Essay Abstract

The nature of quantum theory seems to suggest that underlying the physical world of experiment is a deeper mathematical reality. This essay considers a physics reason for experiment not to reveal the true reality. The spirit of the EPR and Bell approaches is followed to investigate the physics of an underlying-reality being dynamically hidden from experiment by the physics itself. There being a genuine distinction between experimental-reality and underlying-reality avoids Bell's no-go result, but is subject to Gödel's no-go theorem instead. The "unreasonableness" of maths could leave physics with no-where to go, and impose limits on the rest of science.

Author Bio

Michael Goodband has a physics degree from Cambridge University and a PhD in theoretical physics.

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Hi Michael Goodband,

"It all started off so well." But it has reached the point where, as you say, "... every student of physics must find their way to make peace with [the apparent fact that] quantum theory says that in some mysterious way, experimental-reality is not the same as underlying-reality."

You describe the key to your hidden propagator dynamics (HPD):

"The piecewise propagation of causation is hidden by the time scale of the particle propagation dynamics..."

"In simple terms, ... experiments are just too slow to measure what is happening."

It is also possible that experiments are assumed to be measuring one thing, and the actual physics going on (underlying the oversimplified assumption) is simply ignored, or worse, erased by the imposition of constraints that force the measurements into the required (by the assumption) discrete final state.

If, as is reasonable to believe, precession-mode energy is (as part of the scattering dynamics) exchanged with deflection-mode energy, the precession time cycle is, as you say, too fast to register in action. The effect of this energy exchange is to align the spin with the local field, yielding discrete spin results +/-1, but with the scattering angle (indicated by precise particle position) containing information about the initial spin. This is one approach to analyzing the local classical model. You note that: "The experimental fact of discrete spin eigenvalues is even more problematic, but central to Bell-like results."

In short, your N -> NDA -> N becomes θ -> NDA -> N for the deterministic local model, completely compatible with the fact that SU(2) and SO(3) can be mapped into each other.

You also observe that "spin is a dynamic state of relativistic rotation in 3+1 dimensions. The spin-up state is a dynamic eigenstate in which the components of spin in the orthogonal directions are not zero, they are just not eigenstates."

Your HPD theory is a far more general approach than I have taken in searching for a simple (but not too simple) model of local spin dynamics underlying the oversimplistic model that Bell chose. I hope you will find time to look at my simple model and leave feedback.

Best regards,

Edwin Eugene Klingman

    Hi Edwin

    Thanks for your thoughtful comments. There seem to be a number of ways that appear to mathematically give the correct correlation result for the EPR spin singlet state but don't correctly match the physics. The supposition of Hidden Propagator Dynamics is of the same standard as Bell's supposition of Hidden Variable Theory, where having a physical reason for the true physics situation being dynamically hidden from direct experiment, makes it possible to both have the correct physics and match the quantum result.

    I noticed that in your essay you have an element of there being a distinction between the underlying physics - spin eigenstate - and the physics measured in experiment- by interaction with a magnetic field. HPD is a generalisation of this sort of distinction, but addresses the issue of discrete eigenstates in experiment. The issue with rotation groups SO(3) and SU(2) is not how they are related to each other but how they are different. The ability of a HPD theory to reproduce QT results depends on the rotation group for the underlying spin objects being SU(2) and explicitly not SO(3). This was the crucial point made by our mutual acquaintance, as we discussed in a previous essay contest.

    My point about the sequence N->NDA->N is with regard to the process of modelling experimentally measured discrete particle states that are countable by the natural numbers by normed-division algebra valued fields in quantum theory. QT then makes probabilistic predictions for the discrete particle states, giving the sequence N->NDA->N for experiment to QT model and back to experiment again. This isn't changed to θ->NDA->N; the discreteness is fixed by experiment and the underlying physics. It is the ability of a local deterministic HPD theory - over underlying reality - to reproduce QT results for discrete eigenstates - with the same issues as for QT - that is the significant result.

