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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

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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...

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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.

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Author William C. McHarris replied on Jul. 23, 2013 @ 19:47 GMT

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

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

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Manuel S Morales replied on Jul. 7, 2013 @ 21:02 GMT

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

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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).

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Author William C. McHarris replied on Jul. 23, 2013 @ 20:01 GMT

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

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...

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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.

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Author William C. McHarris replied on Jul. 24, 2013 @ 19:42 GMT

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...

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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

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John Brodix Merryman replied on Jul. 25, 2013 @ 21:24 GMT

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 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

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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

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Author William C. McHarris replied on Jul. 26, 2013 @ 19:36 GMT

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...

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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

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Dear William

Your conclusion seems to be a prelude to an " infinite loop" - Even though you have very good analysis.

I am will be rate when the rating system continues to operate.

And to change the atmosphere "abstract" of the competition along with demonstrate for the real preeminent possibility of the Absolute theory as well as to clarify the issues I mentioned in the essay...

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Author William C. McHarris replied on Jul. 27, 2013 @ 03:07 GMT

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

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

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Author William C. McHarris replied on Jul. 27, 2013 @ 22:06 GMT

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

Alan M. Kadin replied on Jul. 30, 2013 @ 14:21 GMT

Dr. McHarris,

Thank you for responding to my comments on your essay, and for your careful reading of my own. I agree that we may be touching on related issues from different points of view.

With regard to quantized spin, I have shown that if one assumes that angular momentum of continuous vector fields is quantized in units of h-bar, then the rest of QM follows automatically, without other assumptions. I suggest that a nonlinear self-interaction leads to a soliton-like structure with an amplitude that corresponds to quantized spin, but I have not (yet) specified the mathematical form of such an interaction that can achieve this. This is still a work-in-progress, but the connections thus far are remarkable, including the fact that a form of general relativity follows simply from this picture. Everyone believes that such a neo-classical picture must have been definitely ruled out in the last century, but I have found no trace of anything like this in the early literature.

Thank you also for pointing out the book by Gell-Mann and Tsallis. I am of course familiar with Gell-Mann's earlier work on particle physics, but not with this more recent work.

I would be happy to discuss these issues with you further after the end of this contest. My email address is listed on my essay.

Alan Kadin

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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

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Anonymous replied on Jul. 28, 2013 @ 22:28 GMT

Hi, Stephen,

What I meant in the Afterword is that, if quantum mechanics really does fundamentally contain nonlinear, even chaotic elements, then trying to apply chaos to quantum mechanics is like trying to apply chaos theory to itself — hence, the loop, which possibly could explain why there are difficulties with so-called quantum chaos — and why chaos theory seems to be successful in...

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Hi, Stephen,

What I meant in the Afterword is that, if quantum mechanics really does fundamentally contain nonlinear, even chaotic elements, then trying to apply chaos to quantum mechanics is like trying to apply chaos theory to itself — hence, the loop, which possibly could explain why there are difficulties with so-called quantum chaos — and why chaos theory seems to be successful in most disciplines other than quantum mechanics. This is different from the feedback loops inherent in nonlinear dynamics itself. You are astute, however, in pointing out the difficulties associated with the Big Bang and any sort of infinite loop. My experience in cosmology is superficial at best, so I certainly don't want to fall into the trap of presuming things about it. Nevertheless, one can raise some questions. The Big Bang theory results basically from a linear extrapolation back to time near zero, which could be problematical if any nonlinearities were involved. In addition, although Big Bang theory has had considerable success, over the years it has required quite a number of patches and band-aids to touch it up, which is generally taken as a warning sign for any theory — many cosmologists have questioned the arbitrariness of inflation, in particular. So perhaps the proponents of alternate theories should not be dismissed out of hand, although such theories have generally done poorly in predicting such things as the observed nuclear abundances in the Universe.

Nonlinear systems customarily have rather large dimensional phase spaces, although, surprisingly enough, chaotic behavior in a particular dimension is quite often reflected in other dimensions. For example, time series analysis has been remarkably successful in analyzing chaotic systems, although at first glance it appears to be rather naive. [For example, plotting results from, say, the (n+1)th or even higher iteration against those from the nth iteration is a common method used to detect the underlying map and to distinguish chaotic, i.e., apparently random, systems from truly random systems.] I see no reason why this shouldn't work in your Harmony Set analysis.

I read and worked on your essay and found it to be remarkable, if difficult for a non-philosopher to fathom. (I have my liberal arts education starting at Oberlin College to thank for being able to follow it as well as I did.) I would like to continue to delve into these topics, and I would like to read your book, "The Armchair Universe," when it is completed. (I also plan to look up your other books, such as "The Druid," for oftentimes lighter fare gives insight into the more formal aspects of thinking.) Anyway, thanks a million for your comments and insight.

Cheers,

Bill

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Author William C. McHarris replied on Jul. 29, 2013 @ 02:37 GMT

Hi again, Stephen,

As you can discern, the previous post is from me. I must have taken too long or gone back and forth one time too many, so I was registered as "anonymous." Again, let me tell me how much I appreciated your essay.

Cheers,

Bill McHarris

An interesting article on this very topic, that of quantum thermodynamics.

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Author William C. McHarris replied on Jul. 29, 2013 @ 21:04 GMT

Hi, John,

Thanks for the reference. Their work is fascinating, and there are some parallels to the work on nonextensive thermodynamics pioneered by Constantino Tsallis. A good introduction to the latter is the book edited by Gell-Mann and Tsallis, "Nonextensive Entropy: Interdisciplinary Applications" (Ref. [7] in my essay). It also brings to mind Ilya Prigogine's work on non equilibrium thermodynamics. You might find his book, "Order Out of Chaos" interesting; Prigogine, however, in his last book, "End of Certainty," argues that nonequilibrium thermo introduces even more uncertainty, à la quantum mechanics, so that determinism is on its way out — it's interesting the way different people can use similar arguments to reach opposite conclusions.

