Dear Prof. McHarris,

I enjoyed your essay and thank you for some interesting new ideas and enabling me to recall others. My Ph.D. focused on nonlinear dynamics in the mid-1990s but I veered into neuroscience, machine learning, astrophysics and now theory. So its been a while since I have thought in these terms.

I wish that you had provided a little more insight into how you think nonlinear dynamics is coming into QM. Perhaps you can point me to some of your key papers (or I could of course just go dig them up).

In our symmetry-based derivations of the Feynman rules

(Goyal P., Knuth K.H., Skilling J. 2010. Origin of complex quantum amplitudes and Feynman's rules, Phys. Rev. A 81, 022109. arXiv:0907.0909v3 [quant-ph].)

we find that associativity of combining measurement sequences in parallel results in additivity. So I am left wondering where nonlinearity would come in. With such a basic symmetry forcing linearity, it is hard to imagine room for nonlinearity. Though as Cristi Stoica points out in his comments above, the classical equations can still be nonlinear, and nonlinear equations can often be broken into linear ones in sufficiently high dimensions.

Despite this, your essay reminded me of work by Pedrag Cvitanovic where he used (classical) periodic orbit theory to derive the energy levels of the Helium atom. I have not kept up with this work, so I do not know where it has led. But your essay made me remember this. At the time, I felt it was quite impressive, and should have shaken the quantum foundations more than it has seemed to.

I also remember coding fractal generating programs based on Barnsley's book Fractals Everywhere. It was always interesting to me that you could think of these processes in two ways: one by an deterministic iterative process and second by a random iterative process. Watching fractal ferns appear on my Amiga computer dot by dot reminded me of electrons appearing on a screen after passing through a slit apparatus. I always wondered whether some nonlinear or iterative process could be behind such confounding behavior.

And now you have sparked a thought for which I thank you and the FQXi people for setting up this essay contest. In my essay, I discuss a new way to think about electron behavior in terms of interactions. Perhaps I should take some time to consider an electron "moving" through two slits by influencing atoms along the walls of the barrier. Could it be that these simple patterns of influence lead to rules guided by the boundary conditions to give rise to the diffraction pattern electron by electron. I have considered this before, and worked for a short while to see what I could work out. But now I am once again emboldened by the fact that I now recall the fractal ferns coming into focus. Perhaps with this perspective, I can make some headway.

Thank you again

Kevin

    Peter,

    what happened to the author? Anyway, my main question got no response. What are the complementary measurements in this context? Clearly there cannot be any, since it is classical. It is easy to violate Bell inequalities by changing the meaning of things ... Theorems are theorems.

    Cheers

    Mauro

    Dear Prof. Harris,

    Thank you for a very lucid explanation of how correlations arise in non-linear systems.

    You mentioned how non-linear dynamics in QM leads to a smoother transition between observer and observed. This is also reflected in quantum information theory. The knowledge of the observer (classical spacetime) arises reflexively from iterative feedback and erasure of quantum entanglement information. (See my essay "A Complex Conjugate Bit and It".)

    Best wishes,

    Richard Shand

      Mauro,

      No 'changing meanings'. Theorems are indeed theorems, but they're all included in the greater 'theorem' that all science is provisional and no 'absolute' proof of anything exists. Bell uses assumptions just as all theorems do. Even the most solid foundational 'Laws' of Physics can be violated. Look what happens to Snell's Law at kinetic reverse refraction - the nonlinear 'Fraunhofer refraction' appears instead!

      The measurements are detector angles and 'positions' along the x axis of a cosine curve distribution between 0 an 180 degrees. Consider my torii as entangled particles translating along the polar axis with opposite spins. They meet detectors as 'planes' A and B tilted at varying angles (or tilting donuts if you prefer!). 'Detection' is of the interaction point at A and B, which is say in the top half ('up') or bottom half ('down').

      We now have another 'dimension' that Bell did not assume existed. We can easily show that when A and B are parallel the results are opposite, and when anti parallel the results are identical. But half way between, when A or B are vertical the donuts hit face on so the result up/down is at maximum uncertainty! But over many samples it is of course ~50%.

