• [deleted]

Hi Christi, and thanks.

I have thought about QFT-CST and about QG only a very little. So little, indeed, that I have a prejudice that I've so far been unable to shake from my head, in favor of working with torsion on an otherwise Minkowski space-time (something of the type of Einstein-Cartan, teleparallelism, or Poincaré gauge theory, but I know too little to know what formalism I would prefer), although perhaps only as an approach to local modeling, because Fourier transforms are so central to QFT, but difficult on a variable metric CST and impossible(?) if the background space-time is dynamical.

Within such a scheme, my first attempt would be to take the torsion tensor to be the dynamical object of a quantum field theory, insofar as the non-linear approach I suggest in my essay may be less concerned with the renormalizable/non-renormalizable distinction than is standard QFT. I don't know how well that would work out, of course.

That's not an answer to your question, but it's a vague answer to the question that your question suggests to me. Best wishes, Peter.

22 days later
  • [deleted]

Dear Peter,

I also have an essay questioning the postulate of quantum theory - "Is there really no reality beneath quantum theory by Hou Ying Yau". Just like you, I spend many years trying to understand physics. I hope you will find the paper interesting.

Sincerely,

Hou Ying Yau

  • [deleted]

Dear Peter Morgan,

I have read what I can of your essay. You have chosen a problem to analyse that I am not sure is a wrong basic physical assumption but may be something to do with the best mathematical representation of nature. Not having studies QFT I was not even aware of the problem that you chose to write about.The level of mathematics that you included is a barrier to clear communication with those who do not have a background in mathematics and maybe not even physics.

There are other entrants talking about mathematical approaches, such as Julian Barbour, who have non the less produced very accessible papers that can be understood by non specialists, are educational and enjoyable. Searching For New Mathematics by Ivars Peterson This article may help explain the problem for non mathematicians.

Those who do have a good grounding in mathematics, (T H Ray, Lawrence Crowell and Joy Christian spring to mind), might be able to give give a valuable critique. Perhaps you could introduce yourself to them if you have not already and they might also be able to suggest other people who would find your essay accessible and something that they would be able to discuss with you.

I am sorry I can not be more helpful. You no doubt feel very strongly about what you are doing as do many of the entrants, myself included. Good luck to you in getting the constructive feedback you are seeking.

Thanks for reading through it, Georgina. I figured out weeks ago that I had misjudged the nature of the contest. I saw up front that it clearly asks for a level between Scientific American and Nature, but I'm not at a point in my research at which I can do that, so I did what I could. Of course if someone doesn't understand an essay, they can hardly give it a high community rating, and indeed it's reasonable for them to give it a low community rating for not hitting one of the contest specifications, of getting the right level. Now I can see that it was not worthwhile trying to do my research here; I suppose one can only present a much more complete idea.

If one is arguing for something that has been in the literature as an idea for a while, as is the case for Julian Barbour, then a non-mathematical way of stating the issues has probably developed. An idea that hasn't yet become old enough to have a non-mathematical statement is probably wrong, as has always been true of my many previous ideas and approaches and as is probably true of my proposal here.

To some extent there's a catch-22 here, which I suppose means that the winner is not likely to achieve the principle aim of the contest as I think of it, the pointing out of an assumption that genuinely hasn't been noticed and that can *usefully* be teased into a different form. AFAICT, the assumption I address is the only assumption questioned in all the essays here, mathematical or not, that I have not seen questioned many times before.

I suppose everyone dies with less constructive criticism than they need. Best not to get too frustrated about it. It's perhaps ironic that I pretty much agree with everything that Peterson says in the interesting article that you link to (which definitely constitutes constructive feedback), but that does not mean that I ever succeed when I try to write lucidly.

Thanks again. Peter.

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Peter,

While I sympathize with your inability to stir up an audience, I have to agree with Georgina that the audience you require is extremely select. There is the unhelpful Catch 22 that such detail oriented work requires equally detail oriented observers to analyze it and nature contains far more detail than observers. If you notice some of the other threads, many are not even participating in discussions of their own ideas.

