Hi Doug

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.

Good Luck,

Than Tin

    Hi Akinbo,

    First sorry it took some time to reply -- I'm at my wife's family's home in a remote part of Thailand and my USB modem is slow. Anyway this is an interesting question about the reality of the Planck length. If one takes the physics we know at low energy as characterized by G, hbar and c (which can be combined to give a PLanck length, mass and time) one inevitably comes up with the Planck scale of 10^19 GeV, 10^{-44} sec or 10^{-35} m. But *experimentally* the only high energy scale we have directly tested is the weak scale which is at ~250-300 GeV. This was the jumping off point for the large extra dimension work of ADD which postulated that the true Planck scale coming from large extra dimensions was/could be much lower than 10^19 GeV. The last run of the LHC did not find evidence for these large extra dimensions.

    I'll mention more in this regard on your discussion page.

    Best,

    Doug

    Hi Than Tin,

    A very nice and correct quote by Feynman. And after all one of his biggest achievements was to re-formulate quantum mechanics/quantum field theory in the path integral formalism i.e. he found another way to "look at" QM.

    I very much like and appreciate analogies. One of my first works after grad school was to write down a Schwarzschild-like solution to the Yang-Mills equations using the analogy "GR and Yang-Mills theory are in some sense both non-Abelian gauge theories thus they should have similar solutions." The idea was that BHs provide confinement and thus these Schwarzschild-like solution of Yang-Mills theory might also provide the long sought after proper of confinement in QCD. The paper is "Exact Schwarzschild - like solution for Yang-Mills theories", D. Singleton (Virginia U.), Phys.Rev. D51 (1995) 5911-5914

    e-Print: hep-th/9501052. It turns out a Soviet physicist had discovered similar solutions about 20 years earlier ("Exact Classical Solutions of Yang-Mills Sourceless Equations" by A.P. Protogenov, Phys.Lett. B67 (1977) 62-64)). Actually (half jokingly) this is one thing one finds out about theoretical physics -- everything was done earlier and better by some Soviet/Russian physicist. Again this is half jokingly.

    About the use of analogies/dualities this is a very rich area of work. Almost every other paper these days has some reference to AdS/CFT which is a duality/analogy between Anti-de-Sitter space-time and conformal field theories. Thus many people appreciate dualities. I do not understand in which sense Planck's constant represents a duality so I'll go over and have a look at your essay. It may take a 1-2 days.

    Best,

    Doug

    Dear Doug, Elias and Tao,

    I just finished reading your essay. Your starting point is the previous result of Banerjee and Majhi (arXiv:0808.3688, arXiv:0805.2220) for the temperature of a black hole (eqn 7 in your essay) where backreaction is taken into account. The crucial point is your ansatz (eqn 9) for the form of the coefficients in the expansion of the quantum action in a power series in hbar, from which you obtain the regularized form of the entropy (eqn 10).

    If correct (and I haven't checked your calculations) then your result is of great importance. It would put on a firm foundation the notion that quantum mechanics and general relativity **can be** reconciled in a self-consistent framework. However, the work remains incomplete in that underlying your calculations is the implicit assumption that the continuous, commutative nature of spacetime remains the same at all scales. As Mittelman noted in previous comments, at some point non-commutative geometry should take over, leading to a black hole remnant as the end result of black hole evaporation. There should be some simple way to reconcile your calculations with those from the NC approach.

    Your work also likely has some connections with Ansari's work on black hole radiation in the framework of LQG (hep-th/0607081, arXiv:0711.1879). Overall your essay is very readable (except for the "public" who have a hard time following any mathematical arguments) and arguably deserves a place in the top three - if not at the very top.

    Cheers,

    Deepak

    Dear Douglas,

    One single principle leads the Universe.

    Every thing, every object, every phenomenon

    is under the influence of this principle.

    Nothing can exist if it is not born in the form of opposites.

