general notions are reasonable and worthy of some model building effort.

    Your notion of observer inseparability has parallels in RQM (Relational Quantum Mechanics).
    http://plato.stanford.edu/entries/qm-relational/
    http://arxiv.org/abs/quant-ph/9609002
    http://arxiv.org/abs/quant-ph/0604064
    http://arxiv.org/abs/quant-ph/0505081

    My issues with the approach is not the lack of a classical particle representation. In essence a classical random field is compared to a quantum field and the theoretical features that don't get broken are compared. The case is then made that discrete transitions may be considered not as a transition in a classical particle but a tuned measurement of a thermodynamic transition. Good so far but, at the present model level, I must still consider this a demonstration of concept or toy model. Many if not most of the known symmetries must still be sprinkled on like raisins. In essence this approach does to fields what that standard approach does to particles IMO, only the standard approach is far better developed and successful. I do nonetheless think this is an important conceptual step in the right direction. Whether or not a fully working model provides us with new physics or even soothes our sensibilities remains to be seen.
     
  14. Oct 21, 2008 #13

    Fra

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    Peter, I'll continue some further comments later. I will not have access to internet until saturday due to a worktrip.
    Yes of course I am aiming for a mathematical model, but I am not playing mathematical games/exercises, neither is my inspiration beautiful math. But that's not anywhere near denying that mathematics is the one language for any quantiative model. I see now that I misunderstood you. :)
    Agreed. I totally misunderstood your comment above.
    Let me get back to these points in a few days. I can't make any sensible comments onthis in the rush I'm in atm.

    /Fredrik
     
  15. Oct 21, 2008 #14

    strangerep

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    Peter,

    (Edit: does anyone know what's wrong with the PF latex
    generator? I've edited below to show the raw latex as
    well, for now.)

    Even though I've read your "Lie Fields Revisited" paper
    (quant-ph/0704.3420) a few times I still don't get what
    you're on about. (Your straw man paper was even more
    obscure.)

    In "Lie Fields Revisited" you start with a field of
    operators over Minkowski spacetime. Then, in sect III
    titled "Interacting Creation & Annihilation Operators
    for a Scalar Field" you look for a deformation of
    the CCR such that the deformation still defines Lie
    algebra. Specifically, you write:

    [tex]
    [a_f , a_g^\dagger] ~=~ (g;f) + a_{\xi(g;f)} + a_{\xi(f;g)}^\dagger
    [/tex]
    [a_f , a_g^\dagger] ~=~ (g;f) + a_{\xi(g;f)} + a_{\xi(f;g)}^\dagger

    where f,g are Schwartz functions over Minkowski spacetime,
    and (it seems to me) the \xi(g;f)are an
    infinite-dimensional analog of structure constants
    "contracted" with the original f,g.

    Then, to make sure you've got a Lie algebra, you impose the
    Jacobi identity to get further constraints on \xi(...).

    Then (afaict) you use a GNS-like construction to obtain a
    Hilbert space from this algebra.

    So far it just seems like you're constructing an infinite
    dimensional Lie algebra (indexed by Schwartz functions),
    then you attempt to make it relativistic by introducing
    an M(u) function with support only in and on the lightcone,
    and then you derive more concrete expressions for
    the \xi(g;f), etc, ending up with your
    eqs(24,25). Then you require microcausality and re-express
    the algebra in terms of "G-modified smearing functions"
    (where this essentially just means multiplying the original
    functions by |M(u)| and then inverse-fourier-transforming
    back to configuration space. You end up with an infinite
    dimensional Lie algebra, now indexed by functions from a
    subset of the Schwarz space.

    But where is the "interaction" in all this? Don't you need
    another field to interact *with*? (Or is this some kind of
    self-interaction theory?) You continue in sect IV, discussing
    "Measurement & Scattering" presumably some variant of the
    LSZ formalism, but it wasn't very clear to me what you're
    really doing. I got the impression you're writing out
    N-point correlation functions in terms of your algebra,
    and attempting to show that (depending on \xi(...) )
    there can be non-trivial scattering. If I've understood
    correctly, then... how does one obtain an interacting theory
    corresponding to real world situations? By matching up
    the lower order parts of \xi(...) with known results, or... what?