I have something of the opposite problem with my entry. It is so elementally basic that no one takes it seriously. It is simply that we assume the effect of time, sequence of events, is fundamental, rather than the action causing them. That it is not the present moving from past to future, but the changing configuration of what exists, turning future into past. For example, the earth doesn't travel the fourth dimension from yesterday to tomorrow, but tomorrow becomes yesterday because the earth rotates. One effect of this you might consider is that it turns time from a linear dimension into a non-linear dynamic, since duration doesn't transcend the present moment, but is the state of the present between the occurrence of events.

Hi Peter,

I feel compelled to echo Georgina's opinion that it would be very difficult to find a referee for your work among the denizens here. (Don't look at me -- I've had Weinberg's 3-volume QFT text for years and every book is in pristine condition.)

If it's worth anything to hear -- I don't think there will ever be a plain language version of QFT; the subject is clearly specialized for experts. Any continuous field theory that attempts quantization has already jumped the comprehensibility barrier of common language -- because we all understand "things," not fields. I suspect that's how string theory captured the popular imagination; the public at large doesn't have a clue of supersymmetry or the field excitations that the theorist derives from QFT, but they know what kind of thing a string is.

I did see your request for someone to find an existing derivation of section 3 weeks ago, but I'm not up to that research, and I couldn't tell you who is.

FWIW, I think your theme suffers from the difficulty of understanding in physics that probability theory has in mathematics -- i.e., not really much is known about it except in formal language. So doing a calculation ends up having a meaning of its own independent of any constructive meaning that the problem it purportedly solves, is trying to convey. That's the reason I switched from number theory to complex systems science, where the problems are clearly correspondent to the real world.

Nevertheless, of the parts of your paper that I understand I am seeing some potentially valuable insights into quantum vaccum field solutions that could very well end up explaining how the field varies so radically from point to point yet sums to zero. That definitely brings things back to reality -- or rather, reality back to "things."

All best wishes, Peter, in the contest and in your further research.

Tom

Tom, thanks also for your remarks. I want to address your "I don't think there will ever be a plain language version of QFT", because I think there is a possibility, and indeed that section III of my essay here /may/ be a starting point for at least a slightly more accessible account. The problem is not the basic formalism, insofar as I claim that QFT is at heart just a form of stochastic signal analysis ---notwithstanding the incompatibility of joint measurements at time-like separation---, the problem is renormalization, which makes the literature and textbook accounts almost entirely obscure. The difficulties of understanding QFT are notoriously extreme, but a lot of work has been done to make Feynman's dictum that they are insurmountable less true than it used to be.

It's in the nature of the evolution of our understanding of mathematical formalisms that they are gradually reformulated, and that each reformulation leads to a wider understanding, until a popularizer at some level takes hold of the new ideas and brings them to wider audiences. Whether it's my work or someone else's that brings QFT into clearer focus is not of course of the essence.

Looking at your FQXi essay this season, I see that you have detected at least something of this process in the Bell literature. If you haven't previously seen my "Bell inequalities for random fields - cond-mat/0403692 (v4, 24th May, 2006), J. Phys. A: Math. Gen. 39 (2006) 7441-7455", perhaps you might find my approach there to /those/ questions a little different from much of the Bell literature (though people also find that paper opaque). IMO, it's just a question of time, perhaps another 5-10 years (or 10-20, ...), before the penny drops for the Physics community that for a wide variety of reasons the violation of Bell inequalities proves almost nothing. At some point it will become possible to say that of course most Physicists always understood that was the case, which it will be possible to justify by pointing out that 't Hooft, Bohm, and other Serious Physicists were never outright refuted, and the derision nay-sayers were subjected to will be forgotten except by Historians. After the paper above I decided to stop worrying about Bell inequalities and move on to thinking much more single-mindedly about QFT.

If you want to understand QFT, I'd recommend trying to engage with Haag's "Local Quantum Physics" for a few years, though it's definitely not easy going. Amongst the standard textbooks, I find the wildly old-fashioned (yet still modern enough) approach and notation of Itzykson & Zuber far more congenial than Weinberg. The path integration of modern textbooks, in particular, obscures the algebraic and combinatorial structure that is the only path to reconciling QFT with ordinary QM, IMO. That doesn't remove the ultimate need for at least some people to understand the relationships between such different approaches, of course.

