Essay Abstract

For the last decade I have been demonstrating that many of the so-called paradoxes generated by the Copenhagen interpretation of quantum mechanics have less puzzling analogs in nonlinear dynamics and chaos theory. This raises questions about the possibilities of nonlinearities in the foundations of quantum theory. Since many scientists do not think intuitively in nonlinear logic, I take this opportunity to dwell on several peculiarities of nonlinear dynamics and chaos: nonlinear logic and the possible connection of infinite nonlinear regression with free will. Superficially, nonlinear dynamics can be just as counterintuitive as quantum theory; yet, its seeming paradoxes are more amenable to logical analysis. As a result, using nonlinear dynamics to resolve quantum paradoxes winds up being simpler than many of the current interpretations being formulated to replace the orthodox interpretation. Chaos theory could be a candidate for bridging the gap between the determinism so dear to Einstein and the statistical interpretation of the Copenhagen School -- for deterministic chaos is indeed deterministic. However, intrinsic physical limitations on precision in measuring initial conditions necessitates analyzing it statistically. Einstein and Bohr both could have been correct in their debates.

Author Bio

Bill McHarris is Professor Emeritus of Chemistry and Physics/Astronomy at Michigan State University. He received his B.A. in chemistry from Oberlin College and his Ph.D. in nuclear chemistry from the University of California at Berkeley in the turbulent 1960's. He came to MSU directly from graduate school as Assistant Professor, becoming full Professor at age 32. For most of his career he worked as Senior Scientist at the National Superconducting Cyclotron Laboratory in nuclear physics/chemistry, but for the last decade has been trying to reconcile chaos theory with quantum mechanics. He is also a published composer and organist.

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William,

If given the time and the wits to evaluate over 120 more entries, I have a month to try. My seemingly whimsical title, "It's good to be the king," is serious about our subject.

Jim

Hello Prof. McHarris,

Thank you for your informative essay, It reminded me of my software engineering dissertation titled "Predicting the Unpredictable", an exercise in cognitive mechanics which used a benign form of "simulated evolution" to investigate the nature of memory and the mechanics of choice at the cellular and neural network level. Nothing self replicating or predatory, but sufficient in itself to break through local minima once random elements where introduced into the "simulated breeding process". Avoiding the twin pitfalls of self replication, and over complication which brings incomprehensibility to the means by which objectives are achieved, I found myself a rock (reality) to which I could tie myself while sorting through the foundations of the philosophical and epistemological musings of Descartes, Kant and the like.

According to you, you have had on foot in Chaos and the other in the Quantum Mechanics domain for some time, and I can appreciate the discomfort which comes with trying to keep these major ice-flows from drifting further apart, but I wonder whether you have considered that chasing one's tail is just the beginning of a process which when interrupted by accident (chaos) has only one way to go; that is, a spiral.

In my essay titled "Hierarchic Space-Time" I present a context within which (bit) must be held by something material (it), which must then recognize the information carried by the (bit). I then go on to present a case where the primordial bit (pbit), which has the property of direction, i.e. pointy bit, brings about a template form from which the material (it) springs. To complete this relationship one must see the material (it) created by the template form as holding momentarily the (pbit) so as to make the (pbit) an instance of information. When the (pbit) measures the (it), and the (it) measures the (pbit), we have a complimentary interaction causing a change in both, which represents not only an instance of information recognized, but the instantiation of the first observer. This observer, as defined, in moving from one place to another is subject to gravity, and in that sense may move in circular or spiral fashion.

I believe you will benefit by reading Prof. Unnikrishnan's essay titled "Matter and its Configuration States in the Making of Information", which I rate highly, and, of course, I welcome any comments you may have on my essay.

Regards.

Zoran.

    William,

    As of 7-6-13, 2:21 am EST, the rating function for your essay is not available. Sorry I can't help you out right now by rating your essay.

    Manuel

      It is an interesting essay.

      I am thinking, after the reading, on the sorting program: there is an analogy with a robot that stacks package in order of weight; so that the program can be a thought of a robot that learn the optimal stacking. The optimal program is so complex that a programmer don't understand the robot reasoning.

      There are some instinctive behaviours in insect (I think to bees and ants) that can be dna based (genetic learning), in million of years of evolution. This can be more understandable, because of the gene number is low, compared with the number of neurons.

      I am thinking that the unintelligibility of the program can be connected to the unnecessary parts: a minimization of the lenght of the program could reduce the Kolmogorov complexity of the description.

