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  • Post #11

Dear Michael, After having a look at your ideas in this essay, I find their correlation with my own solution to the problem of mathematical and physical incompleteness. One can probably say that I propose a particular version of "hidden" quantum dynamics you derive by the general incompleteness analysis. Those hidden dynamical dimensions result simply from the unreduced interaction problem solution (never obtained in usual theory) and exist also at all higher complexity levels, giving rise to the omnipresent (but sometimes indeed externally "hidden") dynamic randomness. As to Gödel's incompleteness, it doesn't exist any more within that causally complete mathematical framework, but can also be considered, within any particular system/level study, as the necessary dynamical links to neighbouring interaction/complexity levels. I hope that such kind of extension of traditional science framework can attract the attention of other researchers, leading to various stagnating problem solution and further knowledge progress...

    It's a strange login system here,:) the previous comment was mine, of course.

    Wonderfully excellent Michael..

    I like that you spell out both applicable interpretations of Korzybski's map / territory paradigm, and how it relates to the essay question. I also like that you make the connection with the normed division algebras explicitly explained, as part of the backbone of Physics.

    And finally; I find your explanation of why the interaction space and observability space have differing domains to be satisfying, and the explanation of why this accounts for things via the hidden dynamics of the propagators mostly lucid. It is good to know there is an actual reality, even if its dynamics are somewhat hidden.

    All the Best,

    Jonathan

      Dear Michael,

      You mentioned "Physics realism: physics is the territory and maths is the map

      Maths realism: maths provides the territory and physics is a map"

      Thats true and its is because there are existing laws of invariance which governs both mathematical structures and physical reality. Its not mathematics describing physics rather their respective laws of invariance match each other.

      In context of Skolem paradox, that's the reason why sometimes athematics and physics describe each other sometimes right(when they match) and other times wrong(when they don't match)."A particular model fails to accurately capture every feature of the reality of which it is a model. A mathematical model of a physical theory, for instance, may contain only real numbers and sets of real numbers, even though the theory itself concerns, say, subatomic particles and regions of space-time. Similarly, a tabletop model of the solar system will get some things right about the solar system while getting other things quite wrong."

      Mathematical Structure Hypothesis by me which states that Mathematical Structures and Physical Reality both originate from Vibration and that makes it possible for one to describe the other. Thats why Godel's Incompleteness theory indicates towards the fact that "In any axiomatic system of mathematical structure, there definitely will remain at least one statement(e.g. concerning self reference),where there will be required intervention from physical realities." And thats why we see that physical theories e.g. string and other theories are used to crack toughest riddle in number theory and other disciplines of mathematics. Riemann Hypothesis is a vibrant case. And vice versa from physics to mathematics(no-go-theorems) which you have classified in two categories of realism.

      If we combine Skolem with Godel what can come out that "Inconsistency/Incompleteness in one frame/world can be made consistent in other frame/world." Godel Incompleteness and axiomatic paradoxes basically reveal that though mathematical structures and physical reality having same origin why we allow time and frame of reference in physical reality but not in mathematics. This limitation leads to such conflicts.(which I have explained in my essay). I want to lead mathematics to evolve and expand in that direction.

      As far as you referred to Bell's theorem and EPR paradox about the no-go theorem in physics, let me quote references from my essay by David Bohm, former associate of Albert Einstein

      "The interrelation of human consciousness and the observed world is obvious in Bell's Theorem. Human consciousness and the physical world cannot be regarded as distinct, separate entities. What we call physical reality, the external world, is shaped - to some extent - by human thought. The lesson is clear; we cannot separate our own existence from that of the world outside. We are intimately associated not only with the earth we inhabit, but with the farthest reaches of the cosmos."

      Entire Universe exists within an atom and the same atom exists within the Universe. David Bohm maintains that the information of the entire universe is contained in each of its parts. This is because of Vibrational origin of External clasical world, which is fundamentally Quantum effect only .(I have tried to explain in my essay). This peculiar geometry leads to Bell's locality -at-distance and EPR paradox. This is related to geometry beyond Russell's paradox . It is possible that A is a subset of B and B is the subset of A in different reference frame and time . But constraints in mathematics in the dimension of time and reference frames leads to contradictions, paradoxes.

      This is what Swami Vivekananda who hinted at relativity theory decade before Albert Einstein and great scientist like Nicholas Tesla, Bose used to take guidance from him.

      'Time, space, and causation are like the glass through which the Absolute is seen. ... In the Absolute there is neither time, space, nor causation.' -Swami Vivekananda.

      The modern science which binds witself within the periphery of TIme,Space, Causation is trapped in the Bell's locality-at-distance andEPR paradox in Quantum Physics.