Although I operate at not much above the level of popular accounts, I believe that a lot of what can be shown about complex systems is probabilistic in character, right? I suspect the relationship between probability and statistics will be forever difficult.

It's becoming more worthwhile having posted here. Thank you.

  • [deleted]

Peter,

This is in reply to your post on my thread. Since you sound more respectfully considerate, than genuinely interested, I repost it here:

Peter,

Thank you for the reply. I would first have to agree we are on opposite sides of a significant fence and I can understand why you might see my side as lacking necessary detail to be informative. My position is that while your side of the fence might be finely structured, it is still emergent from the underlaying dynamic. Which is to say I don't see the need for a platonic realm of fundamental laws governing nature. I see laws as patterns which emerge with the actions and relationships they define. Bottom up and top down are complementary functions that emerge as one. Yes, nature is exponentially complex, but the principles describing it are interactive and complementary. Knowledge and information must be static in order to maintain the very details of which they consist, but that doesn't mean reality is so fundamentally frozen. If reality were frozen, it would be a complete lack of thermodynamic activity and nothing would happen, or exist. A non-fluctuating vacuum. No nouns, or verbs. No factors, or functions.

So for me, it's a matter of how to get from nothing to something. I would start with space as the aphysical infinite equilibrium. In this void, there is a cycle of expanding energy and contracting structure. Now if we were to relate that dichotomy to sentience and knowledge, the energy is the element of awareness and knowledge is the structure it conceives. Much as in my essay I point out that while our awareness is constantly moving onto new thoughts, these thoughts coalesce out of received information and then are replaced. So as awareness goes from past to future thoughts, the thoughts go from future to past. Just as energy is constantly inhabiting structure, then breaking it down and moving onto other forms.

Now consider in your essay, the conceptual process which is going on. Much like a puzzle, modern physics consists of many static components that seem like they should fit together, but however it is done, there seem to be gaps and the solutions often create new problems, as they solve current ones. They are all obviously parts of some larger whole, but not a singular whole. So you find a connection that is "worthwhile," but not "ultimately correct." Possibly it is because there is no "ultimately correct model?" As I point out in the last line of my essay, "Neither academic or religious authority can turn an ideal into an absolute." There is no more a universal model than there is a universal god. Both models and perspective are inherently subjective. Oneness and one/unity and unit are not the same thing.

I know this sounds philosophical, but if your ivory tower is built on sand, would you want to know, or would you prefer not to know?

    I think I have to say that I know it's built on sand. I'm no Platonist, to think that I build my models of anything else (though I've no way that I know of to gainsay someone who thinks Mathematics transcends our experience). You'll have to read between the lines of my various web presences to realize that there isn't much ivory in my tower.

    It looks as if your "there is a cycle of expanding energy and contracting structure" is your sand, or some part of it, where functional-algebraic models for the way we look and for what we see when we look are mine. I take almost everyone to need eventually to accommodate complexity in their models. I'm playing with this stuff that other people have built, as you are; it's good that we have chosen the work of different people as our starting points. Insofar as I prefer a more abstract way of thinking, as I think of it being, I just do what I prefer to do, for as long as I am given to do it and for as long as something shinier doesn't distract me. FWIW, I prefer to construct ways of thinking in which there are no "laws", there are just ways to guide our engineering of models for our experience and of edifices.

    If I construct stochastic 4-dimensional models, in which time is one of the four dimensions, that doesn't mean that I think this is the way the world is. It's just a model, not necessarily different in character from a spherical cow or from a map, except insofar as additional complexity makes a map different from a spherical cow.

    So in response to your "So for me, it's a matter of how to get from nothing to something", I suppose I would say that for me it's a matter of accepting the appearance that there is something, and looking for something that it seems worthwhile, to me, to do with what I see, given what I have to it with. And hoping that my judgement is not always as bad as it sometimes is.

    I've been trying to get back to some computations that I've been trying to get through, pursuing what I introduced in my FQXi essay, which are hard enough that posting here for a few days has been a welcome interlude. Peter.

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    Peter,

    Thank you for the thoughtful and considerate response. I have to say I generally get a more emotional and negative reaction when I try to push the buttons of others in the field.