      It is interesting the free will like chaotic behaviour of the brain, that could be evolutionary to obtain an random behaviour of the animal brain to compete in an environment optimally (it look distinct reasoning to solve a problem, in a way similar to the evolution).

        Bill,

        Whoa!! Hopefully the regular participants in these forums will gravitate to your paper. Physics is stuck in its own hubristic loop and really needs to accept it is being left in the dust by other disciplines.

        Hopefully you will engage as well, as you have much to add to this conversation.

        I would like to offer up one idea, which was the subject of my last years entry;

        We experience time as a sequence of events and physics re-enforces this by treating it as a measure of interval, but since it is only detected as an effect of action, we should think of it not as a measure from one event to the next, but the process by which change happens. Thus it is not a sequence from past to future, but the process by which future becomes past. To wit, the earth isn't traveling some fourth dimension from yesterday to tomorrow. Tomorrow becomes yesterday because the earth rotates. This makes time an effect of action, rather than the basis for it. So the reason different clocks run at different rates is simply because change happens at different rates. The presumed vector of time is duration, yet duration doesn't transcend the point of the present, but is the state of what is physically present between the occurrence of events. This makes time similar to temperature, rather than space. Time is to temperature what frequency is to amplitude. Time is the linear effect, while thermodynamics is the non-linear effect. The two sides of our brains reflect this, as the left side is a linear processor, while the right side is more of a scalar processor, ie. what rises to the surface, "instinctively." Thus it is associated with emotion and intuition. Scalar processes are like pressure, heat, etc. which explains why they are associated which the heart, which is a pump.

        If time were a vector from past to future, logically the faster clock would move into the future more rapidly, but the opposite is true. It "ages" quicker and thus moves into the past faster.

        Not that we don't experience time as a sequence from past to future, but then we still experience the sun as moving across the sky.

        The problem is that as sequence, time is the basis of narrative and cause and effect, linear logic, so it is difficult to not think of it as foundational.

        I could go on, but this makes the point and you may not want to engage in the conversations.

          Dear Professor McHarris

          Your well-thought out and presented essay was recommended in a fqxi blog. You certainly describe many interesting and potent ideas that may well apply to various situations in physics - even a successful computer-generated theory of everything that no one understands one happy day!?

          As an unrepentant reductionist however I feel that there are conceptual errors in Quantum Mechanics - (traceable to Einstein and his point photon) of all people as I described in my last year's fqxi 'Fix Physics!' essay. If so resorting to chaos theory may be unnecessary to solve QM's fundamental problems. In my Beautiful Universe Theory also found here all interactions are local, causal and linear in a universal lattice, like a crystal; but as you suggest even such simple beginnings can lead to complex chaotic physical situations.

          With all best wishes

          Vladimir Tamari

            William,

            I have sent an email requesting that FQXi extend to those of you who had their essay posted on July 5, 2013, be allowed additional days to compensate for the days of not being able to rate these essays.

            My experience in conducting the online Tempt Destiny (TD) experiment from 2000 to 2012 gave me an understanding of the complexities involved in administrating an online competition which assures me that the competition will be back up and running soon. Ironically, the inability of not being able to rate the essays correlates with the TD experimental findings, as presented in my essay, which show how the acts of selection are fundamental to our physical existence.

            Anyway, I hope that all entrants will be allocated the same opportunity to have their essay rated when they are posted, and if not possible due to technical difficulties, will have their opportunity adjusted accordingly. Best wishes to you with your entry.

            Manuel

            Dr. McHarris,

            Your essay provides a fascinating exposition of the implications of nonlinearity for deterministic chaos in quantum theory. Let me suggest one more implication of nonlinearity, regarding solitons. QM is naturally a wave theory, but a linear wave packet does not naturally maintain its amplitude and integrity. For this reason, a purely wave interpretation of QM was never taken seriously, leading to the confusing hybrid of wave-particle duality. In contrast, a soliton in a nonlinear system propagates as if it were a particle in a linear medium, while maintaining its integrity, and repels another similar soliton, in direct analogy to the behavior of an electron. I suggest in my essay ( "Watching the Clock: Quantum Rotations and Relative Time" ) that primary quantum fields such as electrons and photons spontaneously condense into such soliton-like structures in a way that hides the nonlinear self-interaction.

            Alan Kadin

              Hello Pr. McHarris

              Thank you for a terrific read.