      Now the killer; When intersecting at 90 degrees, tilting the detector say 5 degrees will have virtually no effect on the 'position', but when face to face, a 5 degree tilt angle has a major positional effect! So 30 and 60 degrees give results of 75% and 25%. This is Malus' Law in action, and reproduces the predictions of SR at EACH detector (just as von Neumann proposed) as well as when correlated between the two.

      All this is as published in my essay and expanded in the Blog. Aspect did find this "orbital asymmetry", but with no theory to fit it to he discarded that particular ~99.9% of his data! (only discussed in his follow up French paper).

      This is very consistent with Prof McHarris's findings and I believe Gordon Watson's essay, with similarities with Ed Klingman's. I'll re-post this on your blog so you don't loose it. Do ask any questions on mine.

      Best wishes

      Peter

      (I still hope the author will 'report in').

      Dear Sir,

      As the contest in Wheeler's honor draws to a close, leaving for the moment considerations of rating and prize money, and knowing we cannot all agree on whether 'it' comes from 'bit' or otherwise or even what 'it' and 'bit' mean, and as we may not be able to read all essays, though we should try, I pose the following 4 simple questions and will rate you accordingly before July 31 when I will be revisiting your blog.

      "If you wake up one morning and dip your hand in your pocket and 'detect' a million dollars, then on your way back from work, you dip your hand again and find that there is nothing there...

      1) Have you 'elicited' an information in the latter case?

      2) If you did not 'participate' by putting your 'detector' hand in your pocket, can you 'elicit' information?

      3) If the information is provided by the presence of the crisp notes ('its') you found in your pocket, can the absence of the notes, being an 'immaterial source' convey information?

      Finally, leaving for the moment what the terms mean and whether or not they can be discretely expressed in the way spin information is discretely expressed, e.g. by electrons

      4) Can the existence/non-existence of an 'it' be a binary choice, representable by 0 and 1?"

      Answers can be in binary form for brevity, i.e. YES = 1, NO = 0, e.g. 0-1-0-1.

      Best regards,

      Akinbo

      Dear Prof. McHarris,

      I inspired a bit through your essay and it is my previlage to have a humble comment in support of you. What you wrote: "It from Bit or Bit from It?" is a bit like the problem of chicken and egg ..." in your last sentences,I think, I might have an answer in my submission. Where I expressed that "chicken" and "egg" are inseparable and in some scale of observations are nothing but mirror images to each others with the help of some new fundamental constants in the quantized nature.

      If you please manage to have a time to read my essay and make a comment and if possible can rate on it I will be obligated very much.

      With regards

      Dipak Kumar Bhunia

        Dear William. C. McHarris:

        I am an old physician, and I don't know nothing of mathematics and almost nothing of physics, I read your essay and if you think I did not understand anything, you are right I did not, because I lack all the necessary knowledge to do it. What I learned was the kind of mind you possibly have, that could be the ideal to understand the value for physics of my essay. What I did result from a kind of mental accident, because I was not seriously searching. Physics, specially theoretically physicists are really needing at least for the last fifty years the experimental meaning of, as I use to say the so called "time". I think my essay can land real physics down to earth. The only thing I possibly understand of your essay is: When you say "non linear dynamics into quantum mechanics...does not lead us into" "the quagmire of assuming hidden variables" I refer to them in my essay

        I am sending you a practical summary, so you can easy decide if you read or not my essay "The deep nature of reality".

        I am convince you would be interested in reading it. ( most people don't understand it, and is not just because of my bad English).

        Hawking in "A brief history of time" where he said , "Which is the nature of time?" Yes he don't know what time is, and also continue saying............Some day this answer could seem to us "obvious", as much than that the earth rotate around the sun....." In fact the answer is "obvious", but how he could say that, if he didn't know what's time? In fact he is predicting that is going to be an answer, and that this one will be "obvious", I think that with this adjective, he is implying: simple and easy to understand. Maybe he felt it and couldn't explain it with words.