    For me, the concepts basic physics deals with; Energy, order, structure, expansion/contraction, attraction/repulsion, complexity/simplicity, etc. underlay and manifest all aspects of existence. Every person alive, from some kid kicking a soccer ball, to an astronaut, has to understand physics. We live what theorists analyze.

    Obviously there are levels of understanding, but there is no clear line between what people experience and theorists try to divine. Which is to say that I feel I have a stake in the field, even if my thoughts don't meet with approval by those more directly engaged in the various disciplines.

    While you are quite right to say our understanding starts with what is, my strongest impulse is that we stand over the abyss of mortality, so the "nothing" is as much a feature to explain, as complexity.

    For me, I accept there is an infinite amount of complexity I can never conceive, from quantum math, to biological and neurological functions and so the best I can do, is to sense those general patterns and how they interact and manifest in different ways. This gives me some foundation to deal with the unknown.

    I would say life is a game where the goal is to figure out the rules and the first rule is that many rules are subject to circumstance.

    Good luck with putting together your work and finding the right audience.

    • [deleted]

    Dear Peter,

    I read you message concerning the competition voting. You mentioned different categories for the different kinds of essays. I think it is a very good idea. I left a reply there.

    I understand when you say about research lacking fun, thats how I feel right now. I have spent far longer than is healthy thinking about, explaining and defending the things I write about over the last few years. It is disheartening when the enthusiasm is not reciprocated. It is very hard to justify the unpaid time spent on it, and the neglect of other important aspects of life, when the output is not valued and is mostly overlooked.

    The only reward is the tiny scraps of recognition. So though I don't like to ask as it is a bit impertinent and I'm trying hard not to offend anyone; I would greatly appreciate it if you would reciprocate and tell me what you think of my essay -especially concerning the explanatory framework set out in diagram 1. There is a high resolution version in my essay thread.

    Dear Peter,

    I thank you for a very useful contribution to an approach that needed to be explored. I am one of those who prefers to experiment with deviation from Lorentz covariance, but knowing some of the consequences and possibilities of changing other hypotheses is quite valuable.

    Good luck with the contest, and take care,

    Ben Dribus

      • [deleted]

      Peter,

      Your essay is far better than the middling status it has in the community rating. I have given it a basic read through, though I intend to give it more focused attention tomorrow. When I am done here I will give your essay a high score to bump it up the ranking.

      You raise some interesting issues here. You write

      Δ(x-z) = i(G_r(x,z) - G_a(x,z)) = [φ(x), φ(z)]

      which time ordering is behind the commutivity. In my essay I argue on the basis of M-theory that field locality is to be removed. In effect [φ(x), φ(z)] =/= 0 even if x and z are spacelike. This is a departure from your work, but I am wondering if one can have a propagator equation

      Δ(x-z) = i(G_r(x,y) - G_a(z,y)) = [φ(x), φ(z)]

      Where x,y are timelike as are z, y. The equation 5

      ξ(x) = T^†[e^{-iL}]φ(x)T[e^{-iL}]

      would replace e^{-iL} with Jacobi theta functions.

      I will probably have more comments directed more closely to your essay tomorrow.

      Cheers LC

        I doubt any bump will be enough, however the thought is welcome.

        In your second equation here, I'm not sure what "y" is? There's something to bear in mind (at least within the axioms of AQFT), which is that if $\Delta(x-z)$ is a function only of the separation between the points identified by "x" and "z", then the field has to be a generalized free field (LICHT AL and TOLL JS 1961 Nuovo Cim. 21 346-51).

        Do you mean by your last remark that you want a non-unitary evolution? I don't think you mean to replace e^{-iL} by something like [math]e^{-i \ln(\theta(...))}[/math]? What motivation do we have for adopting a Jacobi theta function in /this/ context?

        • [deleted]

        I was conjecturing a Δ(x,z) formed from retarded and advanced potentials with a common point y to the future (timelike or lightlike separation) of both x and z. The propagation from x to y in the retarded case and from y and z in the advanced case is replaced by the commutator. This of course would need to be derived by different means of course. Yet quantum gravity implies a nonlocality of fields, and this seems like a possible way to derive this. The trick is to insure that no information or quantum bits are communicated between x and z. My conjecture here of course could be wrong.