Since we are talking about possible experimental applications, a stunning experimental verification of chaotic and cyclic (ordered) behavior coexisting in an indisputably quantum system (an atom acting as a kicked top) is given by S. Chadhury et al., Nature 461, 768 (2009); a summary appears in Nature News 2009/091007 (7 Oct 2009).

Bill

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"

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M. V. Vasilyeva replied on Jul. 9, 2013 @ 03:55 GMT

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 :)

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Author William C. McHarris replied on Jul. 29, 2013 @ 22:24 GMT

Dear Marina,

I thoroughly enjoyed your essay, too. Much of it is a common-sense version of nonlinear dynamics and feedback relations. It is both lyrical and sensible — and comprehensible in that it is not wrapped up in seemingly eloquent yet obscuring philosophical and/or physics-derived jargon! I think you will find in further reading on chaos theory (the book by James Gleick, "Chaos:...

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Dear Marina,

I thoroughly enjoyed your essay, too. Much of it is a common-sense version of nonlinear dynamics and feedback relations. It is both lyrical and sensible — and comprehensible in that it is not wrapped up in seemingly eloquent yet obscuring philosophical and/or physics-derived jargon! I think you will find in further reading on chaos theory (the book by James Gleick, "Chaos: The Making of a New Science," although a bit dated, is a good starting point), that much of it strengthens your own arguments.

I apologize for the lack of clarity in Fig. 1 — I'm so used to seeing that diagram that I assumed everyone else would be familiar with it, as well. The first frame shows essentially the entire diagram, starting from where it starts to become interesting (just below A = 1) to where it breaks down (A = 4); the regions of "order within chaos" are the white regions or gaps within the dust of the chaotic values. The large period-3 gap in this frame is the two white regions, one above the other, about 95% of the way toward the right-hand extreme. Actually, the second frame shows this much more clearly: It is a blow-up of the last 10% or so of the first frame, starting where the map "bifurcates" into four values. The period-3 gap shows up about 75% toward the right. Again, there are two white regions, and the three final values are the top and bottom values plus the one about 40% of the way up. What is most important about this whole business is that ever smaller and smaller regions of order exist within the chaotic regions, and no matter how great the magnification gets to be (even approaching infinity), one still finds this intimate co-existence. I find this sort of behavior just as counter-intuitive as quantum mechanics; yet it follows logically from simple principles!

Thank you for suggesting Michael Rose's work and views on the breakdown of "reductionism" with respect to genes. I am somewhat naive in biology, something I hope gradually to remedy. (Maybe we can't learn everything, but at least we can try!) I suspect that the idea that reductionism has its limits is more widely accepted in biology than it is in physics. But the whole point of nature being nonlinear means that our (overly) simplified picture of the world cannot hold up to deeper scrutiny.

Again, thanks and best wishes,

Bill

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M. V. Vasilyeva replied on Aug. 1, 2013 @ 20:54 GMT

Dear Professor McHarris,

Thank you for your reply and thank you so much for your kind comments on my essay in my blog. I can't relay how much your approval and high rating means to me, coming from a luminary like you.

...and I know exactly what you mean by a writing style "wrapped up in seemingly eloquent yet obscuring philosophical and/or physics-derived jargon" -- I'm afraid some of my ex-countrymen are often guilty of this. I call it "the academic style", and this applies to Russian academics only (I know, because I've read plenty of English scientific literature to compare). I personally cannot read this style and don't, unless I have to. (it's hard to stay awake lol)

And thank you very much for your explanation re captions. I do remember --vaguely-- these diagrams from James Gleick book, soon after it came out, which was a long time ago (yeah, how fast we forget -- I am planning to re-read it now). And so I could guess where that A = 3.82 was but could not be certain -- the question 'what if I'm mistaken?' always looms over my head -- and so I thought a caption would remove that uncertainty. Thank you for your explanation again!

And regarding Dr. Rose, he was telling about the non-reducibility of evolving biological systems for years, but somehow, it finally clicked in my head only when I read your essay. My brain will never be the same, because a very important neuronal connection was made. There are very few such essays, and even books or articles, that make a brain click. You did that for me and I will never forget that. Thank you!

-Marina

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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.

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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

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Author William C. McHarris replied on Jul. 30, 2013 @ 19:32 GMT

Dear Dr. Singh,

Thank you very much for your kind words and especially for your interest in linking stochastic nonlinear quantum mechanics and chaos theory. I am sure there are at the very least some significant parallels. I have just downloaded your overwhelming paper from RPM/arXiv, and at a first superficial glance, it seems to have important implications. Obviously, because of its length and depth it will take me some time to digest it properly, so I really should defer sensible comments until after I have had time to study it thoroughly. However, bear with me for the moment if I make some preliminary, necessarily superficial remarks.

The comparisons of chaos/nonlinear dynamics with quantum mechanics are also necessarily phenomenological at this time, but examples of them can be found in Refs. [4] and [5] in my essay, together with references and some simple calculations. I think one of the better points of attack lies on the nonlinear classical side, where correlations (à la entanglement) and statistical interpretations of deterministic states (collapse?!) are common. A good introduction to this is in the book, "Nonextensive Entropy: Interdisciplinary Applications," edited by Gell-Mann and Tsallis. Tsallis tends to overstate and oversell his idea of nonextensive entropy, which is purely empirical, but his basic concept seems solid enough, and much of it rests on experimental observations.

Give me a month or so to work through your paper properly, and I'll get back with you. I think we could have some profitable discussions.

Best wishes,

Bill

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

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Author William C. McHarris replied on Jul. 31, 2013 @ 18:57 GMT

Dear Peter,

Thank you for your kind words. I really appreciate your enthusiasm.