    Regards

    Michael

    Dear Michael Goodband,

    Great essay with interesting content. I like the style and directness "is the universe written in maths, or do we just describe the universe using maths?" and "The truth is that particles are only ever measured as ... well ... particles."

    I have thought a lot about Hidden Variables, but your essay introducing the idea of Hidden Propagators is food for thought. The concept of Hidden Propagators is somewhat new to me. That said, I enjoyed your detailed discussion of spin together with the comment "This standard form of the calculation gives the misleading impression that spin states are static, and correspond to mathematical objects in a Platonic realm of Hilbert space giving underlying reality. But this is not what the physics says. Spin is a dynamic state of relativistic rotation in 3+1 dimensions.". The dynamic nature of spin is a very important concept.

    I have one question on your use of the term "hidden". Do you mean hidden in the sense that we haven't figured it out yet? or hidden in the sense that it is necessary to the theory that it not be explained?

    In my essay, I directly model the particles of the standard model from which hidden variables could be extracted. I followed with interest your discussion of the SO(3) and SU(2) rotational groups and would be very interested in your read on how they I have presented them in my essay.

    A very enjoyable and educational read and you deserve a high ranking.

    Best of luck, Ed Unverricht

      Dear Michael Goodband,

      I can't see how your distinction between experimental and underlying reality could be of service for a theory that is supposed to confront Bell's theorem and reproduce the predictions of quantum theory. If I follow, you say that the underlying theory is deterministic and (piecewise) causal, but that the experimental (observed) outcomes are not because, in essence, the experimental situation randomly samples from the underlying reality. So, for example, your rapidly spinning coin can produce different observable experimental outcomes because the way the coin couples to the experimental apparatus does not determine a unique map from the coin state at a moment to the experimental outcome. That is, of course, possible. But no such theory could possibly reproduce even the EPR perfect anti-corrlations. For if the state of the right-hand coin does not determine the outcome of the right-hand measurement and the state of the left-hand coin does not determine the outcome of the left-hand measurement, then the theory cannot predict perfect anti-correlation of the experimental results.

      We have non-local theories in which the results of the experiments are not both pre-determined (e.g. GRW collapse theory), but at least the second measurement result is determined by the outcome of the collapse initiated by the first result. And we have non-local theories in which both experimental results are determined by the underlying state (e.g. Bohmian mechanics), with the non-local dynamics ensuring the perfectly anti-correlated outcomes. But even allowing non-locality into the underlying physics (as you seem to admit) will not recover the predictions if the experimental outcome is never predetermined by the underlying physical state. How can the perfect EPR anti-correlations follow from the theory?

      In any case, the distinction between underlying and experimental reality is implicit in Bell: the lambda can represent whatever you like, using whatever mathematical resources you like. I think you appreciate this--you acknowledge that the underlying physics cannot be local--but why think that the distinction itself has been missed? Bell's question is exactly this: can any local underlying physics, of any kind, reproduce the experimental observations, i.e. the correlation among observed outcomes? He puts no restrictions at all in the underlying physics beside locality.

      Regards,

      Tim Maudlin

        Dear Ed Unverricht

        Thanks for your comments.

        The idea of a Hidden Propagator compliments Bell's consideration of Hidden Variables and doesn't conflict with it at all. The intended sense of "hidden" is that the true underlying physics happens on a timescale much less than any interaction that could be used in experiments. This renders the details of the dynamics unmeasurable by direct experimental measurement - hence "hidden". It is only this distinction that is required for the HPD analysis as it proceeds in a way directly analogous to that of Bell. I don't assume that the details of the dynamics could be found/inferred by other means. If they were, then it wouldn't make any difference to the HPD analysis.

        I will be reading your essay with interest shortly.

        Michael

        Dear Tim Mauldin

        I was hoping that you would read my essay and comment. Firstly, my intention is NOT to confront Bell at all. I'm not seeking to validate the view of EPR, and in fact HPD disproves EPR just as much as Bell. In the exact details my HPD proposition compliments and extends Bell's hidden variable approach. The distinction between underlying-reality and experimental-reality in HPD means that in experimental terms the HPD analysis agrees with Bell's HV result and so doesn't confront it all. The illustration with the coin is only for the purposes of showing how deterministic dynamics in underlying-reality is forced to be probabilistic in experimental terms - thus the EPR view cannot be realised with HPD. But NO theory of spinning coins will produce strong correlations in results - NOT even quantum theory.