              What I like about chaos, in the context you put, is that seemingly complex systems arise from simple systems. It was for a long time incomprehensible to me (especially in the last years of my study) that no one seemed to ask how the universe could decide at the point of its 'arrival' that it would conform to some amazingly complex equations. Kind of, "Here I am, and I will comply with some pretty amazing mathematics--I hope you like multivariable calculus!"

              An open question attends whether my armchair universe exhibits non-linearity in higher dimensions. I think it must, because the structures therein, even in the 1-space analysis, are not differentiable below a certain minimum length, due to the continuum being non-smooth, which implies inbuilt uncertainty as a source of randomness.

              Your idea, in your Afterword, that one might figuratively get caught in an infinite loop is a little puzzling, if the universe had a beginning. Does not this imply that there was an ultimate initiation, so infinite loops cannot be (at least if working toward the beginning of time)?

              I would have liked to see how the non-linearity was to be bolted onto existing equations, so will browse your published works. Equally, if you consider my essay, and can see how to distribute (rotate) the evolving 1D structure shown into 3-space, then any suggestions would be welcome. I expect the world will be fractaline because of the self similarity in the iterations of the evolving Harmony Set.

              Best wishes

              Stephen Anastasi

                Esteemed Prof. McHarris,

                I thoroughly enjoyed your essay. It resonates with my vision of the workings of the world at the heart of which I see a recursion. It did not occur to me until I read your essay that this was called a nonlinear logic and nonlinear dynamics. Also, even though my degree was in computer science (a while ago), I have never heard about the evolutionary computer programs and the fascinating results they suggest about how living things most likely evolve and our chances at understanding them. I will definitely read more on all this now.

                My only problem with your essay was that you did not have better captions under the frames in Fig. 2 about which you later say: "One of the clearest manifestations of this can be seen as the gaps in Fig. 2; one that stands out is the large period-3 gap in the vicinity of A = 3.82." I could not find approx.values of A shown there and I wish I could. Otherwise, it is a ten.

                I wonder if it would not be too much of me to ask you to comment on my essay -- mainly because to me it seems that we speak of the same things, you professionally and I as a non-professional (and please never mind the non-academic tone in the end part.) Thank you!

                http://fqxi.org/community/forum/topic/1869 -- "The Play of Mind in Emptiness"

                  Mr. McHarris,

                  I appreciate Your essay. Especially the reference to the notion of bifurcation. Probably, I will insert a similar argument to my research.

                  For now I'm just developing a particular version of the polar coordinates.

                  Thank you and I hope you read my essay, now with zero score.

                  Best regards.

                  Dear Prof. McHarris,

                  I wonder if you're familiar with the work of evolutionary biologist, gerontologist Dr. Michael Rose. Just now I was trying to find a graphic from one of his presentations that shows the complex network of upregulated genes in the population of 'Methuselah flies' bred to greatly outlive the wild type. It makes a good illustration to the message in your essay that there are "logical processes that cannot be understood, much less be broken down into reductionist, simply analyzable parts".

                  This is bad news for the community interested in longevity, who hope that we could tweak a few genes here and a few genes there and voila we get a super-long-lived organism. I could not find that graphic but it shows a massively nonlinearly interconnected system that it is very difficult to understand, less so manipulate to achieve a desired outcome. It makes clear how difficult --if not impossible-- it would be to avoid unintended or even undesirable consequences because of numerous nonlinear feedback loops.

                  Your essay resonates very well with Dr.Rose's point that still prevalent molecular-biological reductionism is not valid scientifically. Frankly, until I read your essay, I too was hoping that such a manipulation was possible in principle. Alas. Thank you again for your very interesting essay :)

                  Dear Dr. Harris,

                  I have read with genuine pleasure your essay and your suggestion that deterministic chaos can inject into quantum theory essential features of nonlinear dynamics which can help understand the problems of quantum mechanics. Could you kindly guide me to the mathematical literature of your work on this subject, vs a vis a vis the application of chaos to quantum theory, with the intent to explaining say the quantum measurement problem, and the proof of the Born probability rule. I work on stochastic nonlinear quantum mechanics, and have a background in classical chaotic dynamics, but I had not thought of putting the two together - hence your advice in this regard would be of definite interest to me.

