Essay Abstract

It is widely believed that mathematics provides the fundamental basis for physics. On the contrary, it is argued here that pictures of real objects moving in real space provide the proper basis for physics, and that mathematics merely provides quantitative models for calculating the dynamics of these objects. Such models may distort or even hinder the development of new physics, particularly if a consistent physical picture is lacking. This is discussed in connection with quantum mechanics, which discarded realism in favor of mathematical abstraction almost a century ago. A realistic, spin-quantized wave picture of quantum mechanics is presented that avoids the paradoxes and abstractions of the orthodox quantum theory. Quantum indeterminacy stems from an inappropriate application of a statistical point-particle model to extended soliton-like wave packets. Quantum transitions are continuous, rather than the abrupt transitions of the Hilbert space model. Quantum entanglement is an artifact of mathematical constructions incompatible with local realism. These are not merely matters of philosophical interpretation; several experimental implications are presented. It is time to remove the mathematical blinders that have prevented consideration of realistic quantum pictures.

Author Bio

Alan M. Kadin has been thinking about quantum foundations for 40 years, since his Princeton undergraduate thesis on hidden variables in quantum mechanics. His Ph.D. in Physics at Harvard was on superconducting devices, followed by postdocs at SUNY Stony Brook and University of Minnesota. Dr. Kadin pursued a research career in superconducting devices, in both industry and academia, at Energy Conversion Devices (Troy, MI), University of Rochester, and Hypres, Inc. (Elmsford, NY). He has been submitting FQXi essays since 2012.

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Dear Alan,

Thank you for your pleasurable contribution, As you highlighted, I agree that: "It is time to remove the mathematical blinders that have prevented consideration of realistic quantum pictures".

"... admonition has become virtually religious dogma, and must change if physics is to advance".

What happned at the time when Galilei lived should not be repeated, and as i been reading the essays here; generally it is accepted by many that, it is time to start changing the attitude towards physics and begin with a new spirits. As I been addessing in my essay, math and physics only intersect in certain extent, and queries like emergence of consciousness in particles are hardly touched in physics among other discrepancies. To have a broader picture there is a need for suppliments and a convergence between physics, life science and our consciousness and also realising the fact that we live in a discontinuous world.

Warm regards

Koorosh

    Dear Koorosh,

    Thank you for your comments. I will read your essay.

    My key point is that the paradoxes of quantum mechanics are a clear indication that something is seriously wrong in the hybrid mathematical models used as the basis for quantum mechanics. The simple realistic model that I have presented makes predictions for experimental results that differ from conventional quantum theory, but apparently have never been tested.

    The theoretical physics community is in denial about the shortcomings of quantum theory, believing that it must be correct because there is a mathematical formalism. I am reminded of the story of "The Emperor's New Clothes," in which the emperor's new suit is in fact non-existent, but (almost) everyone claims to see it, because the authorities have convinced them that it is visible to anyone who is not stupid.

    Well, Einstein never accepted the non-realistic aspects of quantum theory, and I think Einstein was right.

    Alan

    Dear Alan,

    The majority of the mainstream physicists view that we can explain the physical world using logic based on mathematical relations, rather than logic based on the physical properties. But you propose the alternate approach. From the essays that are posted here, it appears that so many people have the same idea as that of yours. I am also one among them; I will call this a 'physicalist' approach. My essay will be posted soon.

    Jose P Koshy

      The ``pilot wave'' model is silent on the source of the pilot wave. In your model, what is the source of the wave?

      I by ``picture'' you mean a conceptual model consistent with human scale experience, I agree.

        Dear Alan Kadin,

        Thank you for entering your first-class essay in this is contest. I am in full agreement with almost everything you say. Most particularly with your emphasis on nonlinearity, typically masked by Hilbert space linearity.

        You focus on replacing the QM physically unreal linearly polarized (LP) superposition of R and L wave functions for a photon, with physically real circularly polarized (CP) photons. The analog for particles is the superposition of 'spin up' and "spin down' states with striking formal resemblance to the QM LP model of the photon.