    Then, in sect V, you perform an analogous construction for
    the free(?) EM field, but not for an EM field interacting
    with matter (unless I've missed something).

    I was left wondering what's the point of all this if there's
    no real-world interactions in the theory somewhere. (?)

    I'm also a bit perplexed about your emphasis on classical
    random fields (dreadful name, imho). There seem to be
    similarities with the more advanced modern treatments of
    classical mechanics, wherein one uses a "momentum map" to
    pass from ordinary functions over a phase space manifold to
    functions over the dual of a Lie algebra and searches for
    interesting representations by investigating coadjoint
    orbits over this dual space. For fluid mechanics, one needs
    inf-dim Lie algebras so maybe there's some vague connections
    between this and your stuff, but they're unclear to me. Some
    people try to draw connections between this and QM (e.g., de
    Gosson, who talks about a classical version of the
    Heisenberg uncertainty principle arising from what he calls
    the "symplectic camel" theorem).

    Anyway, apologies if I've misrepresented any of your stuff.
    (My answer to your poll question is that incomprehensible
    writing style is a large factor...)

    Hope that helps.
     
    Last edited: Oct 21, 2008
  16. Oct 21, 2008 #15
    Bear in mind that I'm going against the grain of modern Physics somewhat by taking a more empiricist approach than is the current fashion amongst Physicists with fundamental interests. If a mathematics is capable of modeling correlations that's interesting to me. In the context of empiricism, emergence is not as unacceptable. The availability of many different formalisms is better than being limited to only one, for the purposes of thinking of the next level of theory. A higher level theory would, I hope, seem more "innate", which I agree would be a merit for a theory, albeit not an overriding one.
    I've come to realize in the last week or so that my approach more-or-less gives up causality. A random field models correlations, but these do not require any causal model. Since in many experiments correlations are all that are measured, however, causality in such cases could reasonably be said to be metaphysical. Locality may be delicate because of the introduction of negative frequencies, however anti-particle fields are time-reversed versions of fields, which in some approaches to QFT are rather problematic for causality. I'm certainly applying thought to this question amongst (too many) others. I can see an argument that abandoning causality as metaphysical prevents a realist understanding from being as full-blooded as conventional understandings of classical physics usually are, but insofar as I am satisfied by an empiricist philosophy (which is pretty far, and my satisfaction is qualified by the post-empiricist critique rather than by modernist realism), not having a full-blooded realism does not concern me as much as it may concern you.
    Although I'd heard of RQM before, I don't remember ever having looked at it in any detail. I can see some similarities (in the SEP article, which is the only one I've looked at thus far), but some of the technical references look very interesting. Thanks for this!
    Agreed that what you've seen so far is not yet developed enough. The JMP paper is more allusive than I would like it to be (as Strangerep accuses, but I'll (try to) respond to his detailed comments separately), but it is a solid class of models. Restricting to positive frequencies in the formalism of that paper results in something that looks exactly like quantum optics, if we introduce a bivector-valued continuous random field. Perhaps we should bear in mind that interpretations of QFT are not usually thought to be adequate.
     
  17. Oct 21, 2008 #16
    I also had trouble with the TEX generation (one of the great strengths of PF), but assumed it was finger trouble on my part.
    It's hard to express the overall view, because it's different enough from existing interpretations that almost everything is different. Determining what are the most salient differences, particularly what differences will give a sharp perspective for people who've been thinking in terms of particle properties for decades, is a slow business. More papers are coming; I try to change the perspective each time.
    Yes, a field can be said to interact with itself, however the term "interacts" is more causal than the Lie field formalism really supports. The lowest essential is that the vacuum state of a nontrivial Lie field is unlike the vacuum state of a free field because the probability density associated with the field is non-Gaussian.