I studied your essay and found it exciting. It is so dense that I couldn't follow all of your arguments, but the basic idea of the IQbit arising from fuzzy logic and arising in what binary logic considers the excluded middle sounds novel and well worth pursuing further. I also downloaded and read your essay, "Subjugation of Scepticism in Science" (with John Minkowski at Academia.edu), which sets the tone for many of the essays in this contest. It's true, science is similar to religion in that things go in and out of fashion, and there is a formidable barrier for currently unorthodox ideas. You might enjoy several of the essays in "Quantum (Un)speakables," edited by R.A. Bertlemann and A. Zeilinger (basically the elaborated proceedings of a most fascinating conference commemorating the tenth anniversary of Bell's death) — they talk about the decades when major journals such as "Physical Review" would reject papers questioning the Copenhagen interpretation without even bothering to send them out for review.

Actually, some of the ideas you touch on are similar to mine. For example, the Monty Hall paradox is an excellent example of how people jump to conclusions without understanding Bayesian probabilities, something rather important in interpreting Bell's inequalities. A good, simple, common-sense introduction to Bayesian statistics can be found in Chap. 8 of Nate Silver's book, "The Signal and the Noise." (Cf. my comments in the exchange below.) As for statistical predictions, they are inevitable if one accepts contributions from chaos. They are the link between determinism (Einstein) and Born/Bohr.

Again, I really appreciate your comments and your enthusiasm. It livens up the discussion.

Cheers,

Bill

Peter Jackson replied on Aug. 4, 2013 @ 17:20 GMT

Bill,

You're very welcome. Well earned. thanks also for your post on mine. I think we're onto something very important for progress and certainly paradigm changing. Where do we go for one of those? Do they exist any more? It looks to me like they've stopped doing them!?

Peter

(PS. Could be an opening then!)?

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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

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Peter Jackson replied on Jul. 10, 2013 @ 15:07 GMT

Mauro,

I hope Bill will engage, but I've just found a more expansive Bell proof consistent with the one in my essay, in his excellent 2011 J. Phys. Conf. paper.

Quantum paradoxes explained.

This doesn't offer the physical analogy as my essay (also see my post to Matt Leifer) but does extend Sisskind's 3 disc analogy. Bill even also gives the Cardano sample space analogy!

Put very simply; we can find more observables if we look 'between the lines' (for the elipto-helical 'Intelligent Bit' freedoms). So we're not limited to asking red?/green? but can also ask 'how bright' of each.

I did get the impression you missed that in my essay. Perhaps not all better explanations must come from 'little monsters'.?

Best wishes

Peter

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Member Giacomo Mauro D'Ariano replied on Jul. 15, 2013 @ 08:52 GMT

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

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Peter Jackson replied on Jul. 16, 2013 @ 17:22 GMT

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...

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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').

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Author William C. McHarris replied on Jul. 31, 2013 @ 19:53 GMT

Dear Mauro and Peter,

I read your exchange with interest and apologize for not replying sooner — I've been traveling (a combination of science and music), so things got put off.

I agree that one should not try to use chaos as the "little monster" that can explain everything, especially at this early stage, when things are pretty much empirical and by analogy. Actually, the...

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Dear Mauro and Peter,

I read your exchange with interest and apologize for not replying sooner — I've been traveling (a combination of science and music), so things got put off.

I agree that one should not try to use chaos as the "little monster" that can explain everything, especially at this early stage, when things are pretty much empirical and by analogy. Actually, the violations of Bell's inequalities are more related to Bayesian statistics than they are to chaos. The point of attack is on the classical side, for classical nonlinear systems can exhibit correlations (analogous to entanglement) essentially as large as those in quantum mechanics. Thus, the violations of the inequalities are ruling out the lack of correlations (in linear systems?!) rather than classical mechanics per se. (If you look back at the so-called "classical" derivation of, say, the CHSH inequality, which is the most experimentally friendly version and the one commonly used, you will find that there are really no correlations built in — they are just glossed over, whereas the on the quantum mechanical side one normally starts with a singlet state, which as about as entangled as you can get.) These classical correlations have been studied extensively in systems as diverse as tornados and energy distributions of cosmic rays, and they exhibit so-called nonextensive (Tsallis) entropy. The book "Nonextensive Entropy: Interdisciplinary Applications," put together by Gell-Mann and Tsallis (Ref. [7] in my essay) covers this in a relatively straightforward fashion. Currently, the whole business is mostly experimentally driven, so mathematical derivations are at a minimum, but they have had surprising success with quite diverse systems.

A final word. Perhaps I am naive, but coming from an experimentalist's perspective, I find it odd the way people jump from statistical correlations to individual cases. All of the Bell-type inequalities rely on correlations found in large numbers of data, when "enough events have been recorded to be statistically significant and meaningful." (This is true even for the three-state GHZ correlations, which don't rely on an inequality.) Yet, when it comes to the interpretation, people say such things as, "When the spin direction of Alice's particle is measured as 'up,' this has caused its wave-function (previously assumed to be in entangled limbo) to collapse, and since it came from a singlet state, this causes the wave-function of Bob's particle to collapse INSTANTANEOUSLY into a 'down' state." Experimentally, there has been no analysis of individual particle-particle data — the correlations are meaningful only after many thousands of events have been collected and compared statistically. Surely this is a weakness in the argument!

Again, thanks for the dialog.

Bill

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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

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Author William C. McHarris replied on Aug. 1, 2013 @ 18:33 GMT

Dear Antony,

Thank you for your complimentary remarks. I also read your essay, which was quite well written. The idea of a Fibonacci sequence explaining the behavior of black holes is a novel, clever idea, but I wonder about whether or not it really applies to the physical situation. To be sure, it's a clever mathematical construct, but with enough variables, one can fit almost anything. On the other hand, it's just such clever group-theoretical constructs that wound up predicting the omega-minus particle.