        It is in looking at the mathematical details of how QT produces strong correlation results that we can see it is implicitly the result of the dynamic state of spin with discrete eigenvalues exploring possible S2 orientations where the S2 is a subspace of the full rotation group manifold S3. Bell's HV analysis is only in terms of discrete experimental measurements (hence its generality), but the other side of the inequality is the QT result which comes from spin correlations - whether it is neutron spin or photon spin correlations. This is why Bell's inequality wouldn't apply to a spinning coin with rotation group U(1) - both HV theory and QT would predict the same thing in this case. Strong correlations require SU(2) rotation group - even SO(3) won't do it.

        The HPD analysis directly considers this distinction between the 2 sides of the inequality: QT with maths that seems to be about an underlying mathematical reality, and Bell's HV side which is in terms of any theory that could causally and deterministically predict the experimental results. This distinction is implicit in Bell, but on different sides of the inequality and not solely on the HV side. HPD considers a physical reason for this distinction where one consequence is that it is NOT deterministic in terms of experimental results - so there is NO part of the theory which corresponds to Bell's lambda as this is the experimentally deterministic bit. So HPD arrives at the same conclusion as Bell in experimental terms - NO causal theory can deterministically predict the outcome of spin correlation experiments. But a causally deterministic theory over underlying-reality can reproduce the same correlation results as QT in experimental terms when it is NOT deterministic - HPD gives a simple dynamical reason for why determinism would be lost.

        HPD is more subtle than it looks at first glance. There are a number of issues that HPD addresses separately:

        1. Determinism -> Probabilities (Bell's HV requires this, HPD explicitly loses this - hence no conflict with Bell)

        2. SU(2) eigenvalues: in space this is the rotation group of physically linked objects, and so the orientations of the objects in a singlet state have a physical linkage. So a second orientation measurement will have an underlying physical linkage to the first in ANY physics theory (in classical physics or QT)

        3. Dynamics of discrete eigenvalues (S0) that explore S2 which is a subspace of S3

        4. Locality: the HPD distinction between underlying-reality and experimental-reality can lead to a distinction in definition.

        It is with the point 4 that the interpretation of QT results gets really interesting. My objective is to extend Bell's HV analysis with HPD because it enables the meaning of QT to be explored using what experimental results say MUST be the case. I would appreciate your serious consideration of the subtly of HPD and how it extends Bell's HV through points 1-3 above. The combination of HV and HPD then constrains what experimental results say about point 4.

        Best Wishes,

        Michael

        Michael - Thanks for the remarkable essay. While much of it is beyond my training, I did appreciate the irony of math playing tricks on physics and vice versa. My essay explores this very issue in the apparent paradoxes in both math and physics and reaches a conclusion similar to, but broader than, yours --- that there is a Hole at the Center of Creation. I would be interested in your view on my thesis and whether it has parallels to your far more technical presentation.

        Sincerely - George Gantz

          Dear Michael,

          I'm still having trouble following the thought...sorry. Let me try again.

          Take a pair of electrons in the singlet state. When you say that the particles are "exploring possible S2 orientations" it sounds as if the state is changing in time "exploring" and therefore the result of a spin measurement will depend on exactly when it is made. But if so, the natural question is how the other electron always manages to display the opposite result. The perfect anti correlation can, of course, be ensured by a non-local physics at the underlying level, and that can be implemented in a deterministic way (e.g. Bohm) or an indeterministic way (e.g. GRW). But in either case, the underlying state must determine the experimental outcome of at least one of the experiments.

          Let's see how the non-locality is implemented in these 2 theories. In Bohm, the quantum state is just the singlet state and the two electrons always have definite positions. Their motion is determined by the quantum state. Doing an actual experiment on one side influences the wave function (it must, since the particle couples to the apparatus), in a way that influences the behavior of the other particle. Everything at the fundamental level is deterministic, and the experimental probabilities are recovered via a probability measure over the space of possible initial conditions.