        A nonlinear internal circulation of flow within the local field that is sustained and has the approximate behavior of a (non-point) local peak intensity can, FAPP, be conceived of as a 'particle' (or at least a dipole) in the localized wave. This intrinsic spin of the local particle then has more the character of the CP photon, and does not require a local B field for its definition, although a local B field will cause the spin to align or anti-align with the field, as per Stern-Gerlach, and as per your treatment in figure 7.

        In my essay I begin by showing how counting-based measurement leads to Hilbert-space-like feature representation, and conservation of these features yield eigenvalue equations. This, as you note, has led to a fascination with the (admittedly fascinating!) math, at the expense of physical realism.

        I then focus on Bell's theorem and a local physical model of magnetic dipoles that yields exactly the same results as quantum mechanics and as experiment. This, of course, is what Bell claims to be impossible. I suggest that Bell was confused and mis-identified Pauli's provisional precession eigenvalue equation with Dirac's fundamental helicity eigenvalue equation with the result that he (mis-)interpreted the SG scattering, an indirect measure of spin, as spin itself, thus requiring only two possible outcomes, an obvious conflict with the observed scattered distribution. Bell's constraint guarantees that no local model will work, but is a meaningless quantum mechanical artifact, as you say.

        I hope you read my essay and I look forward to your comments. I find your essay a marvelous contribution to this contest.

        In particular, in your figure 7 you state that "each spin will rotate into alignment with measurement field". This represents a decrease in precession-based energy and a corresponding increase in the deflectional energy. I've solved this energy problem and show that it yields measurements of deflection that violate Bell's theorem, supposedly impossible. Bell's imposition of constraints on these measurements, based on his oversimplification of the physics (he assumes precession remains unchanged) is not a basic part of quantum mechanics, but has nevertheless been used to banish the most fundamental reality: local realism. As you note, this admonition has become virtually religious dogma, and must change if physics is to advance.

        My very best regards,

        Edwin Eugene Klingman

          Dear Alan,

          I really enjoyed reading your essay which is a classical take on quantum mechanics. I particularly liked your discussion of matter as soliton waves - but waves of what.

          The subject of my essay is a quantum of energy discovered (some physicists might say invented or imagined) by Walther Nernst circa 1930. Hh (Hubble times Planck) is the amount of energy that would be lost from each photon per cycle as it is redshifted. Its equivalent mass is on the order Hh ~ 10^-68, small enough to be the "atoms of light" DeBroglie talks about in your first reference. By the way, nice job on the on-line references.

          If I am interpreting Nernst's ideas correctly, the zero-point energy of the electromagnetic field forms a reservoir of potential energy in the form of very long waves. It occurs to me that these could be the source of both solitons and deBrogle's pilot waves.

          Best regards,

          Colin

            Dear Sir,

            Your essay was quite refreshing after a lot of dull essays. Your argument that quantum mechanics constitutes a mechanism for real continuous fields to behave as discrete particles is interesting and important. We can view it as micro manifestation of macro systems or particles within particles like the different internal systems including bacteria in our body or fish and other creatures in the sea or planets and asteroids in the solar system, extended to the universe. If we picture this way, all quantum systems including spin, superposition, entanglement, duality, tunneling, etc., have macro equivalents. Regarding complex numbers and extra-dimensions, kindly read our essay in support of your view.

            For example, since measurement is a process of comparison between similars, a wave, which is perceived as a moving packet, cannot be measured by (compared with) any known unit. It is real, because, reality is whatever exists (has a limited structure that evolves in time and is perceptible), is intelligible (knowable) and communicable (describable using a language). A fish can also exist in the wave, which guides (pilots) the fish. If two opposing waves neutralize each other, there is no way of knowing their state thereafter - both are spread out everywhere. This is an example of superposition. Two ends of a robber band or a pair of socks are examples of entanglement, which, contrary to common belief, do not last over infinite distance. Movement of Mercury and Venus on their axis is macro examples of spin. The internal structure of Jupiter and proton are equivalent.