The thing one has to worry about is that there are far more mathematical constructs than there are physical applications, and deciding which ones are really relevant is not a trivial task. Can you extend your model to make predictions?

Best wishes,

Bill

Antony Ryan replied on Aug. 1, 2013 @ 19:52 GMT

Dear Bill,

I can indeed make predictions and I'll reply on my thread.

Best wishes,

Antony

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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

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Author William C. McHarris replied on Aug. 4, 2013 @ 21:50 GMT

Dear Chidi,

Thank you for your kind words. I read your essay with pleasure, too. It's quite fascinating.

Your essay is fairly consistent with the Copenhagen interpretation, and I think this is where we differ. With a nonlinear element in quantum mechanics (implying feedback), we don't have to worry about the distinction between system and observer or where to delineate the locale of separation. Instead, quantum mechanics becomes ontological, and the Uncertainty Principle can be interpreted in its old-fashioned sense in that the observer doesn't cause the wave-function to collapse, but he or she does perturb the system, affecting successive measurements. Thus, feedback is not a phase space but its implications can affect the phase space. I hope I have understood your question and this perhaps starts to answer it.

Best wishes,

Bill

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

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Anonymous replied on Aug. 5, 2013 @ 01:51 GMT

Hi,

Thanks for your comments.

I found your essay fascinating, with much to commend it. However, I am curious when you make a fundamental distinction between biology and physics. Although biology is infinitely more complicated than physics, scientists working in nonlinear dynamics are making baby steps toward interpreting it. For example, nonlinear network theory has made considerable progress in explaining how very complicated networks, such as the internet, function. And it is conceivable that simple brains (perhaps at insect level) eventually will be understood on the basis of feedback in networks. We're in a modern position similar to that of organic chemistry in the early 1800's, when it was thought that some sort of "vital" component was present in organic compounds that wasn't necessary for more straightforward inorganic compounds. But then urea was synthesized in the laboratory, disproving the necessity of this vital component — after all, organic chemistry is simply the chemistry of carbon, which can be considerably more complicated than the chemistry of most other elements, but there's nothing "vital" about it. Something similar is undoubtedly true about biological systems. They may be so complicated that we can never completely fathom them, but there should be no fundamental difference between them and physical systems. (This may well be the situation where "in principal" and "in practice" wind up being being so different that for all practical purposes they are essentially antipodal.)

I look forward to seeing your comments on my essay,

Bill

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Dear Prof. McHarris,

Your essay presents some very interesting points. With respect to explaining the quantum from classical chaos, Chapter 16 from Ian Stewart's Does God Play Dice? The New Mathematics of Chaos makes a similar point. Also, I was impressed by your struggle to work with two different communities of scientists, apparently little interested into each other's field. In...

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Dear Prof. McHarris,

Your essay presents some very interesting points. With respect to explaining the quantum from classical chaos, Chapter 16 from Ian Stewart's Does God Play Dice? The New Mathematics of Chaos makes a similar point. Also, I was impressed by your struggle to work with two different communities of scientists, apparently little interested into each other's field. In particular, I can imagine you encountered many quantum skeptics, people who don't believe classical mechanics, being it chaotic, can explain the quantum, due to results like EPR, Kochen-Specker, delayed choice. I am among these, and like Prof. D'Ariano, I would be very interested to see a chaos-based mechanism leading to violations of Bell inequalities. On the other hand, classical chaos is still full of surprises, so who knows? I find myself thinking that some strange phenomena usually attributed to classical chaos, are in fact due to global consistency. But at this time I find this very unlikely, so I don't entertain such thoughts.

At first sight, it may seem that quantum mechanics can't provide support for nonlinear chaos, but this is not quite so. And I am not thinking here at the position defended so well by Prof. Tejinder Singh above and in his essay. I am thinking that even the linear quantum mechanics doesn't contradict nonlinearity at the classical level. The reason is the following: although most classical equations are nonlinear, after quantization, we get linear equations. Why? Because quantum linearity happens in a much larger space, an infinite dimensional Hilbert space. It is known that nonlinear equations can be linearized, i.e., expressed as linear equations of higher order, but in quantum mechanics, something even better happens. Each nonlinear degree of freedom is replaced by an infinite number of linear degrees of freedom. Nonlinearity remains hidden in the Hamiltonian.

Could you please provide some links to your papers, and other papers showing the analogies between quantum mechanics and chaotic phenomena mentioned in your essay?

Best regards,

Cristi Stoica

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Anonymous replied on Aug. 5, 2013 @ 16:24 GMT

Dear Cristi,

Thanks for your comments. I also read your lovely essay and was very favorably impressed by it. I included a few comments on the thread below your paper.

The link to my paper from the DICE Conference is Chaos and the Quantum. This paper includes a number of references your might find useful, although the idea of nonlinear influences in quantum mechanics is very much...

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Dear Cristi,

Thanks for your comments. I also read your lovely essay and was very favorably impressed by it. I included a few comments on the thread below your paper.

The link to my paper from the DICE Conference is Chaos and the Quantum. This paper includes a number of references your might find useful, although the idea of nonlinear influences in quantum mechanics is very much in an early, empirical stage.

I think in principle we are saying much of the same thing in that nonlinear equations can be represented by (many, many more) linear equations of higher order. But, of course, this quickly becomes cumbersome. For all practical purposes chaos theory was unknown when the formulators of quantum mechanics were active, so they forced it into a linear format. One of my favorite quotations comes from Mielnik [Phys. Lett. A289, 1 (2001)], when he was worrying about the superluminal signals that ensued when he was working on (weak!) nonlinear effects:

"I cannot help concluding that we do not know truly whether or not QM generates superluminal signals—or perhaps, it resists embedding into too narrow a scheme of tensor products. After all, if the scalar potentials were an obligatory tool to describe the vector fields, some surprising predictions could as well arise! ...the nonlinear theory would be in a peculiar situation of an Orwellian 'thoughtcrime' confined to a language in which it cannot even be expressed. ...A way out, perhaps, could well be a careful revision of all traditional concepts..."