    I simply invite you to discover this in a few words,

    but the main part is coming soon.

    Thank you, and good luck!

    I rated your essay accordingly to my appreciation.

    Please visit My essay.

    Hi Doug,

    Thanks for the very helpful and interesting comments over on my page and for the suggested reading here. I really liked your essay and think you deserve to do well, so hope my rating helps.

    Best wishes & kind regards,

    Antony

      Hi Anthony,

      No problem and if you read through the dimensional reduction stuff and want to discuss feel free although this is not my area but rather than my my colleague Jonas Mureika who got me interested in this and did explain to me some of the ins and outs of the idea. Actually Jonas also mentions that certain high energy cosmic ray events seem to be anomalously planar which they claim can be taken as evidence for dimensional reduction (if at high energy one has dimensional reduction then ones claims the decay products would only be distributed in a plane or line at higher energy. I'm not sure why kinematic effects would not do this, but Jonas and the authors of the paper he cites in the paper seem to think these events are odd and Jonas's explanation is dimensional reduction.

      Thanks and Best of luck,

      Doug

      Dear Douglas Singleton, Elias Vagenas, & Tao Zhu :

      I am an old physician and I don't know nothing of mathematics and almost nothing of physics,

      But maybe you would be interested in my essay over a subject which after the common people, physic discipline is the one that uses more than any other, the so called "time".

      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

      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

      Dear Douglas Singleton, Elias Vagenas, & Tao Zhu :

      I am an old physician and I don't know nothing of mathematics and almost nothing of physics,

      But maybe you would be interested in my essay over a subject which after the common people, physic discipline is the one that uses more than any other, the so called "time".

      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

        Dear All

        A standard-issue big city all-glass high-rise stands across the street from my usual bus stop. When I look up the high-rise facade, I can see the reflections of the near-by buildings and the white clouds from the sky above. Even when everything else looks pretty much the same, the reflections of the clouds are different, hour to hour and day to day.

        After I boarded the bus, I rushed to get a single seat facing four others on a slightly elevated platorm. From my vantage point, I can't help noticing the shoes of the four passengers across from my seat are not the same, by either the make , the design, or the style, and that is true even when the four passengers happen to be members of the same family.

        I could change the objects of my fascination from shoes to something else, to buttons on the dresses for example, but I do not think the result would have been any different. Diversity or Uniqueness would still rule the day! (There is a delightful essay on the subject of uniqueness by Joe Fisher in this contest.)

        I am pretty sure people are fascinated by the diversity and the uniqueness in the world, when the other side of it is the inevitable boredom of sameness every time.

        However, we have a need to know where all this beautiful and enchanting diversity comes from. Borrowing Wheelerian phraseology of "How come the quantum?", I ask "How come the diversity?" A standard physics answer is "Entropy always increases." (I am not a physicist, and I don't know if that is the final answer.)

        Whenever I'm out of my depth, I go back to my theory of everything (TOE), which is a mental brew of common sense, intuition, gut, analogy, judgement, etc. etc. , buttressed when I can with a little thought-experiment.

        The thought-experiment is simple. Imagine cutting a circle into two precisely, identical, and equal parts. Practically, there is no way we can get the desired result, because one part will be bigger or smaller in some way.

        Physics - especially quantum physics - says it don't matter, do the superposition!

        But superposition is fictive, an invention like the Macarena dance, and it has given us a cat, alive and dead at the same time.

        I have heard that angels can dance on the tip of the needle, and now I'm finding out some of us can too!

        Cheers and Good Luck to All,

        Than Tin

        Doug,

        Many thanks for the suggested reading - I will take a look. No panic about my essay - there are so many to get through - it is an enjoyable, but massive task.

        Best wishes,

        Antony

        Hello again Doug - sorry about the messages above too - going stir crazy trying to touch back with every thread I've commented on.

        I certainly will look at this.