            Regarding two-slit experiments, we have repeatedly wondered why no one has conducted the experiment with protons instead of electrons. That would show the fallacy. Though we know much about electrons, we still do not know what an electron is. This ignorance leads to fantasy. Energy always provides thrust. It pushes. There is nothing like pull - it is always push from the opposite direction. Then how can energy or particles (God particle!) 'bind' to provide mass? Did you ever wonder why strong and weak forces 'bind' and electromagnetic forces and beta decay move out from higher concentration? While other interactions are either intra-body or emanate from out of a body in a monogamous pattern, why gravity is inter-body treating them as point particles and behaving polygamous? With your bent of mind, we request you to think about these.

            Regards,

            basudeba

              Jose,

              My view is that a mathematical model is essential to provide quantitative analysis, but a model may have embedded assumptions, and one should not accept such a model without questioning. Quantum theory provides a striking example where the established mathematical model (the Hilbert space approach) has become completely unconnected from the physical reality that it describes, leading to paradoxical and inconsistent results.

              I look forward to your essay.

              Alan

              John,

              In my view, the universe was initially filled with primordial fields, immediately after some kind of Big Bang. At an early stage, these fields self-organized (condensed) into localized "particles" with quantized spin; this is the aspect of quantum theory that has been heretofore hidden. Then the particles condensed into atoms and molecules, which in turn formed gases and solids, leading to stars and planets, then to galaxies and clusters, in a hierarchical fashion.

              Once the primordial fields were formed, everything followed via local deterministic dynamics. Humans came quite late and are completely incidental to the physical universe.

              Alan

              Edwin,

              Thank you for your very detailed comments with a number of excellent points. I will read your essay carefully.

              With regard to the history of Bell's Theorem and quantum entanglement, I would recommend reading the 2008 book by Louisa Gilder, entitled "The Age of Entanglement: When Quantum Physics Was Reborn" . As she describes, Bell was actually a quantum skeptic who wanted to believe in Hidden Variables, an unpopular viewpoint among theoretical physicists of his time.

              But I pointed out in my essay something that was not evident either to Bell, or to Einstein in his EPR paradox. Namely, that quantum entanglement was an artifact of formal mathematical constructions used by Pauli to build the exclusion principle into the fabric of quantum theory. On the contrary, if the exclusion principle is instead a reflection of a real-space physical interaction, then this construction (and all of its non-realistic implications throughout quantum theory) are unnecessary and non-physical. Further, I show directly how the correlations in the EPR paradox may be understood in a simple realistic picture for electron spin, and how the interpretation of the single-photon experiments may be in error. This may yet be tested in new experiments.

              You might also be interested in viewing the video by Teresa Mendes in last year's FQXi contest, entitled "Physics Needs a Paradigm Shift".

              Alan

              Dear Basudeba,

              Thank you for reading my essay and for your comments. I will read your FQXi essay and will think further about your suggestions.

              Regarding quantum interference and diffraction experiments, these have been done not only with electrons, but also with neutrons, atoms, and even large molecules. These results are normally taken to prove that all objects are both small particles and extended de Broglie waves. However, as I point out in Note B at the end of my essay (and described in my earlier FQXi essay, "The Rise and Fall of Wave-Particle Duality" ), an alternative explanation (due to Van Vliet) is available whereby the same results are obtained via quantized momentum transfer to a small particle, without any wave nature assumed. Thus, there is no reason to give up local realism.

              Alan

              Dear Joe,

              Thank you for reading and commenting on my essay.

              I am not sure if I understand correctly what you are saying, but it seems that you reject the entire concept of modern science. While every snowflake is strictly unique, science seeks the regularity and reproducibility in nature, and to describe this regularity (in form and behavior) in quantitative terms. Quantitative modeling of reproducible behavior is the realm of mathematics. The fact that mathematics accurately describes physical reality, at least in many cases, merely reflects this regularity.

              My essay focuses on the difficulties associated with inappropriate mathematical models, applied specifically to quantum theory. Models may have embedded assumptions, which can lead to non-physical predictions. But if the math is sufficiently abstract and divorced from realistic pictures, it is difficult to clearly identify these assumptions. Furthermore, math can only be a partial guide to the development of future physical theory, which must ultimately come from experiments and physical intuition.

              Alan

              Dear Alan,

              I agree with your statement:

              "it is argued here that pictures of real objects moving in real space provide the proper basis for physics, and that mathematics merely provides quantitative models for calculating the dynamics of these objects. Such models may distort or even hinder the development of new physics, particularly if a consistent physical picture is lacking".

