Essay Abstract

All different formulations of Quantum Mechanics show that Quantum Reality do not obey some laws of classical logic. So far, this has been seen more as a curiosity or as a deficiency in our models. However, Quantum Computation results show that these non-classical logic features are not just a deficiency in our models, but the true essence of Quantum Reality. Once we accept this, we should start using non classical logics, not just to measure, but also to understand Quantum Reality. The first consequence of this, it is that widespread notions like those of Planck Scale limit, the Measurement problem and the Discrete vs Continuum duality, become non-sense concepts in a non-classical logic conception of reality. Until now it seems we have unconsciously ignored that properties of the structures we study depend on the principles of logic we employ in studying them. Fortunately, when we use this non classical logics to UNDERSTAND reality, their semantics open new shocking perspectives to relate General Relativity and Quantum Mechanics.

Author Bio

I am a mathematical physicist mainly interested in Geometry and the Foun- dations of Physics and Mathematics. Nowadays I am finishing my Ph.D. in Mathematics at the University of Florence. I am working on the simplification of a possible Topos theoretical foundation of physics and I am also trying to understand if topology could be a dynamical feature of reality using results from low dimensional topology .

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  • Post #2

Dear John Benavides,

I wish all the best to you. You will certainly successfully finish your PhD. After a while you will get aware that the already announced some years ago delivery of the first functioning as promised quantum computer will be further delayed. Do not worry, you will find excusing technicalities in a good essay from a previous contest.

Do you have an alternative? Perhaps not a rewarding one. You could read my essay that deals with the same matter as yours but arrives at a rejection of the usual topoi and the like. I see a considerable part of progress in physics available by revelation of very basic mistakes even in mathematics rather than lazy mutilation at will of logics. So you might train your ability and refute my apparently bold

ideas . Please do not hesitate. Any factual attack is welcome.

Regards,

Eckard

Dear Eckard Blumschein

Thank you for read my essay.

I think, you are misunderstanding something. You cannot separate mathematics and logic. If you are saying you have found some problems with some basic notions in mathematics it is because the logic that you are using to think about these notions do not agree with the logic that define and govern them. I read your essay and what you see as problem is because you are unconsciously denying the excluded middle principle of classical logic that allows to abstract numbers with the limit point of the extension they represent. I agree with you extensions are more fundamental, but what you are ignoring is that if you say we should not identify extensions with its points, what are you saying is that we shouldn't use classical logic to describe the continuum, that kind of misconceptions is what my essay is about. On the other hand you don't need a quantum computer to justify that quantum reality is ruled by a non classical logic, you just need a half-silvered-mirrow and light to construct a a machine that cannot be described using classical logic.

Regards,

J.B.

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    • Post #4

    Hi John,

    Thank you for sharing your essay. I liked it, but found myself catching on one point that I'm keen to hear your opinion on. While the kind of mathematical tools you describe sound like an excellent way to understand and extend thinking on quantum mechanics, are you *certain* that, as you put it to Eckard, 'you only need a half silvered mirror and light to create a machine that can't be described using classical logic'.

    If there existed an algorithmic model using classical logic which produced the kinds of result seen in the double slit experiment, or a Bell-inequality violation, or some other clear example, would that not constitute a refutation of the *need* for such forms of logic. (Please note that I make a distinction between need and usefulness. The approach you outline certainly seems useful.)

    My thanks in advance for any opinions you may choose to share,

    Alex

      Dear Alex

      Thank you for reading my essay.

      About your question, the problem is the following: using a machine based on half silvered mirrows, we can create a machine that simply takes a proposition and as result give its negation. You can create a machine without quantum mechanics which does the same ruled by classical logic. The problem is that you cannot explain with classical logic why the first machine gives the results it gives. To understand how the first machine works you need quantum mechanics i.e a new logic. I recomend you to read the paper of David Deutsch that I cite in my essay, it is a divulgative work very short that explains everything very clear I am sure you will enjoy it a lot.

      Thanks again for your comments, let me know if I answer your question or if I misunderstand something.

      J.B.

      Hello John, I was only able to skim read your essay as I'm not as technically or mathematically minded as you are. I was impressed with your biography in stating that you are considering a dynamical feature of reality w.r.t a topology. I have a simple idea which might interest you. Have you ever considered an Archimdedes screw as the mechanical model of a GRAVITON? If this particle/wave helical structure travelled around a wraparound universe then it would emerge on the other side as an ANTI-GRAVITON, or in other words, DARK ENERGY. It's too good a model to be ignore for any longer imo. Did Newton miss this simple trick?

      Best of luck.

      Alan

        Dear Alan

        Thank you for your comments

        I think at the end we will discover that we should not quantize gravity, probably there is nothing like a graviton. In the terms of my essay what I think is gonna be the solution is that the intrinsic structure of quantum reality will tell us why on the big scale we see a spacetime where matter is ruled by the curvature of the spacetime. I hope you will try to read again my essay to understand what I am trying to say with this.