        We have anthropologic proves that man measure "time" since more than 30.000 years ago, much, much later came science, mathematics and physics that learn to measure "time" from primitive men, adopted the idea and the systems of measurement, but also acquired the incognita of the experimental "time" meaning. Out of common use physics is the science that needs and use more the measurement of what everybody calls "time" and the discipline came to believe it as their own. I always said that to understand the "time" experimental meaning there is not need to know mathematics or physics, as the "time" creators and users didn't. Instead of my opinion I would give Einstein's "Ideas and Opinions" pg. 354 "Space, time, and event, are free creations of human intelligence, tools of thought" he use to call them pre-scientific concepts from which mankind forgot its meanings, he never wrote a whole page about "time" he also use to evade the use of the word, in general relativity when he refer how gravitational force and speed affect "time", he does not use the word "time" instead he would say, speed and gravitational force slows clock movement or "motion", instead of saying that slows "time". FQXi member Andreas Albrecht said that. When asked the question, "What is time?", Einstein gave a pragmatic response: "Time," he said, "is what clocks measure and nothing more." He knew that "time" was a man creation, but he didn't know what man is measuring with the clock.

        I insist, that for "measuring motion" we should always and only use a unique: "constant" or "uniform" "motion" to measure "no constant motions" "which integrates and form part of every change and transformation in every physical thing. Why? because is the only kind of "motion" whose characteristics allow it, to be divided in equal parts as Egyptians and Sumerians did it, giving born to "motion fractions", which I call "motion units" as hours, minutes and seconds. "Motion" which is the real thing, was always hide behind time, and covert by its shadow, it was hide in front everybody eyes, during at least two millenniums, at hand of almost everybody. Which is the difference in physics between using the so-called time or using "motion"?, time just has been used to measure the "duration" of different phenomena, why only for that? Because it was impossible for physicists to relate a mysterious time with the rest of the physical elements of known characteristics, without knowing what time is and which its physical characteristics were. On the other hand "motion" is not something mysterious, it is a quality or physical property of all things, and can be related with all of them, this is a huge difference especially for theoretical physics I believe. I as a physician with this find I was able to do quite a few things. I imagine a physicist with this can make marvelous things.

        With my best whishes

        Héctor

          Hello, Zoran,

          Thank you for your kind words. I enjoyed your combination of science and philosophy. It seems to me your "never-ending" spiral is another example of nonlinearity, with the material it affecting the metaphysical obit, which in turn affects the it ... I fear I'm not too much in to Kant, but your discouse on Descartes was fascinating.

          Cheers,

          Bill

          Thanks.

          An evolving robot is an analogous situation, and, because of the feedback loops, it involves nonlinear logic, which cannot be analyzed easily. The example of electronics gates (see the Scientific American reference) is still another analogy. I think the basic "unintelligibility" of the programs is innate. The length and complexity is related to the evolutionary history, as are the leftover appendages.

          Treating the brain as an evolving neural network would probably produce the same type of results, but presently this problem is quite a ways beyond our experimental capacities. And I would hesitate to make any serious predictions, for if such complex results can arrive from extremely simple physical situations, just think of the complexities upon complexities that cold result from an evolutionary network. This is where I think people such as Kurzweil err -- it really isn't likely that so-called intelligent machines are going to outthink humans (or even animals) in the finite future -- after all, evolution has had mail lions if not billions of years of laboratory experience! Thus, for all practical purposes, free will is just that -- unpremeditated decision making.

          Cheers,

          Bill

          Hi, John,

          Thanks a million for your kind words -- and especially for recommending this essay as a "must read" in the FQXi blog!

          Yes, I agree with you that much of physics is caught up in a hubristic loop. This is the main topic of the books, "The Trouble with Physics," by Lee Smolin, and "Not Even Wrong," by Peter Woit. You would enjoy them. Smolin's book is easier to grasp, as he has a way with words, but in its quiet way Woit's book is even more damning about the non-falsifiability of string theory. I have seen bits and pieces of a book just about to be published, "Farewell to Reality," by JIm Baggott, which also appears to carry on this line of attack.