    If there are multiple fields that interact with each other, which generate probability densities over the tensor product space, we can nonetheless write marginal probability densities for a single field. Adding extra fields to the algebra adds additional states over the single field that in general cannot be constructed in the Hilbert space of states that can be generated by the single field alone.
    I'm not sure. I tried to write more, but it didn't come out well. For the future.
    Correct. There is no matter. That's because 1) Fermion fields are non-commutative, which is a step into more intricate mathematics, left for the future. 2) Fermion fields are not observable. Only products of two Fermion fields at a point are observable, because of gauge invariance, but a product of two Fermion fields at a point is mathematically ill-defined (because the fields are distributions). 3) The electromagnetic potential is not observable, and in a Hamiltonian formalism the interaction between the electromagnetic field and charged fields is expressed using minimal coupling. Since the Hamiltonian formalism for interacting fields is mathematically ill-defined, the renormalization group notwithstanding, I would prefer not to take the Hamiltonian formalism as my template. Not having another template, however, makes me need more ingenuity for the construction of a new model.

    I prefer to try to construct a theory using only observable fields as far as possible (or, rather, creation and annihilation operators directly associated with observable fields). The EM field is observable, that's good, but without matter fields there are states over the EM field that cannot be constructed using only the EM creation and annihilation operators. It's not clear to me whether we detect matter fields only through their effects on the EM field, but I'm sure there's something I'm missing here.
    Well, perhaps an algebraic modification of quantum optics. Quantum optics is useful enough despite having no matter in the theory. Beyond that is for the future.
    I used to agree. I used the term "classical statistical field theory" for a long time, until I discovered that there was already a term for what I was using in mathematics. CSFT is anyway not quite right, because the approach is probabilistic rather than statistical. "Classical Probabilistic Field Theory" would be OK, perhaps, but it's a mouthful. Probability is about random variables; when someone came up with an indexed set of random variables as a mathematical object, they called it a "random field", but a random field only becomes an interesting mathematical object, particularly in physics, when the index set has some additional structure, particularly there is a topology, a metric structure, etc., to give us continuity, and hence "continuous random fields".
    I've never had enough motivation to get my head around momentum maps. Fluid mechanics with an explicit model of thermal and quantum fluctuations might well use a mathematics that includes something like random fields.

    Versions of the Heisenberg uncertainty principle arise in classical signal analysis, loosely because signal frequency cannot be measured in a finite time.
    I believe the writing style problem is because I don't understand what I'm doing well enough rather than because I can't write, although I'm not sure which is worse.

    It all helps, if I'm listening well. Many thanks. Hope my responses help a little.
     
  18. Oct 24, 2008 #17
    I have studed that kind of topics such as you.
    I somtimes call that as research about axiom of quantum mechanics.
    unlike your approach, my approach is algebraic one.
    but I did not submitted to any journal of physics regarding that kind of topics.
    because that is a topics of philosophy not of physics, and rejection was expected.
    It is perplexed thing for me to see a article which contains no math in this forum.
    In my opinion, if we want to investigate this topics deeply, we must declare the fact that what we investigate is philosophical problems.
    I do not degrade a value of philosophy. I think this kind of problems are very important.
     
  19. Oct 24, 2008 #18
    Hi,
    This paper is here under slightly false pretenses: it was transferred by the PF administrators from "quantum mechanics", so it doesn't properly satisfy the requirements set out in the "Independent Research" forum stickies. I posted this topic in the QM forum out of ignorance of PF procedures. I take the transfer to this forum to preclude me posting anything to the QM forum again, at least in good conscience and without fear of reprisals from the PF administrators, which I regard as unfortunate for me because I had a number of interesting comments from people cruising through there.

    To the content of your comment, however, I point out that you can get a fair amount of mathematics from the cited papers. The most significant algebraic content is in the J. Math. Phys. reference, but there is some algebra in all the papers I have published in Physics journals. Mathematics alone does not get a paper accepted in Physics journals, there has to be a discussion that relates the mathematics to the world, which can be a delicate matter if part of the mathematics is unconventional, but you're right that discussion can more easily become Philosophical if there is no Mathematics. If you find that the JMP reference is similar to your unpublished algebraic thoughts, you might find enough to make a submission to a Physics journal for which rejection might not be expected. Let me know, and anyway good luck with your own research.
     
  20. Oct 24, 2008 #19
    PF do not permit to post any personal theory.
    If I write in it, that will be against to rule of PF.
    So I sent you a e-mail.
     