        The replacement with theta functions is a way of possibly treating black hole singularities. In that case the evolution equations contain a singularity and are meromorphic, rather than unitary. The theta function is

        θ(z,t) = sum_{n=-∞}^∞exp(πin^2t 2πinz)

        which takes the place of unitary functions such as e^{-iL}. I will not right now go into a complete discussion on this, but these modular functions I think in general replace unitary functions

        One way to see a motivating reason for this is with the following metric with 1 - 2m/r = e^u. so then

        ds^2 = e^udt^2 - e^{-u)dr^2 dΩ^2.

        We now have to get dr from

        dr = -2me^u/(1 - e^u)^2du.

        Now the metric is

        ds^2 = e^udt^2 -2m[e^u/(1 - e^u)^4]du^2 dΩ^2.

        The singularity is at u = ∞, where the dt term blows up, and the horizon coordinate singularity at u = 0 is obvious in the du term. My rational was that the singularity had been removed "to infinity" in these coordinates. This makes the black hole metric similar to the Rindler wedge coordinates, which does not contain a singularity. In the accelerated frame or Rindler wedge there is singularity. The treatment of the Schwarzschild metric in the near horizon approximation Susskind uses is one where the singularity is sufficiently removed so that field in the Rindler wedge may be continued across the horizon without concerns. In this metric of mine the singularity is at infinity so the analytic functions for fields in the Rindler wedge are replaced with meromorphic functions with a pole at infinity.

        The singularity at infinity causes trouble with the end point of the radiance process for it has to "move in" from infinity. The final quantum process of a black hole is a problem not well known in any coordinates. By the time the black hole is down to its last 10^4 or 10^3 Planck mass units the black hole itself is probably quantum mechanical. In my coordinates (assuming they are unique to me, which is not likely) the singularity at infinity may not have to "move" from infinity. There may be some nonlocal physics which causes its disappearance without having to move at all. This nonlocality is a correspondence between states interior to a black hole and those on the stretched horizon. The Susskind approach does not consider the interior, and he raises this as a question towards the end of his book "The Holographic Principle."

        Unitarity is represented by a complex function e^{-iHt} and so forth, which is analytic. The loss of unitarity does not mean there is a complete loss of everything; in particular quantum information can still be conserved. A simple analytic function of this sort describes standard quantum physics. Gravity as we know is given by a hyperbolic group, such as SO(3, 1) ~ SL(2,C), where the latter has a map to SL(2,R)^2. The functions over these groups have posed difficulties for quantum gravity, for they are explicitly nonunitary. The trick of performing a Wick rotation on time or with τ = it is a way of recovering the compact groups we know in quantum physics.

        It does turn out I think that we can think directly about quantum gravity by realizing that the SL(2,R) is related to a braid group with Z --- > B --- > PSL(2,Z), and that the braid group is contained in SL(2,R). Braid groups have correspondence with Yang-Baxter relations and quantum groups. The group SL(2,Z) is the linear fractional group, which is an elementary modular form. An elementary modular function is

        f(z) = sum_{n=-∞}^{n=∞}c(n)e^{-2πi nz}

        which in this case is a Fourier transform. In this case we are safely in the domain of standard QM and QFT. In general modular functions are meromorphic (analytic everywhere but infinity) and analytic condition is held on the upper half of the complex plane.

        Of particular interest to me are the Eisenstein series of modular functions or forms. These define an integer partition function, which is an acceptable partition function or path integral for a stringy black hole. I include a graphic here illustrating an Eisenstein function. This has a certain self-similar structure to it, or what might be called an elementary form of a fractal. In this picture unitarity is replaced with modularity. In this more general setting the transformation do no promote a field through time by some operator, but that the operator simply computes the number of states or degrees of freedom in a way that is consistent. Unitarity is then a special case of this, which happens to fit into our standard ideas of causality.

        The Eisenstein series describes a partition function or path integral for a black hole. The theory is not one of unitary evolution, but simply one of counting states or degrees of freedom on the horizon. In effect physics is more general than unitarity, where unitarity is a necessary condition to describe the semi-classical states in postulate #2.