          As fundamentally an experimentalist who worked his way into more and more theory after becoming disenchanted with many theorists' lack of a grasp on experimental "reality," I have witnessed many dead ends and ins and out of fashion. When performing gamma-ray spectroscopy on deformed nuclei, I was appalled by the way scientists would push the conclusions of their models far beyond reason. For example, in analyzing the spacing of rotational bands, some would assign meaning to third- and fourth-order terms, speaking of "watermelon-shaped nuclei with dimples at 45 degrees"! And for several years a concept known as "pseudo-spin" (a mathematical simplification letting one deal with two middle-sized matrices rather than the small spin matrix and an enormous orbital matrix) was the "in" thing, with papers describing pseudo-spin properties of nuclei as if they were real -- by people who should have known better. This sort of thing is probably true of string theory now, for, to paraphrase what is often said of quantum mechanics itself, I don't think anyone really understands string theory. And it is wrapped up in tortuous, obtuse mathematics that makes it all the more inaccessible. Thus wouldn't be so bad, except one cannot test it experimentally -- testing behavior at the Planck scale is not conceivable even in the far future. Physics could stand a new injection of Occam's razor.

          I enjoyed reading your essays, especially the one from last year. It contained as surprising amount of common-sense insight, even if couched in non-standard terms. Physicists tend to be parochial about this. I am reminded of Linus Pauling's so-called shell model of nuclei. It was based on group theoretical concepts he gleaned from his work on chemical (atomic and molecular) structure. And it was met with derision. The story I was told was that Physical Review had a policy of rejecting any of Pauling's submissions without even bothering to send them out for review.

          But in retrospect, and from one who had to teach many courses on molecular structure, his model makes quite a lot of sense -- it was just couched in "nonstandard" terms, which nuclear physicists refused to bother with.

          Again, thanks,

          Bill

          Dear William

          Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

          said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

          I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

          The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

          Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

          Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

          I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

          Since "Nature is Analogical", we are free to probe nature in so many different ways. And you have touched some corners of it.

          Regards,

          Than Tin

          Hello, William,

          I appreciated your Essay very much as I have been working with an extension of logic to real systems that goes beyond yours (Cf. my 2008 book, Logic in Reality, Springer, Dordrecht). My logic in grounded in the self-dualities and dualities of physics, but I can show that the "antagonisms" at the quantum level percolate upward to the macroscopic level, a kind of isomorphism. I hope you will read and comment on my Essay. Thank you and kind regards,

          Joseph Brenner

          Brenner,

          Could you give an example of non linearity and feedback loops that involves gravity? I wish the paper would have gone into this more. Otherwise very well written.

          Amos.

          Bill,

          Thank you very much for reading and giving consideration to my writing. I accept the way I approach these subjects usually gets me dismissed rather quickly, but I don't come at physics from a mathematical or technical context, but from living a physical life and an interest in history and society. From which I early on came to realize how much/all of human activity is best understood in physical terms. Even much of what seems nonsensical often boils down to scalar and non-linear behavior, which is why I find your work very fascinating. Because of this, I do understand the short term, reactive thinking which motivates this non-linear herd behavior of crowds. So when a bunch of physicists show the same reactive behavior as a flight of starlings, I don't feel terribly hurt or envious of them, since my interest is with trying to figure out reality, not be part of any particular crowd. One thing I do know, is there is an incredible amount that I can never know, so what is most important is being able to edit out all that I don't need to know, even if it is important in other contexts. That was a theme I tried developing in this year's entry, that perspective is fundamentally subjective. For an example of what I'm really trying to put together, here is an [link:www.dailykos.com/story/2012/03/17/1075305/--What-is-Your-Occupation?detail=hide]essay[/link} I wrote about two years ago.

          I have to say I find Peter Woit's blog very informative and it is one of my usual reads, but I seem to have rubbed him the wrong way, as I'm one of many who is blocked from commenting. Not the first for me.

          Have you ever heard of Carver Mead? He sounds quite interesting.