I often wonder what Wheeler himself, had he been working several decades later, would have done with modern chaos theory. (Although it was known more or less outside of meteorology starting in the 1970's and 1980's, it was by no means widely disseminated among most main-stream physicists — I hesitate to label Wheeler as a "main-stream" physicist! And it was well into the 1990's, with the growth of quantum information theory that anyone started to think seriously about applying it to the basics of quantum mechanics.) Wheeler was so responsive to new, novel ideas that I suspect he might have run with it.

I found your paper so interesting that I have located many of your other papers, and I would like to continue our discussion after I have had time to peruse and understand them more thoroughly.

Best wishes,

Bill

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Author William C. McHarris replied on Aug. 5, 2013 @ 16:27 GMT

Hi, again,

It seems one gets logged out if he takes too long to formulate an answer, so my post above is listed as "anonymous." But, as you can discern, it's from me. Again, thanks for your comments.

Bill McHarris

Dear William (if I may),

You have written an intriguing and engaging essay, and I can only agree with your main point that one should keep the possibility in the back of one's mind that nonlinear dynamics might explain some aspects of quantum mechanics that are currently not so clear.

Even so, there is an elementary point about which I am not sure, and I would appreciate if you could clarify. Suppose that nonlinear dynamics and chaos theory is behind the interference pattern one observes in the double split experiment with a beam of particles. Shouldn't the sensitive dependence on initial conditions imply that under some initial conditions the there will be noticeable variations in the interference pattern from one experiment to another in which the set up is almost but not quite identical?

I can understand that in the case of a single-particle beam, one might ascribe the inability to predict where each individual particle lands on the screen to such sensitive dependence. My question is about whether it is not possible that under some initial conditions the overall pattern is changed, somewhat analogous to the chaotic structures you presented in which order presents itself within disorder. I can't see why this would not be possible, and if that is correct, then it seems to me that this could be used to test the idea. But I'm not sure about this, so I hope you can provide an answer.

I wish you all the best on your endeavor,

Armin

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Author William C. McHarris replied on Aug. 5, 2013 @ 20:25 GMT

Dear Armin,

Thank your for your astute comments.

Yes, sensitive dependence on initial conditions offers the possibility for explaining the two-slit expedient. Classical chaotic scattering can produce patterns that look very much like diffraction patterns. This sort of behavior is discussed in detail in a series of papers in a special issue of "Physics D," introduced by a paper by Bleher, Grebogi, and Ott; a more straightforward discussion is given in the book, "Classical Dynamics: A Contemporary Approach," by José and Salatan; both are listed under Ref. [6] in my essay. The basic idea involves the intimate mixture of chaos and order in various locales of phase space for chaotic systems. This admixture can be very fine, since bifurcation diagrams for such systems tend to be self-affine, mathematically at least, all the way to infinite magnification. If a system finds itself in such a regime, then an almost infinitesimal variation in initial conditions can cause it to move back and forth between ordered (cyclic) and chaotic behavior, which means the difference between a particle's landing in a predictable location and being scattered "unpredictably" (not really fundamentally, but for all practical purposes it might as well be). Hence, the apparent diffraction pattern. This is only one of the so-called paradoxes of the Copenhagen interpretation of quantum mechanics that can more or less be explained by analogy, having a parallel explanation in terms of nonlinear dynamics. Superficially, nonlinear dynamics and its extreme (chaos) can be just as counterintuitive as quantum mechanics, but upon deeper scrutiny, their peculiarities come about more logically.

Best wishes,

Bill

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...

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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

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Author William C. McHarris replied on Aug. 6, 2013 @ 20:08 GMT

Dear Prof. Knuth,

Thank you very much for your comments. I read your essay, and I was overwhelmed by the beauty of it! Imagine being able to come up with relativistic space-time symmetries from a different but straightforward and logical approach. Not being all that familiar with ordering theory, I had to take most of the derivations on faith, accepting the physical analogies as stated,...

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Dear Prof. Knuth,

Thank you very much for your comments. I read your essay, and I was overwhelmed by the beauty of it! Imagine being able to come up with relativistic space-time symmetries from a different but straightforward and logical approach. Not being all that familiar with ordering theory, I had to take most of the derivations on faith, accepting the physical analogies as stated, since they seem quite reasonable and not at all forced. I downloaded your arXiv paper, "The Physics of Events," and I'll study it thoroughly during the next month, so perhaps I can have more astute questions and/or comments after that.

I'll also download your other paper, "Origin of Complex Quantum Amplitudes," and work on it. My comments above to Stoica make a start to answering the linearity vs nonlinearity compatibility problem. But, from an experimentalist's physical aspect, I think that your ideas of influence and response indicate a fundamental feedback, a sure sign of nonlinearity. And the influence-response picture fits in with the original interpretations of the Uncertainty Principle, which fell out of favor with the rise of the Copenhagen interpretation. Maybe we can have a more cogent discussion this autumn.

I also wonder why Cvitanovic's work didn't attract more attention. Perhaps he was simply ahead of this time. His 1987 Physical Review Letter came before the quantum information burst and before most people were really aware of chaos theory. Perhaps now is time for a revival of applying periodic orbital theory to "simple" systems such as the He atom or the H molecule-ion. (With good numerical agreement, I think chemists would welcome this sort of analysis.)