        Your essay went up by quite a bit when I scored it last night. I think it went back down some. To increase your community rating it is best to read other essays and leave commentaries there. You will of course find a whole host of essays that are nonsense. I try to down vote those to clear them from the upper ranks. Comments left on the blog site of other reasonable authors, with some attention drawn to your essay, can help raise your rating. If you "demolish" bad essays higher up it is of course best not to write anything. There is a bit of the "art of the schmooze" involved with this.

        Cheers LC

        Taking Lorentz covariance to be broken at small scales is of course a much pursued option. I'm not against such ideas, but there seem to be so /many/ possibilities, and not, I think, quite enough empirical justification for any of them. I can't figure out which approach I like enough to work with.

        On the other hand, the kind of nonlinearity I introduce here is not an attempt to change interacting QFT, it's more an attempt to understand and make more accessible (albeit falteringly) the role that is played by renormalization, which I take to be an empirically successful mathematics (notwithstanding the reservations one might have about the quantum gravity regime, say, dark matter, etc.), without introducing the sophistication of generalized functional methods, which I take to be more inaccessible. I would hope that a more transparent mathematical structure and better understanding might lead to better engineering in future.

        FWIW, I have just re-read a review article on renormalization, Physics Reports 511 (2012) 177-272, that motivates the mathematics almost entirely in terms of language that is very much that of signal processing, "the natural description of physics generally changes with the scale at which observations are made. Crudely speaking, this is no more high-minded a statement than saying that the world around us looks rather different when viewed through a microscope. More precisely, our parametrization of some system in terms of both the degrees of freedom and an action specifying how they interact generally change with scale." This could all be subsumed by a discussion in terms of different choices of window functions. Of course details are important, so that this kind of introductory discussion cannot be taken too much to heart, but it seems striking that all the observations we make are supposed to be made using the same type of microscope, whereas if we work in a formalism such as I propose, we might use a different window function, representing a different regularization for each observation. [I take it that this micro-addendum to my essay will be seen by almost no-one, and I realize it's not really a propos of the comment that has engendered it, but whatever.]

        Reading through your essay, I think it's justifiably high in the community rating, and you have my best wishes, but I find myself nonetheless finding that the whole thing is not to my taste (which is too personal a feeling to leave as a comment on your essay, however). It's very much with apology, because it's somewhat classic that people who are drawn to algebraic QFT-type approaches have been left far behind the mainstream and have become quite marginal. Ah well.

        Dear Peter,

        I appreciate your response, and particularly your honesty. "Taste," (or intuition, as it might be called) is not to be dismissed out of hand. You may have noticed from my bio that I study algebraic geometry (mostly complex algebraic geometry), so nonmanifold models were not initially much to my taste either. The journey toward considering such things is not something one can put in a 12-page essay!

        I think that your remarks about window functions are interesting, and I have great respect for approaches that make systematic use of scale. I studied harmonic analysis/wavelets a fair bit before going toward the algebraic side. Take care,

        Ben

        I've eventually succumbed to commenting briefly (and not substantively for the purposes of the essay contest) on your more-or-less equating "taste" and "intuition". I think taste has an additional component, that of intention. That is, I think of taste in Mathematics/Physics as more colored by what we wish to achieve, whereas I think of intuition as more directed to how to achieve what we wish.

        This is somewhat comparable to some ways of defining rationality in Philosophy; Wikipedia offers, inter alia, "A rational decision is one that is not just reasoned, but is also optimal for achieving a goal or solving a problem." That is, for my point here, /what/ goal or problem we choose to address is more a question of ethics, something that is not open to reasoning in the same way as is the /way/ in which we address the goal or problem that we choose.

        Of course such boundaries are quite fluid in practice. We might well persuade someone, for example, that their goal of the moment does not further their achieving a more ultimate goal.

        Your comments, of course, have been thoughtful and helpful, here and in the other places that I have seen; please take this as just a by the way.

        Best wishes, Peter.

        • [deleted]

        Dear Peter,

        Your essay is interesting for me. I think you can find some of answers of your questions here:

        essay

        Best wishes