          Regards,

          John

          Dear Vladimir,

          Thank you for your comments. I read your last year's essay and was very favorably impressed, especially by the first section likening modern physics to a not-planned but accrued edifice whose chambers didn't fit together very well. It was succinct and well expressed. (I'll read your paper n the Beautiful Universe Theory as soon as I get through dealing with answering the accumulated comments in this blog.)

          Three quick comments:

          First, about linearity and reductionism. For chaos to set in the equations must be quadratic or higher order; thus, the complexity resulting from simple systems cannot arise by this mechanism in linear systems (and I don't know of any other obvious mechanism). And nonlinearity means interaction between and among the parts, which is inconsistent with pure reductionism.

          Second, I agree with you that just because one can get numerical agreement from a particular model or set of equations does not mean that this model is physically correct. The epicycle model of the known universe was a good example of that: With enough variables one could produce arbitrarily good agreement, but besides being physically incorrect, that model quickly became complicated and unwieldy. Thus, for example, your description of nuclear structure could well have merit. Pauling had a similar model based on finite group theory (see my comments to John Merryman above).

          Third, particles undergoing chaotic scattering can produce quasi-diffraction patterns (Ref. [6] in my essay), so Einstein's analysis of photons as particles is consistent with "duality." And the photoelectric effect is very, very hard to explain on the basis of waves. I hesitate to state any absolutes, but Occam's razor is clearly on the side of electrons as particles. (And remember that heavier particles such as neutrons and even buckyballs, which are definitely particles, demonstrate wave-like diffraction patterns.)

          This is probably not the place, but I would welcome continued discussion after I have had time to digest your full paper.

          Best wishes,

          Bill

          Dear Hai,

          Thank you for your comments. I read your essay and found it fascinating, if a bit difficult to follow. You raise an interesting question as to the possibility of ever having an "absolute" theory. My guess is that we will simply do better and better with ever-better approximations; as chaos theory has demonstrated, many (really, most) real-life classical systems, although deterministic in principle, can be known and partially predicted only by probabilities.

          Best wishes,

          Bill

          Dear. Dr. Kadin,

          Thank you for your kind comments. I read your essay and was most impressed, and I see more or less how your working with nonlinear self-interactions could be similar to the incorporation of nonlinear dynamics/chaos into quantum mechanics. It could well be that we are attempting similar things. After all, there are many equivalent ways of describing systems.

          I followed your arguments in the essay superficially, but I am going to have to read and STUDY your arXiv papers on the New Quantum Paradigm before I can make more cogent comments, so I would welcome further discussions later this year. One quick, perhaps naive question right now: How does your extended rotating vector field produce the observed quantized spin? In the essay it seems tacked on somewhat arbitrarily.

          It will be interesting to discuss entanglement, as well. Classical nonlinear systems have correlations that look like entanglement, as is discussed at great length in the book, "Nonextensive Entropy," by Gell-Mann and Tsallis, the result of a conference at the Santa Fe Institute (Ref. [7] in my essay).

          Again, thanks and best wishes,

          Bill McHarris

          Dear William,

          A pretty exciting essay! I wish you had included more quantum mechanical details, but we all know how quickly nine pages runs out. I have now read two of your other papers and am still excited.

          The topic is especially interesting to me because of a technique I've recently developed which adds non-linearity to the Einstein weak field equations. Adding non-linearity to equations from which the non-linearity has been removed may sound silly, but the result is equations that can be solved more easily. And there are other advantages to this approach. The technique is briefly described in my current essay which I invite you to read and hope you will comment on.

          Thank you for entering your current essay and for years of work attempting to educate the world about the surprises that arise from non-linearity. Yours is very valuable essay.

          My best regards,

          Edwin Eugene Klingman

            Dear Sir,

            Your highly thought provoking essay is an excellent analysis of an important subject. Here we compliment your essay.