And it's amazing to find someone else who generated fractal ferns on an Amiga! (Another promising platform that didn't survive.) As an extension of this sort of thing, the time is ripe to explore electrons in the two-slit experiment using chaotic scattering. I think the two-slit experiment is a prime example of using an overly-simplified model to reach questionable conclusions. Most of the analyses use pictures where the dimensions are far, far greater than the actual wavelengths, where the experiments would show nothing. Performing a detailed microscopic analysis, with the electrons indeed interacting with the individual atoms forming the slits could well produce a situation for chaotic scattering, with its resulting quasi-diffraction patterns. I hope you find this a worthwhile endeavor.

Again, congratulations on an impressive essay. I made a few remarks on its thread.

Cheers,

Bill McHarris

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Member Kevin H Knuth replied on Aug. 7, 2013 @ 17:57 GMT

Thank you Bill for your comments and your generous words regarding my essay.

Perhaps Cvitanovich's work is not well-known in these circles.

I have not been on the FQXi forums, but perhaps discussing it there might be a useful endeavor.

I also am delighted that you too used an Amiga!

We seem to have a proclivity for obsolete platforms!

Looking forward to continuing discussions...

Kevin

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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

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Author William C. McHarris replied on Aug. 7, 2013 @ 18:22 GMT

Dear Richard,

Thank your for your observations. Yes, the interplay between observation and system makes for feedback, which can easily generate nonlinear behavior. I enjoyed reading your essay, which covered many of the same sort of ideas. It's all to the good that we are now able to question the strait-jacketed, forced Copenhagen patterns.

Best wishes,

Bill

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

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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

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Author William C. McHarris replied on Aug. 7, 2013 @ 18:42 GMT

Dear Dipak,

Thank you for your kind words. Yes, chicken and egg, rather observer and observed, are in a sense inseparable, which leads to feedback and nonlinear behavior. I read your essay with pleasure — it's a neat, fresh approach to the question from a more philosophical approach. My biggest question concerns how we can discern an analog vs a digital Nature. If our detection (sensory) system happens to be digital, we cannot distinguish between analog signals and digital signals on a much finer scale than our system's scale; similarly, if our detection system were analog, Nature probably requires much higher resolution than we possess in order for us to discern the difference. Could you comment on this?

Thanks,

Bill

Dear William. Hello, and apologies if this does not apply to you. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so. With best wishes.

Vladimir

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Author William C. McHarris replied on Aug. 6, 2013 @ 20:44 GMT

Dear Vladimir,

Yes, I rated your essay a week or so ago. I thought it was a terrific essay.

Best wishes,

Bill

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...

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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

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Anonymous replied on Aug. 7, 2013 @ 19:31 GMT

Dear Héctor,

Thank you for your kind comments. And you are much too self-depricating — your resume is most impressive, and it was a pleasure to read an intelligent essay written from a different perspective. (Minor English language flaws didn't detract significantly, by the way.)

What I most liked about your essay was its common sense approach. Scientists, physicists in...

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Dear Héctor,

Thank you for your kind comments. And you are much too self-depricating — your resume is most impressive, and it was a pleasure to read an intelligent essay written from a different perspective. (Minor English language flaws didn't detract significantly, by the way.)

What I most liked about your essay was its common sense approach. Scientists, physicists in particular, can get themselves tied up in knots when considering time, as is well documented by the FQXi contest on the Nature of Time. Einstein shied away from time as an absolute to be explained and considered it to be merely a variable. As you may well note from my essay, I come down strongly on the side of Einstein in the Einstein-Bohr debates. Einstein, after all, was not the head-in-the-clouds person the popular press makes him out to have been. His forte was his ability to relate theory to down-to-earth experimental facts. (Bohr was the abstract philosopher, who delighted in tortuous arguments.) His greatest successes were when he had experimental facts to guide him. (HIs spinning his wheels in later years was partly due to the fact that then he didn't have experimental guidance to follow.) A fascinating book is "Einstein's Clocks, Poincaré's Maps," which relates the years leading up to Relativity. Poincaré was a considerably stronger mathematician than Einstein, and by all rights he should have been the one to formulate relativity. Yet he was stuck in tradition and failed to make the necessary leap that Einstein made — and Einstein made this leap partly because of his practical experience at the Swiss Patent Office in getting clocks coordinated and on time.

When treating time as a mere variable, relativity is nowhere nearly so shocking with time dilation, the twin paradox, etc. And one can make the time variable linear, which leads to more complicated behavior in other variables, or one can force linearity onto other variables, which causes time to undergo all sorts of conniptions. Your idea that our understanding is locked into an epistemological, limited understanding is noteworthy, but we are stuck with what our senses can tell us. Of course, this does not answer the question, "It from Bit or Bit from It?" — it may well be the epitome of Charles Ives' Unanswered Question! I think the strength of this FQXi contest lies in its diverse perspectives, and I find yours to be significant.

Best wishes,

Bill

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Dear William

Richard Feynman in his Nobel Acceptance Speech (http://www.nobelprize.org/nobel_prizes/physics/laureates/19
65/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

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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

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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.

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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

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Author William C. McHarris replied on Aug. 13, 2013 @ 18:00 GMT

I received the following e-mail message from Dr. Klingman on 8 August:

*Dear Bill McHarris,

*I made the mistake of waiting until I had read your other papers before commenting on your essay. This put me near the end of the comments on your page. After you returned and began diligently answering each comment, I watched daily for you to reach mine. But we ran out of...

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Edwin Eugene Klingman replied on Aug. 14, 2013 @ 19:03 GMT

Dear Bill,

Thank you for your gracious response. I knew that we shared several ideas about the current state of physics, having read your essay and some of your other publications. We apparently share an understanding of human foibles and fashion. But primarily I'm excited about your perspective on non-linearity as potential source of 'weirdness' in QM.

From your comment on my thread...

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Dear Bill,

Thank you for your gracious response. I knew that we shared several ideas about the current state of physics, having read your essay and some of your other publications. We apparently share an understanding of human foibles and fashion. But primarily I'm excited about your perspective on non-linearity as potential source of 'weirdness' in QM.