      Nic Herbert, a physicist who heads the C-Life Institute, suggests that we have merely discovered an elemental oneness of the world. This oneness cannot be diminished by spatial separation. An invisible wholeness unites the objects that are given birth in the universe, and it is this wholeness that we have stumbled into through modern experimental methods. Herbert alludes to the words of the poet Charles Williams: "Separation without separateness, reality without rift."

      It would be a mistake to suppose that these effects operate only with relevance to the invisible world of the atom. Professor Henry Stapp states that the real importance of these findings is that they translate directly to our microcosmic existence, implying that the oneness that is implicit in Bell's Theorem envelopes human beings and atoms alike.

      The interrelation of human consciousness and the observed world is obvious in Bell's Theorem. Human consciousness and the physical world cannot be regarded as distinct, separate entities. What we call physical reality, the external world, is shaped - to some extent - by human thought. The lesson is clear; we cannot separate our own existence from that of the world outside. We are intimately associated not only with the earth we inhabit, but with the farthest reaches of the cosmos.

      I have mentioned these things through references

      Anyway your essay is great.

      Regards,

      Pankaj Mani

      It is a beautifully compelling argument, Michael!

      As we already knew, you and I agree on two critical points that cut against the grain of most interpretations of conventional quantum theory:

      1. Bell's theorem experimental results only prove their own prior assumptions, such that there can be no correspondence between mathematical theory and physical result.

      2. A unified theory is necessarily extra-dimensional.

      My own essay deals with (1) and not the other -- so I am happy to see you pick up the topological argument. It was an enjoyable read.

      You should get the high score you deserve -- we need more publications that take the EPR argument seriously. I like your strategy of deconstructing Bell.

      All best,

      Tom

        Dear Michael,

        Your effort to re-establish causality in the interpretation of QM measurements should certainly be applauded.

        You write "Any serious definition of physics is based on causality" so that for "continuous fields" "if a theory has non-NDA-valued fields, then it's not physics." But in my understanding of QM (the theory) there is no causality although they may exist some sort of determinism. You are introducing the idea of propagation of the causation. I don't understand how it can be reconciliated with the mere existence of EPR pairs and entanglement unless there exist something like instantaneous causation. In my understanding of QM the concept of preparation of the instruments is fundamental (orientation of the polarizers...) and this is modeled with operators/observables whose ompatibility/commutativity predetermines the possible issues of measurements. The source of the paradoxes lies in the possible incompatibility between the algebra of operators and that of eigenvalues (as well explained by authors like Peres, Mermin and others). In QM the arguments are counterfactual which is just the opposite of causality.

        Is there a way to distinguish your 'causal approach' and QM approach? I have to admit that I did not read your other essays on this subject.

        Best regards,

        Michel

          Dear Michael,

          You say of the distinction between underlying-reality and experimental reality: "In simple terms, the distinction is because experiments are just too slow to measure what is happening."

          But I ask, isn't this distinction rather because experimental reality is necessarily incomplete in that it must be at any instance carried out with one and only one base unit of/or measurement out of the infinitely many there can be?

          My essay adopts the position that there can be one and only one de facto observer. So the human term "observer" is like the mathematician's "constant" (number bases) or the physicist's "quantum" [of observables]: there can be one and only one effective.

          This does not in principle invalidate every other observer, it only means that the "observer" state is what separates the real from the virtual (it is the Heisenberg CUT so to speak). It is the singularity. Indeed the state "observer" should be what we mean by a conservation law or "stationary state" (think: harmonic oscillator) or simply "invariance" .

          This will mean quite frankly that your underlying reality must be ontology wise the "nothing-in-particular" (the virtual or entropy or uncertainty), same in fact as any observer state. It is the "nothing" which defines things. For we cannot actually define matter with material attributes. Just as we do not define the coulomb with a coulomb or the joule with a joule etc.

          We must define "things" (ontology) with "nothing" (null ontology), and vice versa.

          Will appreciate your critical comment at my essay.

          Chidi

            Andrei,

            I too hope that the approach you have developed will attract the attention of other researchers. Your work has certainly got my attention.

            Micahel

            Thank you George.

            You're right that your essay explores a similar issue. In 2012 I wrote a paper that used Gödel's incompleteness theorem to succeed where Ludwig Wittgenstein failed. His second line in Tractatus Logico-Philosophicus was a statement of maths realism:

            1.1 The world is the totality of facts, not of things

            that incorrectly led to the conclusion:

            7 What we cannot speak about we must pass over in silence

            If we instead start with physics realism then we correct his conclusion to read:

            What we cannot speak about in direct terms we must describe another way.

