Hi, John,

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

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

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

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

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

Again, thanks,

Bill

Dear William

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

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

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

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

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

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

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

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

Regards,

Than Tin

Hello, William,

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

Joseph Brenner

Brenner,

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

Amos.

Bill,

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

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

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

Regards,

John

Dear Vladimir,

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

Three quick comments:

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

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

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

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

Best wishes,

Bill

Dear Hai,

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

Best wishes,

Bill

Dear. Dr. Kadin,

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

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

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

Again, thanks and best wishes,

Bill McHarris

Dear William,

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

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

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

My best regards,

Edwin Eugene Klingman

    Dear Sir,

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

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

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

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

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

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

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

    Regards,

    mbasudeba@gmail.com

    • [deleted]

    • Post #45

    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

    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

    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

      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

      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

      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

      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

      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:

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

      Where mathematical constant are:

      [math]2\pi=6.2831853, t=log(2\pi,2)=2.6514961295, cy=e^{2\pi}= 535.4916555248 [/math]

      Physical constants:

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

      Also:

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

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

      Regards Branko

      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

      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,