From your comment on my thread I'm uncertain as to whether you are familiar with gravito-magnetism or mistake it for gravity plus electromagnetism. The 'magnetic' aspect of gravity is analogous to but completely separate from electromagnetism. As indicated in my essay, the gravitic C-field is sourced by mass density (in motion) and electrons and quarks are arguably the densest mass in the universe. This seems generally to have been ignored, along with the nonlinear nature of the field. If the nonlinearity is not taken into account the field is considered too weak to have much effect. However I believe the nonlinearity, combined with the extreme density, do produce effects, and I am optimistic that my approach will produce quantitative results, not just a qualitative explanation of current anomalies. If you read my previous essay, The Nature of the Wave Function (also suffering from a nine page limit) you may find a better explanation of how the C-field relates to QM. As a result of questions and comments I've received about that essay, I've extended the approach and hopefully improved the theory. If the nonlinearity works as my preliminary calculations suggest, then it plays a greater role in particle physics than has been supposed. I hope to solve several specific problems in this area within the coming year.

Briefly, Einstein's full nonlinear field equations deal with almost 200 derivatives with 20 constants to be solved for. This, on top of the nonlinearity, makes the topic extremely nonintuitive. But the linearized equations resemble Maxwell's equations sufficiently to permit analogical thinking, upon which much intuition is based. I intend to be guided by this analogical thinking while adding the nonlinearity back into the problem in (what I hope to be) a computable approach to the problem.

I would very much like to keep in touch with you.

Thanks again and my very best regards,

Edwin Eugene Klingman

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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...

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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

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Dear D-r William,

I have read your interesting essay and I have find many common points with my confidence. First I want just emphasize that the ,,Copenhagen interpretation,, it just was the political decision only (and not scientific approach!) The long term troubles are start from here! However, your approach on the ,,chaos,, description of the behavior of QM object I see not so right because this concept (chaos) is just non applicable for the single object (as well as the ,,probability,,) The cause of nonlinearity, in my view, is hidden in the mutual deep interconnection of all possible parameters of Quantum object.

The nonlinearity may be represented as the classical transitional process, that is principally is possible to build on the base of wave equations. I am inclined to look your critical approach as very valuable. I hope you will find time to check my work Es text and we can continue talk.

Sincerely,

George

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basudeba mishra replied on Aug. 1, 2013 @ 11:02 GMT

Dear Sir,

We just happened to read a book written in the 9th Century by Jayant Bhatt titled "Nyaya Manjari", where in the Volume II, 8th Chapter page 294, he has discussed observer created reality to scientifically refute it. The book is in Sanskrit, but its translations in other languages are also available.

He argues: some people say that the objects exist only when we observe them. This implies the existence or non-existence of an object rests on whether we observe it or not. But nonexistence are of various types. There is prior nonexistence of an object before it is transformed from being to becoming (cause and effect). Thereafter, it exists independent of observation or otherwise. This gives rise to number sequence. There is temporary non-existence, which is related to its transformation in space or time independent of the observer. This gives rise to negative numbers. There is destruction or death, which is the opposite of prior nonexistence. Then there is non-commuting nonexistence like position and momentum: a fixed position implies nonexistence of momentum with mobile coordinates and vice versa.Lastly, there is the absolute nonexistence, which means, it is impossible as per physical laws like the horns of a rabbit.

Regards,

basudeba

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Hello Prof. McHarris,

Thank you for your informative essay. Your number A=3.82; could it bi closer to 3.829

This number fits better into my equation:

$\gamma= 2^{(cy+p+3t)/(2+2a^{2}m)}=1.0013784192$

Where mathematical constant are:

$2\pi=6.2831853, t=log(2\pi,2)=2.6514961295, cy=e^{2\pi}= 535.4916555248$

Physical constants:

$a=1/\alpha=137.035999074, \mu=1836.15267245,m=log(\mu,2)=10.8424703056$

Also:

$p=log(Mu/mp,2)=cy/2-(\mu/a+1)/(\mu/a+2)-1=265.8107668189$

I'd like to get your comment on my equation.

Regards Branko

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Having read so many insightful essays, I am probably not the only one to find that my views have crystallized, and that I can now move forward with growing confidence. I cannot exactly say who in the course of the competition was most inspiring - probably it was the continuous back and forth between so many of us. In this case, we should all be grateful to each other.

If I may, I'd like to...

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Dear William

I just read your interesting and novel essay. I think that nonlinear dynamics is gaining acceptation in physics in recent years. In particular, in fluid mechanics, optics, soft and hard condensed matter physics. You mention that nonlinear dynamics may give a different view of quantum mechanics. My question is whether the mysterious phenomena such as entanglement could find a common sense explanation. What are your thoughts on this respect; what would be the interpretation under the nonlinear approach of the two-slit interference and entanglement experiments?

Finally, I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis assuming that space is a nonlinear continuum medium.

I'll be looking forward to hearing any comments you may have.

Regards

Israel

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Dear William

It seems that my previous post was erased.

I found your essay very interesting and insightful. I'm interesting in understanding how nonlinear dynamics can explain quantum phenomena such as entanglement and the double slit experiment. I mean what would be the physical interpretation of those experiments. I would appreciate any comments you may have.

I think that you essay is of great impact and I have already rated it with the highest score.

I'd like to invite you to read my essay and leave some comments. There I discuss about Wheeler's dream and propose a potential way to get out of the present crisis.

I'll be looking forward to hearing any comments you may have.

Regards

Israel

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Dear Prof. McHarris,

Thank you for the very interesting essay that is also close to my ideas.