        Thanks again and best wishes,

        Antony

        Hi Hector,

        Yes there are many ways to approach "time" -- Newtonian time, relativistic time, psychological time (how a person perceives time), etc. One of the most profound (in my opinion) people to deal with how people perceive and "store"/remember time was the French novelist Marcel Proust in his massive work "Remembrance of Things Past" which if one does a more direct rather than poetic translation is "Recovery of Lost Time".

        A colleague of mine at CSU Fresno, Bob Levine, has done studies of how people perceive time. He has a thesis which in simplified form (hopefully not so simplified that I misrepresent) is that all/most of what people do is done in order to "buy" more time or make a given amount of time more pleasant, exciting, relaxing etc.

        Anyway I will try to have a look at your essay.

        Best regards,

        Doug

        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

        Dears Colleagues,

        I have just ended to re-read your intriguing Essay. As I previously told you, it is complementary to my one and, in my opinion, it further improves the elegant approach by Zhang, Cai, Zhan and You. Thanks also to have stressed the importance of the black hole information paradox within the theme of this Essay Competition. In fact, there is some guy who strangely claims that it does not address the core questions of this Essay Contest.

        In any case, I enjoyed a lot in reading your Essay and I think that your results are of fundamental importance, not only for the core of this Essay Contest, but also for the whole theoretical physics. Thus, I am going to give you the top rate.

        Cheers,

        Ch.

        Douglas, Elias, Tao - congratulations on an outstanding essay. I'm glad I managed to read it and get my rating in to help before the end of the contest.

        I see a background of time assumption in your equations. I wonder what correlated photons of Hawking radiation would look like under the subtime interpretation?:

        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).

        Kind regards, Paul

          Best of Luck for the Magnificent Eight !

          I am throught the 180 essays, all rated. For me 2/3 of them were poor and other 1/6 curious. The rest (1/6) have I rated over 4/10.

          You are among the authors of the top essays from my sight - alphabetically :

          Corda, D'Ariano, Maguire, Rogozhin, Singleton, Sreenath, Vaid, Vishwakarma,

          and I hope one of you will be the winner. (Please, don't rate my essay.)

          David

          Hi Paul,

          A technical measure of the correlation, C, between photons of energy E_1 and E_2 emitted is given by the somewhat opaque expression

          C(E_1+E_2 ; E_1, E_2) = ln(Gamma(E_1+E_2))-ln(Gamma(E_1)Gamma(E_2))

          where Gamma(X) is the probability for a photon of energy X to tunneling through the horizon and appear as Hawking radiation. Essentially one is comparing emitting one photon with energy E_1+E_2 versus two separate photons E_2 and E_1. This is discussed in more detail in an early articl eon the subject by my co-author Elias. The exact reference is

          "Hawking radiation as tunneling through the quantum horizon",

          Michele Arzano, A.J.M. Medved, Elias C. Vagenas, JHEP 0509 (2005) 037

          e-Print: hep-th/0505266

          For a truly thermal spectrum the correlation function above is zero -- C=0 -- and one says the photons are uncorrelated. If C=/=0 there is some correlation.

          Now the next question how woul done check this experimentally -- until recently I would have said "I don't know" and in fact I still have to say this, but now I know where to look. There is a recent PRD article

          "Towards experimentally testing the paradox of black hole information loss"

          Baocheng Zhang, Qing-yu Cai, Ming-sheng Zhan, Li You (Tsinghua U., Beijing). Phys.Rev. D87 (2013) 4, 044006

          e-Print: arXiv:1302.1341 [gr-qc]

          which from the title and also abstract (the paper is downloaded and sitting on my laptop but still needs reading) promises to give a way to test the correlations of emitted photons. I'm not sure if the proposal is in terms of analogy systems or what but it is interesting and might be address your question about what correlated photons would look like in the lab.

          Best,

          Doug

          Hi David,

          Thanks for reading our essay the kind words and rating.

          Best,

          Doug