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  • 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,

    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

    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

    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

    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

    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

    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

    Dear Bill,

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

    Best wishes,

    Antony

    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

    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 express some of my newer conclusions - by themselves, so to speak, and independently of the logic that justifies them; the logic is, of course, outlined in my essay.

    I now see the Cosmos as founded upon positive-negative charges: It is a binary structure and process that acquires its most elemental dimensional definition with the appearance of Hydrogen - one proton, one electron.

    There is no other interaction so fundamental and all-pervasive as this binary phenomenon: Its continuance produces our elements - which are the array of all possible inorganic variants.

    Once there exists a great enough correlation between protons and electrons - that is, once there are a great many Hydrogen atoms, and a great many other types of atoms as well - the continuing Cosmic binary process arranges them all into a new platform: Life.

    This phenomenon is quite simply inherent to a Cosmos that has reached a certain volume of particles; and like the Cosmos from which it evolves, life behaves as a binary process.

    Life therefore evolves not only by the chance events of natural selection, but also by the chance interactions of its underlying binary elements.

    This means that ultimately, DNA behaves as does the atom - each is a particle defined by, and interacting within, its distinct Vortex - or 'platform'.

    However, as the cosmic system expands, simple sensory activity is transformed into a third platform, one that is correlated with the Organic and Inorganic phenomena already in existence: This is the Sensory-Cognitive platform.

    Most significantly, the development of Sensory-Cognition into a distinct platform, or Vortex, is the event that is responsible for creating (on Earth) the Human Species - in whom the mind has acquired the dexterity to focus upon itself.

    Humans affect, and are affected by, the binary field of Sensory-Cognition: We can ask specific questions and enunciate specific answers - and we can also step back and contextualize our conclusions: That is to say, we can move beyond the specific, and create what might be termed 'Unified Binary Fields' - in the same way that the forces acting upon the Cosmos, and holding the whole structure together, simultaneously act upon its individual particles, giving them their motion and structure.

    The mind mimics the Cosmos - or more exactly, it is correlated with it.

    Thus, it transpires that the role of chance decreases with evolution, because this dual activity (by which we 'particularize' binary elements, while also unifying them into fields) clearly increases our control over the foundational binary process itself.

    This in turn signifies that we are evolving, as life in general has always done, towards a new interaction with the Cosmos.

    Clearly, the Cosmos is participatory to a far greater degree than Wheeler imagined - with the evolution of the observer continuously re-defining the system.

    You might recall the logic by which these conclusions were originally reached in my essay, and the more detailed structure that I also outline there. These elements still hold; the details stated here simply put the paradigm into a sharper focus, I believe.

    With many thanks and best wishes,

    John

    jselye@gmail.com

    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