            The physical systems that suffer this description problem are the self-referential systems that Christine Cordula Dantas discusses in her essay, and another way of describing such irreducible systems is given by Andrei Kirilyuk in his essay. In my 2012 FQXi essay I described how quantum theory itself was also "another way" of describing the physical world because a particle is itself a self-referential dynamic system.

            Michael Goodband

            Thanks Tom.

            I would characterise my strategy as extending and complimenting Bell's hidden variable theory approach because his indirect assumptions preclude certain physical possibilities. His main target seemed to be the EPR desire to banish probabilities from physics and restore determinism. My hidden propagator dynamics approach reaches exactly the same conclusion on this point - determinism in experimental predictions is gone forever. I don't have any problem with what Bell did; the issue is that his conclusion doesn't have the status of universal generality claimed for it - it is on this that we agree.

            My HPD approach extends Bell's analysis in a new and interesting way that leads to inevitable conclusions when the logic is followed in physics. My intention was to reach for those conclusions, of which one is that a "unified theory" is inevitably extra-dimensional. The other big conclusion that I didn't have room to discuss in my essay is to do with the nature of locality in underlying reality and experimental reality.

            All the best

            Michael

            Michel

            Unfortunately the essay length restriction prevented me from getting to the issue of locality, which is that causal propagation (i.e. less than/equal c) in underlying reality doesn't necessarily always result in time-like separation of experimentally measured events. In empty space, it does necessarily follow. But that is one of my points - the space of a spin singlet is not empty. In physics, SU(2) is the rotation group of physically linked objects. A non-quantum theory origin for physical objects with SU(2) rotation group is as spatial topological defects in a higher dimensional space, where the physical linkage between the objects is through the higher dimensional space. In 3+1 dimensions the space around such objects will have a characteristic feature that alters the relationship between causal propagation and space-time separation - namely the signature of the space-time metric changes sign (see Kerr metric).

            After the HPD section I then discuss the form the HPD theory would have to take in order to reproduce other experimental results: namely that a particle would have to be described as a self-referential particle reaction network in underlying reality. For the scenario of topological defect/antidefect pairs that all possess a region of space-time where the sign of the temporal part of the metric changes sign, this would result in a difference in how locality in underlying reality looks in experimental reality. If you add up a path of causal propagation that goes through equal paths in space-time where the sign of the temporal part of the metric is +1 and -1, then the result is a space-time separation of simultaneity between the beginning and end of the path. Thus strictly causal propagation in underlying reality can lead to apparent simultaneity in experimental reality. This is what underlies the locality issues with quantum theory, where we cross over between the underlying causal reality and the world of experimental measurements.

            This is conceptually the tricky bit, and could fill a FQXi essay itself. With this last feature, a HPD theory will reproduce all the features of quantum theory. The point I have been making in my 2012 FQXi essay, Agent Physics and this paper is that quantum theory is inevitably how you have to describe the underlying physics for the purposes of experimental predictions in physics.

            Michael

            Dear Chidi

            We have a fundamentally different metaphysical view of reality: maybe the difference between physics and philosophy of physics. In my essay I take the physics of the running coupling constants and the relations between the physical constants h-bar, c and G at face value as saying there is new physics on the Planck scale. Since the Planck time is far less than the interaction time of any experimental measurement, we have the condition that there is effectively an underlying reality that happens on a scale too small and fast to be measured - thus our experimental reality is not directly measuring underlying reality. So my distinction is a conclusion of the physics realism view that there is such a thing as physical reality - independent of our definitions and observations of it - and we measure it: underlying reality is reality, we just don't see it directly as it is.

            Michael

            Dear Michael,

            Thank you, I cannot escape understanding your 2012 essay and other writings from you. I like eccentric ideas as soon as I consider them scientifically sound. Then "it is the rule of the game" I will try to be honest in rating your essay.

            Best regards,

            Michel

            21 days later

            Dear Michael,

            I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

            All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

            Joe Fisher

            5 days later

            At it its core, math is about numbers. Natural number arises from counting orders and naming convention for the uniqueness of a places in a sequence. In that sense, the physical world is a book written in natural numbers.

            Using an analogy, the English alphabet has 26 letters, and with the alphabet infinite books can be written. We examine the books and find that each book consists at least one of the five vowels, and each word is less than 100 letters long, and so forth.

            We are puzzled by how a random book can be that way. But need not be so, if we realize that the rule of writing a book is quite simple although the end product is somewhat complex. We start with a letter, then a word, and then a passage, a chapter and so on. Each step has some simple but irreducible rules. This process masks the simple relationship between a book and the alphabet, if we simple look at them without the steps in between.

            rujing_tang at yahoo com

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