              My physical theory called Model Mechanics gives alternate physical explanations for all the abstract mathematical objects such as fields/virtual particle and curvature of space-time. In addition Model Mechanics gives rise to a new theory of gravity called DTG and a new theory of relativity called IRT. Model Mechanics is able to unify all the forces of nature (including gravity). Therefore Model mechanics is a good candidate for a Theory of Everything. I invite you to read my essay in the following link and give me your informed comments. Thank you.

              http://fqxi.org/community/forum/topic/2319

              Regards,

              Ken Seto

                Ken,

                Thank you for reading the abstract of my essay, the source of the quotation above. I hope you will read the remainder of the essay as well.

                A central result of my picture is that there is no fundamental difference between the microworld and the macroworld, no separation between quantum and classical dynamics. This is contrary to the orthodox viewpoint that the microworld is dominated by quantum uncertainty, superposition, and entanglement. In fact, in Note A at the end, I derive classical trajectories directly from the wave equations for real localized relativistic quantum fields.

                After I read your essay, I may have additional comments on your web page.

                Alan

                Alan,

                I'm glad you will read my essay carefully, as I believe that it supports your essay very strongly. You and I have significant overlap in our interpretation of physical reality, including Pauli's exclusion principle. I did enjoy Louisa Gilder's work and I'm sure you are familiar with Baccigalluppi's "Quantum Theory at the Crossroads", where so much of the early confusion arose.

                I do suggest an experiment to confirm my model, which, if positive, would seem to prove quantum mechanics incomplete, which is necessary if, as you say to Ken below, there is "no separation between quantum and classical dynamics". I'm happy that you too suggest new experiments. I will review the Theresa Mendes video.

                I wish you the very best in this contest, and I'm happy to see José Koshy's comment above. It's very possible the dam is about to burst. Or we may represent just the first drops of rain.

                Edwin Eugene Klingman

                Alan,

                I read your essay and I will read it again more carefully.

                You provided alternate physical interpretations to replace the mainstream abstract quantum processes. I agree with this approach completely. In fact that is the exact approach I used to formulate Model Mechanics.

                Regards,

                Ken Seto

                Dear Alan,

                I am devastated to learn that you would openly admit that you do not know what reality is. I reject the abstract concepts of abstract science. Real scientists have proven that all real physical construction is unique, once. For you to stupidly continue to believe that your insane quantum computers could quantify unique defies sense.

                Depressed about your ignorance,

                Joe Fisher

                Dear Alan Kadin,

                Does math hinder or help physics? The title of your essay says math hindered the development of QM, and is followed by an articulate express argument. (Some other essays seem to argue implicitly that math is a sub-optimal intermediary medium for physics.) I hope you will not mind some comments despite my knowing little about QM.

                Math is helpful (and sometimes indispensable) when it describes, explains, summarizes, condenses, provides insight, predicts, etc. Math is unhelpful when it obscures, is irrelevant, inapplicable, makes the conceptual thread hard to follow etc. An example would be 20 pages of equations of no discernible meaning, that no one will have the strength or interest to check. Another example would be A L = P, meaning actors with lines create a play; plus and minus signs do not of themselves invest ordinary words with insight.

                Let's take your title now. Your diagnosis and cure may be right. I propose another possibility (which does not exclude your approach). The complexities and seeming incongruities of the mathematics of QM (such as the many worlds hypothesis, entanglement and the two slits experiment) might not be a failure of mathematics. Rather, apparent shortcomings might be a clue that a crucial postulate, assumption, theory, picture (as you say), conceptual reference frame or unknown unknown is missing. This suggests looking not outside mathematics but for better mathematics.

                A paradigm example is Ptolemy's Almagest, a stupendous mathematical and astronomical achievement. Ptolemy wrote summarily that obviously the earth does not rotate on its axis, as some other astronomers had suggested, because clouds would appear to move at high speeds in the sky in a direction opposite that of the spinning earth, and birds, unable to keep up, would fall out of the sky. If he had the concept of inertia he might have come to a different conclusion.

                Perhaps a question raised by your interesting essay is: are we missing something?

                Regards,

                Bob Shour