  21. Oct 26, 2008 #20

    Fra

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    Hello Peter. Both of my responses to your two raised points below are really biased by my choice of problem. This was the original comment I made to your papers and I think it also fits in with some of the other responses you've got in this thread. Both my opinons on the points you raise IMO traces down to the physical construction of the probability concept. Repeatedly we use probabilistic concepts IMO without full physical implementation and most questioning of this by many researchers are considered irrelevant to physics.

    As I see the the main issue with the EPR paradox, is the questionable assumptions going into it, that supposedly corresponds to concepts like "local realism" etc. Since I do not have any such ideas of local realism at all, the motivation for finding "loopholes" comes out at somewhat silly, since the entire reasoning isn't very convincing in the first place.

    So my opinion of the epr-paradox, isn't that there are just some possible minor loopholes, but rather that the entire notion of probability is tossed around, without it beeing clear what it's intrinsic physical meaning is. Ie. the paradox simply makes clear how some of the classical realist logic has a hard time making sense of what we see.

    But to connect as much as I can, to your reference to the amplifying apparatus, memory loopholes etc, this is partly incorporated in my notion of "observer", and the notion of probability is implicit in the makeup of the observer. IE. I think of probability as a sort of subjective logic probability. But not even for a given observer is it possible to predict deterministically the evolution of this probability. In my view, a kind of probabilistic distribution of possible actions are determined by close to local determinism, but not quite - only in the sense that the observer has no resources to construct a measure that questions the uncertainty in this action distribution; which to me means that the indeterminism is unmeasurable. And a further into the future, it makes no sense to verify a past choice as right or wrong, as the observer can not remember the full timehistory in that ordinary sense.

    This can sort of be interpreted as a kind of hidden variable reasoning, but with the major difference that not only is the value of the variables hidden, the INDEX is also hidden. I am still working on the mathematical models and maybe another time I could explain how I think of this in detail. This is why I asked you how you do the "indexing". To me this is a non-trivial step. I think to distinguish the index contains information. There is something fishy here that does relate a bit to an ergodic hypothesis. So once you chose and index, you are adding information (that I wonder where it comes from).

    Abut the correspondence of the "size" of the apparatus, is the "complexity of the observer". To me the relevant measure or "size" in this respect is complexity, which I associate to the inertia of the observer. The finite size (finite inertia) of real observers does impose limits of the observers confidence in intrinsic predictions.

    And the observer is continously evolving as it interacts with it's environment, therefore in principle the observer depends on each observation. I guess you can see this as an extreme form of the arguments in the memory loophole.

    So part of the problem with hidden variables, is that the notion of the structure implicit in the notion of variable does contain information. It contains a kind of implicit ergodic hypothesis. If the variable is really hidden, then the notion of there beeing a variable isn't distinguishable. This is really similar to the fact that in a interrogation you can by choosing the questions, manipulate the situation even though you can not in principle control any answers. There is no such thing as an neutral question.

    The way around this I envision is to consider an eternal evolution, which evolves not only the microstates, but also the microstructures(think index structures) in a way that there is no fundamental microstructure or microstructures, there is rather just an evolution.

    But on the large scale this evolution is not deterministically predictable by any inside observer.

    Only by a very "large" observer, can the evolution of a smaller system be somewhat closer to deterministic evolution at some level. But this only means there is some level of determinism, like in QM (which evolves the wavefunction deterministically), it doesn't mean there is a classically realistic deterministic model. The reason for thta IMO is that no observer, not even a very massive one can access the communication channels between parts of the environment. So the QM indeterminism is here to stay, what I am in favour for is adding more indeterminism, but in a way that also brings unification.

    The key focus is notions like for example

    P(q|p) meaning the probability of q, given p. That boils down to the definition of logical operations such as (q and p) which I have an idea on howto define in a natural way by a new logic that will explain the uncertainty relation as well as the complex amplitude statistics.

    The normal expansion P(q|p1 or p2) compared to |(psi(q;p1)+psi(q;p2)|^2 is really problematic, and this is what I am working on. It involves also the inertia. So the inertial concept relates to the superposition. This partly associates to penrose thinking but he tries to use gravity to explain the collapse, I try the other way around. To me the collapse is noting but an information update; I think from this, given some plausible arguments gravity and inertial concepts follow.

    /Fredrik
     
    Last edited: Oct 26, 2008
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