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

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!)?

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

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  • Post #67

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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  • Post #68

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

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 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 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.

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 extracted from quantum phenomena!), nor how algorithmically-well they may be massaged & shunted through any device that uses them.

Nor whether they are processed non-linearly !!

Unequivocally they - digits - make for wonderful COUNTING & CALCULATING assistants, witness our own now many & various, most excellent, counting, calculating devices BUT according to my investigations real thinking is an entirely different phenomenon from mere counting, calculating & computing.

For which phenomenon - real thinking - real information is required.

My own investigations led me to discover what I have come to believe real information is & as it so transpires it turns out to be an especially innocuous - not to omit almost entirely overlooked & massively understudied - phenomenon, none other than the sum total of geometrical objects otherwise quite really & quite properly present here in our universe. Not digits.

One grade (the secondary one) of geometrical-cum-informational objects lavishly present here in our cosmos, is comprised of all the countless trillions & trillions of left-over bump-marks still remaining on all previously impacted solid objects here in our universe - that is to say, all of the left-over dents, scratches, scars, vibrations & residues (just the shapes of residues - not their content!) (really) existing here in the universe.

Examples of some real geometrical objects of this secondary class in their native state are all of the craters on the Moon. Note that these craters are - in & of themselves - just shapes - just geometrical objects. And the reason they are, also one & at the same time, informational objects too, can be seen by the fact that each 'tells a story' - each advertises (literally) some items of information on its back - each relates a tale of not only what created it but when, where & how fast & from what angle the impacting object descended onto the Moon's surface. Again, each literally carries some information on its back. (Note : Not a digit in sight !!)

How we actually think - rather than just count, calculate & compute - with these strictly non-digital entities, specifically these geometrical-cum-informational objects, in precisely the way we do, please see my essay.

Yes, geometrical-cum-informational-objects do, indeed, get processed non-digitally by our brains - & I'm quite sure that many of these processes are thoroughly non-linear - with massive amounts of feedback/feedforward loops, but which processorial work results in 'collations' - not in SOLUTIONS TO 'algorithms' or arithmetical or algebraic calculations - just collations - just 'regroupings' of select geometrical objects according to pre-established re-grouping (collating) protocols !!!!!

I did not make the distinction between computing with digits & real thinking with real information, sufficiently strongly in my essay.

This contest is such a wonderful 'sharing' - Wow - & open to amateurs like myself - Wow. How great is that !!! Thank you Foundational Questions Institute!!! What a great pleasure it has been to participate. What a joy to read, share & discuss with other entrants !!!

Margriet O'Regan

    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

    Dear Vladimir,

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

    Best wishes,

    Bill

    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

      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

      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 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

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      • Post #81

      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

      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

        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