In afterword you claim: “Nonlinear dynamics and chaos theory shows us that disparate parts of nature are intimately linked together much more tightly than we could previously have imagined. Wherever there is feedback there is crossover. We could well be fooling ourselves with our “straightforward” linear, reductionist models. Could it be significant that chaos theory has had successes in almost every scientific field other than quantum mechanics…”

I would add something to this afterword:

The universe is a dissipative coupled system that exhibits self-organized criticality. The structured criticality is a property of complex systems where small events may trigger larger events. This is a kind of chaos where the general behavior of the system can be modeled on one scale while smaller- and larger-scale behaviors remain unpredictable. The simple example of that phenomenon is a pile of sand. When QM and GR are computable (during Lyapunov time only) and deterministic, the universe evolution (naturally evolving self-organized critical system) is non-computable and non-deterministic.

Best regards,

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Dear All

Let me go one more round with Richard Feynman.

In the Character of Physical Law, he talked about the two-slit experiment like this “I will summarize, then, by saying that electrons arrive in lumps, like particles, but the probability of arrival of these lumps is determined as the intensity of waves would be. It is this sense that the electron behaves sometimes like a particle and sometimes like a wave. It behaves in two different ways at the same time.

Further on, he advises the readers “Do not keep saying to yourself, if you can possibly avoid it. ‘But how can it be like that?’ because you will get ‘down the drain’, into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”

Did he says anything about Wheeler’s “It from Bit” other than what he said above?

Than Tin

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I've lost a lot of comments and replies on my thread and many other threads I have commented on over the last few days. This has been a lot of work and I feel like it has been a waste of time and energy. Seems to have happened to others too - if not all.

I WILL ATTEMPT to revisit all threads to check and re-post something. Your comment on my thread was one affected by this.

I can't remember the full extent of what I said, but I have notes so know that I rated you very highly.

Hopefully the posts will be able to be retrieved by FQXi as I left a thorough reply to your comments on my thread.

Best wishes,

Antony

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Dear William,

We are at the end of this essay contest.

In conclusion, at the question to know if Information is more fundamental than Matter, there is a good reason to answer that Matter is made of an amazing mixture of eInfo and eEnergy, at the same time.

Matter is thus eInfo made with eEnergy rather than answer it is made with eEnergy and eInfo ; because eInfo is eEnergy, and the one does not go without the other one.

eEnergy and eInfo are the two basic Principles of the eUniverse. Nothing can exist if it is not eEnergy, and any object is eInfo, and therefore eEnergy.

And consequently our eReality is eInfo made with eEnergy. And the final verdict is : eReality is virtual, and virtuality is our fundamental eReality.

Good luck to the winners,

And see you soon, with good news on this topic, and the Theory of Everything.

Amazigh H.

I rated your essay.

Please visit My essay.

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Hello Bill - I'm a seventy yr old lady so I can call you that !!!!

I love it that you question 'mainstream' & are looking for alternatives such as might be found in non-linear processes with their concatenating feedback - & feedforward - loops.

My own investigations have led me to conclude that ‘information’ is NOT digits – no kind nor amount of them (including any that can be...

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Author William C. McHarris replied on Aug. 7, 2013 @ 21:18 GMT

Dear Margriet,

THank you very much for your lovely comments. I truly appreciate them. And I must say your are very astute and have a lot of common sense — it gives a breath of life to this contest.

I read your lovely essay, and I agree with your views. (I also rated it highly.) As you gleaned from my essay, I am strongly in favor of an ontological, realistic view of Nature — I come down strongly on the side of Einstein in his debates with Bohr. And if quantum mechanics were to contain significant nonlinearities, it could well do away with the distinction between it and classical mechanics, which (almost!) all of us agree is ontological. Because time is short and the FQXi server seems to be slowing down, I'll reserve further comments both your your letter and to your essay until things have quieted down. (I think we can still make comments after the voting has ended.)

If by Antipodean you mean Australian, I spent a marvelous month there last fall, traveling to Sydney, Melbourne, Adelaide, and Port Douglas for the solar eclipse. A marvelous, beautiful — and friendly — country!

Best wishes,

Bill

Hi, votes are vanishing again.

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Hi, votes are vanishing again.

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Dear William,

Now is last day to completing somewhat our discuss and conversations.

I has find your work interesting for me, I have read it and has invited you to discussion (see my post above.) I did not get answer however. I think you was busy, just tired or with some other reason. Anyway, I must give my rating to your essay as really one good work, presented in contest that I have do.

Regards,

George Kirakosyan

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Author William C. McHarris replied on Aug. 7, 2013 @ 21:07 GMT

Dear George,

Thanks for your comments. I was late is getting started with my answers and have simply become overwhelmed. I did read your essay and rated it very highly. I'll respond more fully to your above comments in a day or two.

Best wishes,

Bill

Dear William,

Excellent and well written essay! I found your statement, "...beauty in equations does not make a theory true - or relevant. Only experimental investigation - and the ability of a theory to be falsifiable can do that" to be reflective of the findings of a 12 year experiment I have recently concluded. Although you have a different approach to the topic than I do, I found your essay to be insightful and intuitive and most worthy of merit.

I could go on and on... perhaps another time.

Best wishes,

Manuel

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Author William C. McHarris replied on Aug. 7, 2013 @ 21:05 GMT

Dear Manuel,

Thanks for your kind words. I really enjoyed your essay, as well, and I rated it highly. Since time is short and the server seems to have slowed down to a crawl, I'll respond more fully later.

Cheers,

Bill

Dear William,

I have now finished reviewing all 180 essays for the contest and appreciate your contribution to this competition.

I have been thoroughly impressed at the breadth, depth and quality of the ideas represented in this contest. In true academic spirit, if you have not yet reviewed my essay, I invite you to do so and leave your comments.

You can find the latest version of my essay here:

http://fqxi.org/data/forum-attachments/Borrill-TimeOne-
V1.1a.pdf

(sorry if the fqxi web site splits this url up, I haven’t figured out a way to not make it do that).

May the best essays win!

Kind regards,

Paul Borrill

paul at borrill dot com

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