        J.B.

        Dear John,

        I read your paper with interest. I have a question about an intriguing statement you make: 'For the first time we will be able to understand that if quantum reality were not chaotic and non deterministic, probably our classical world would not be so smooth and well behaved.' I wonder if you could elaborate on this. It seems plausible, but I would like to understand better why you think this should be so. Perhaps it is related to the example you give immediately after, the example of DNA as a "lower level simple universe" expanded into the complexity of a living organism? If so, I would point out that DNA acts not unilaterally, but in concert with the environment, to "unfold" the organism. It is already, then, a very complex "universe"!

        I suspect that relations of one form or branch of mathematics to another can provide important insights about the physical world, by analogy, as you are pointing out. But unless one believes that mathematics is identical to the physical world, any exact mapping of mathematical truths to physical reality remains an assumption, an idealization.

        Thanks and best wishes,

        Dan

          Dear John,

          Quantum mechanics is only mysterious theory as long as we cling to causality. The flaw of causality is that if we understand something only if we can reduce it to a cause, and we can understand this cause only as the effect of a preceding cause etcetera, to end at some primordial cause which cannot be reduced to a previous cause, then causality ultimately cannot explain anything.

          If in a universe which creates itself out of nothing, particles have to create themselves, each other, then (the properties of) particles must be as much the product as the source of their interactions, their energy exchange. As the same holds for force between them, a force in principle cannot be either attractive or repulsive. That is, particles can only exist, have properties (attract/repulse) if they have some kind of backbone so they can, within limits, absorb energy in an increase of their kinetic energy rather than in a change of identity. However, if the rest energy of particles ultimately is as much the product as the source of their energy exchange, of their behavior, then interaction energies obviously never can become infinite at infinitesimal distances.

          A universe which finds a way to create itself without any outside intervention can hardly stop doing so: gravity, the contraction of masses and the related expansion of spacetime between the mass concentrations they form, is the expression of this continuing creation process. As long as we cling to the causal, classical 19th century ideas about mass and charge, to the belief that particles only are the source of fields and forces, we condemn ourselves to waste our time on string theory and Higgs bosons. I'm afraid that physics has become too opaque a mixture of truths, half-truths and inconsistencies, to be able to solve any fundamental problem at all. For details, see my essay.

          Best regards, Anton

            Dear Dan

            Thank you for your comments.

            About your question what I am trying to say is that we should stop thinking that at some limit, reality is not anymore classic to become quantum, this is a notion that has sense if we conceive reality within classical Logic. But once we accept other logics, for example a intuitionist one, the classic limit notion looses any sense. The example I give in the essay show then how to relate two realities (logics) in a more fundamental level a new kind of limit if you want. In this conception is the intrinsic structure of the non-classical logic world (fluctuating quantum reality) which determined what the classical-logic world sees (smooth, well behaved classical reality). You are right about the DNA example, what I am trying to say is that this new way of relate two different level realities could be useful to explain some phenomena that we see now as emergent phenomena, the DNA case is probably more complicated as I said but the idea opens new perspectives.

            Finally your concern about mathematics is valid, but for example Einstein was able to develop general relativity because Minkowski gave him a mathematical powerful abstraction, this is what quantum mechanics is missing and is what I am trying to develop.

            Let me Know if I answered your questions.

            J.B.

            Dear Anton

            You are right, there are a lot of problems to conceive reality if we insist using notions based in our classical-logic conception of reality. The causality problem arises because we describe evolution problems using Cauchy problems that cannot be conceived without initial conditions. Once we accept that classical logic (and then classical mathematics) cannot be used to abstract more profound problems, we will find new ways to understand causality and many other phenomena that cannot be explained in the classical framework.

            J.B.

            Yes, thanks, John.

            I am still trying to see if there is more to understand in the relationship between a chaotic non-deterministic quantum world and the smoothness and orderliness of the macro world.

            Dan

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            • Post #13

            Hi John,

            Thanks for pointing me at the David Deutsch paper. I greatly enjoyed it, and went on to make sure I understood the idea of the Mach-Zehnder interferometer upon which the work appears to be based. The interferometer seems a tidy application of the idea of particle self-interference.

            Particle self-interference is something I believe I can model. By this I mean that I have a simulation in which a particle travels through two slits and interferes with itself to produce a pattern of fringes on a screen of detectors. When I move a detector two one of the slits, I get occasional detections at that slit, and the interference pattern goes away. This program uses no complex numbers or wave equations. All its logic is classical and algorithmic.

            You seem like a someone with a strong grasp of the logical implications of QM, and also someone for whom my claim will sound deeply unlikely, or at least that's what I'm hoping.

            Would you be interested to see a short video of interference in action or discuss the ways in which my simulation might be flawed. I'd like to refute it's potential if possible.