            Mathematics is the science of accumulation and reduction of similars or partly similars. The former is linear and the later non-linear. Because of the high degree of interdependence and interconnectedness, it is no surprise that everything in the Universe is mostly non-linear. The left hand sides of all equations depict free will, as we are free to chose or change the parameters. The equality sign depicts the special conditions necessary to start the interaction. The right hand side depicts determinism, as once the parameters and special conditions are determined, the results are always predictable. Hence, irrespective of whether the initial conditions could be precisely known or not, the results are always deterministic. Even the butterfly effect would be deterministic, if we could know the changing parameters at every non-linearity. Our inability to measure does not make it chaotic - "complex, even inexplicable behavior". Statistics only provides the minimal and maximal boundaries of the various classes of reactions, but never solutions to individual interactions or developmental chains. Your example of "the deer population in Northern Michigan", is related to the interdependence and interconnectedness of the eco system. Hence it is non-linear.

            Infinities are like one - without similars. But whereas the dimensions of one are fully perceived, the dimensions of infinities are not perceptible. (We have shown in many threads here without contradiction that division by zero is not infinite, but leaves a number unchanged.) We do not know the beginning or end of space (interval of objects) or time (interval of events). Hence all mathematics involving infinities are void. But they co-exist with all others - every object or event exists in space and time. Length contraction is apparent to the observer due to Doppler shift and Time dilation is apparent due to changing velocity of light in mediums with different refractive index like those of our atmosphere and outer space.

            Your example of the computation of evolutionary sequence of random numbers omits an important fact. Numbers are the inherent properties of everything by which we differentiate between similars. If there are no similars, then it is one; otherwise many. Many can be 2,3,...n depending upon the sequence of perceptions leading to that number. Often it happens so fast that we do not realize it. But once the perception of many is registered in our mind, it remains as a concept in our memory and we can perceive it even without any objects. When you use "a pseudorandom number generator to generate programs consisting of (almost) random sequences of numbers", you do just that through "comparison and exchange instructions". You develop these by "inserting random minor variations, corresponding to asexual mutations; second, by 'mating' parent programs to create a child program, i.e., by splicing parts of programs together, hoping that useful instructions from each parent occasionally will be inherited and become concentrated" and repeat it "thousands upon thousands of time" till the concept covers the desired number sequences. Danny Hillis missed this reasoning. Hence he erroneously thought "evolution can produce something as simple as a sorting program which is fundamentally incomprehensible". After all, computers are GIGO. Brain and Mind are not redundant.

            Much has been talked about sensory perception and memory consolidation as composed of an initial set of feature filters followed by a special class of mathematical transformations which represent the sensory inputs generating interacting wave-fronts over the entire sensory cortical area - the so-called holographic processes. It can explain the almost infinite memory. Since a hologram retains the complete details at every point of its image plane, even if a small portion of it is exposed for reconstruction, we get the entire scene, though the quality is impaired. Yet, unlike an optical hologram, the neural hologram is formed by very low frequency post-synaptic potentials providing a low information processing capacity to the neural system. Further, the distributed memory mechanisms are not recorded randomly over the entire brain matter, as there seems to be preferred locations in the brain for each sensory input.

            The impulses from the various sensory apparatus are carried upwards in the dorsal column or in the anterio-lateral spinothalamic tract to the thalamus, which relays it to the cerebral cortex for its perception. At any moment, our sense organs are bombarded by a multitude of stimuli. But only one of them is given a clear channel to go up to the thalamus and then to the cerebral cortex at any instant, so that like photographic frames, we perceive one frame at an instant. Unlike the sensory apparatuses that are subject specific, this happens for all types of impulses. The agency that determines this subject neutral channel, is called mind, which is powered by the heart and lungs. Thus, after the heart stops beating, mind stops its work.

            However, both for consolidation and retrieval of sensory information, the holographic model requires a coherent source which literally 'illuminates' the object or the object-projected sensory information. This may be a small source available at the site of sensory repository. For retrieval of the previously consolidated information, the same source again becomes necessary. Since the brain receives enormous information that is present for the whole life, such source should always be illuminating the required area in the brain where the sensory information is stored. Even in dream state, this source must be active, as here also local memory retrieval and experience takes place. This source is the Consciousness.

            Regards,

            mbasudeba@gmail.com