                  As you would know, extensive work on stochastic nonlinear quantum theory [ GRW / Spontaneous Localization] has been done over the last three decades or so, to explain the quantum classical transition, the collapse of the wave-function during a quantum measurement, and the Born rule. I am a little puzzled why you do not make mention of it, although its essence - random determinism, perhaps bears some semblance to deterministic chaos. Admittedly, theories such as GRW are phenomenological in nature, but given so, I think they are quite successful at what they set out to do, and are being subjected to stringent experiments, and are also perhaps relics of underlying fundamental theories such as Adler's Trace Dynamics [To beat my open trumpet, may I advertise here my recent review article with my colleagues on this subject, published in Reviews of Modern Physics 85 (2013) 471, available also at http://arXiv.org/abs/arXiv:1204.4325]

                  I would be seriously interested in application of nonlinear chaotic dynamics to quantum foundations, and will be grateful to hear from you.

                  Best regards,

                  Tejinder

                    • [deleted]

                    Dear Dr McHarris,

                    I commend you on your excellent work and essay, cutting straight through confusion to bring unity and clarity to and from chaos.

                    I particularly agree; "Mathematics can state things with certainty; physics cannot."

                    I find this conclusion in my essay from a coherent episto/ontological 'discrete field' model resolving nonlinear optical effects but the idea has been subject to criticism. I also propose that the Law of the Excluded Middle, and assumption A = A do not apply in nature, leading to a resolution of the EPR paradox consistent with Godel's n-valued 'fuzzy logic'. I would greatly appreciate your views and advice on those propositions. The Intelligent Bit

                    I also particularly agree and support your important comments;

                    "nonergodic behavior can easily ape "action at a distance."

                    "strongly nonlinear effects at the heart of quantum mechanics."

                    "Einstein and Bohr both could have been correct in their debates."

                    "nature is far more intricate and beautiful than we could imagine."

                    "physicists consider (nonlinear dynamics and chaos) to lie in an obscure corner of science."

                    "it is impossible... to determine a set of initial conditions with... enough precision... to produce a predetermined final state."

                    I believe your essay stands head and shoulders above most, and that the work is of great import. I don't however agree that 'statistical predictions' are the correct solution, but do find that using the proposition A~A, implying layered noncommutativity, should allow closer mathematical approximations and a logic freed of paradox. Again I'd greatly value you view. The mathematics would need development.

                    Congratulations on your essay, which I hope will become a landmark.

                    Peter

                      Dear William,

                      I would be curious about the chaos-based mechanism leading to violations of Bell inequalities. Can you report it in brief? The fact that there are diffraction patterns is irrelevant. What is relevant is the existence of instantaneous correlations, versus a choice of the observable that is measured locally. What plays the role of the direction of the spin measurements? Sorry, but my opinion is that chaos plays the role of the little monster explaining everything. We need to understand mechanisms, not to put them under the carpet of chaos.

                      My best regards

                      Mauro

                        Dear Professor McHarris,

                        Beautifully illustrated and well written essay. A pleasure to read. It does indeed seem odd if chaos theory answers so much elsewhere in nature to not apply to the quantum world.

                        The infinite regression section I particularly enjoyed, as cosmogony is a favourite area of research for me.

                        Time permitting, I'd be honoured if you could take a look at my essay based around Fibonacci sequence and entropy.

                        Best wishes,

                        Antony

                          Dear McHarris,

                          For me your essay is near delicious.

                          My question: when we think of any initial condition in chaos theory as rather the "phase-space" (what I've called "the observer" and maths/science calls the "invariance" or "conservation law") is it then likely that it is this "phase-space" that constitutes the "none" in non-linear dynamics (i.e. the Markov property)?

                          Implication is that a "feedback" (think, a "sensory modality" or "irritability" or "measurement") is actually a phase space and vice versa. This eliminates in your own words "part of the problem of determining the border between observer and observed." (in the sense now of Huygens' Principle).

                          That is,the de facto "observer" determines uniquely the de facto observables or predictability/determinism?

                          I always end by asking the pro like you are to please read my essay too: What a Wavefunction is, not elegant perhaps but will prove very useful insight. A promise!

                          All the best,

                          Chidi

                            Dear Prof. McHarris,

                            Perhaps, you are interested in my essay as it deals with biology too along with physics and mathematics. Just as you have thought of applying nonlinear dynamics and chaos theory to solve problems in physics, so do I think of applying them in the field of biology to solve the problem of the evolution of Life.

                            I have down loaded your essay and soon post my comments on it. Meanwhile, please, go through my essay and post your comments.

                            Regards and good luck in the contest.

                            Sreenath BN.

                            http://fqxi.org/community/forum/topic/1827