            My thanks in advance in any thoughts or opinions you may have.

            Alex

            (An outline of the algorithm used is provided in my essay if you're interested. The effect is achieved by employing a different, but still entirely classical, notion of locality.)

              Dear Alex

              I read your extraordinary essay. The coincidences with what I am trying to propose are so shocking that my legs are trembling. I try to explained why, I think you have the information I am missing. The discrete models that you are proposing are just a partial description of the order I am trying to find, that it explains why we see the properties of the classical world we see. Particularly, the fact of no locality in my approach is expressed by the fact that when we collapse to a classical world we are taking a generic ultrafilter on the order topology which is a global fact. The way you relate the nodes of the graph is just the structure of the order, for example, the Continuum Hypothesis example shows that if the order is not choosen right, we don't get the result in the classical world, this is what it is happening in your models. When you say how we should iterate your models what are you doing is describing how the order topology should behave locally, i.e. you are choosing the ultrafilter.

              Finally your concern about the logic we should use it is missing something. We already use classical logic to describe and model quantum reality, it is what the classical approach does, but we can't understand very well quantum reality. What you do is construct your model by try and error and you try to explain why some iterating model gives the result you are looking for and others not. Why I am trying to say is that, if we introduce non classical logics, in my case a intuitionist one, we can explain these phenomena perfectly.

              I would like to hear your opinions again.

              J.Benavides

              John,

              To one with a meager understanding of higher math, your argument is esoteric and difficult to comprehend.

              Mathematical models certainly help to understand the parts of reality we are modelling but I can't see them as a substitute for reality, and that reality takes on the models characteristics.

              I contend that we can't truly know reality but that simulations can aid in the effort, but my deficiencies in math may taint my opinion.

                Dear James

                Thank you for your comments.

                I hope you will give me another chance and you will try to read my essay again. I understand your concern about the role of mathematics. Mathematics can become dangerous if they become the objective, and their beauty, an intrinsic justification. This for example is what it is happening with string theory and topological quantum field theory. What I am trying to propose is different because the motivation is to understand better reality, in this sense mathematics could be the key, as the curvature was the Key that Einstein used to create General Relativity. I know that what I am proposing sounds very weird because it have never been used in physics before, like Lorentzian manifolds where never used before Einstein, but I think I am giving strong arguments to justify my choice I think what I exposed is what we are missing and the main reason because the unification program has failed.

                J. Benavides

                7 days later

                John

                I found your essay highly intuitive and logical, even as one who'se looked elsewhere but maths for logical solutions. You said; "If we can get a model of quantum reality in this context, for example taking as the base space some kind of causal set, we will have a complete description of the hardware."

                I have tried using what we CAN be reasonably sure of at the small scale, to pattern match with the classical, and derived what looks worryingly like a toe, and which I can't disprove. I hope you may rad my essay and can follow the logic. Yours deserves a higher rating and I'll oblige. I hope you may feel the same of mine, though poles apart in viewpoint we observe the same reality.

                Best wishes

                Peter

                  Dear Peter

                  Thank you for your comments.

                  Reading your essay and also reading the essays which propose a digital model based on a discrete lattice and computation, I see that the discrete features that you describe together with the discrete features of the digital-computer approach are converging with my ideas but in my context can be explained in more deep level as the construction of a variable-set structure on a partial order. It would be interesting if you try to considerate your approach from this point of view, to see if you find new interesting explanations or motivations.

                  J. B.

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                  • Post #19

                  Hi to both of you,

                  I agrre with Eckard, the maths are cool and essential but when the physicality want be explained, of course the rationalism of our continuity and our discreteness become so important.

                  The topos of Mr Baez is for computing and its sortings, for the physicality it's an other story.All that to say that in fact we can't confound a simulation on computer and on the other side the real physical dynamic in 3 Dimensions. The maths imply so many confusions about our physicality, a time travel, the external cause of mass as higgs, the multiverses, the strings and this and that...all that is a pure irony for the rationalism and its axiomatization of physics and its pure laws.

                  The computing is a tool, an of course we can invent topologies or the topology...that is the question.

                  This difference is essential at my humble opinion.

                  Regards

                  Steve

                  Dear John,

                  Your essay interested me with its desire to explain reality through a pure analysis of quantum behavior by eliminating remaining classical concepts left in the theory. That seems like a logical and perhaps necessary step if it is to produce a satisfactory unifying theory. The introduction mentions gravity but it is not mentioned again in the rest of the essay. Is gravity expected to be explained by the history of the causal sets? Would that be the same as considering gravity as something we cannot evaluate in the non-collapsed quantum state, and gravity only appears in the collapsed humanly visible state?

                  I see your essay making a valid logical argument which makes it very interesting. My own approach is very similar in requiring the theory to be explained simply in terms of its core assumptions. It is interesting how our core assumptions are different, but I want to say I highly value your ideas.

                  Kind regards, Russell Jurgensen