          In the GRW theory, the state of the electrons is just the single state, with the particles separating from each other. Again, nothing is being "explored" in terms of spin. The coupling to the first experimental apparatus causes a (non-local) collapse of the wave function to an eigenstate of the observed direction of spin. In an EPR set-up, where we check the same direction on the other side, this ensures the anti-correlation. If we check at some other angle, a second collapse occurs with the right probabilities to violate the Bell inequalities.

          I'm not sure how to understand what you mean by "how QT produces strong correlation results". In one sense, QT is just a mathematical apparatus for making predictions, so there is no physical account of what is going on at all. Bohm and GRW are examples of precise (non-Relativistic) physical theories, and we can ask how they produce the results. The accounts are quite different in almost every detail, but neither involves anything that looks like "exploring". So maybe you can just clarify what you mean by "exploring" in this context, and where you see it in QT. The spinning coin is, in a sense, "exploring" different orientations in space: its orientation is constantly changing in time. I understand that you do not mean to have the example taken so seriously, but I can't tell how to understand the analogy.

          Regards,

          Tim

          Dear Tim

          The conflict Einstein started with his views of quantum theory is somewhat polarised with entrenched concepts. I'm not interested in one winning over the other, I'm looking for a third way. Determinism cannot be restored - my HPD shows the same - so I'm not looking for it. Quantum theory is just maths without the physics. Bohm's theory with a non-local QT-like field still has the same issue - assuming a form of underlying Platonic reality that determines physics. Instead of just settling for this implicit assumption - or denying that it has even been made - I'm looking to see if it is possible starting with a blank sheet to explain physics experiments using physics. I appreciate this is an old-fashioned idea.

          So, blank sheet.

          1. In physical space, SO(3) is the rotation group of free objects, but when two objects are physically linked their rotation group is SU(2), e.g. Dirac belt trick.

          2. In relativity, rotation is complicated by space and time dimensions interchanging, but in the rest frame of an object, the spin operator is the same as the SU(2) rotation operator. So in the rest frame of an object we can regard spin as being synonymous with rotation.

          3. In physical space, spin/rotation is a dynamic state, not the apparently static state that the maths of QT suggests. The implicit assumption of an underlying Platonic reality with a static spin state doesn't remove the dynamics from physics.

          4. A particle is measured as a particle in a detector, such as when a particle is stopped by a screen and is then in its rest frame where the spin group is the same as the rotation group SU(2).

          Let's look at the consequences of this. Staying in physics, leaving QT maths well alone. Consider our dynamic state of two spinning particles each with spin ½ in a spin singlet state. In physical space, this first requires the objects to have the correct SU(2) rotation group, which requires the objects to be physically linked in some way. This gives a causal connection between the dynamic state of one particle and the dynamic state of the other. So if one particle changes its orientation of dynamic spin - such as being causally influenced through the physical linkage to another rotating object - then this change will be causally transmitted through the physical linkage to the other particle so that spin/rotation is conserved - at spin 0.

          This just follows from the 4 points above about relativity, so there isn't much room for dispute. The critical features are:

          1. Spin is SU(2) rotation in the rest frame of an object.

          2. SU(2) is the rotation group of physically linked objects.

          3. Rotation is a dynamic state.

          4. Spin/rotation is a conserved quantity in physical space, so if the orientation of one physically linked rotating object changes through internal dynamics without a cause external to the linked pair then the orientation of the other must change for rotation conservation.

          Next bit of physics. The pattern of the running couplings revealed by particle collisions at increasing energies suggests that there exists new physical interactions occurring on an energy scale beyond that of any practical means of measurement, e.g. Planck scale. This implies the existence of interactions on a timescale far shorter than any interaction that can be used for the purposes of measurement - so these interactions are hidden by being too dynamically quick to be directly measured. This is standard physics and has justified the search for physics unification, so again not much room for dispute.

          HPD puts these bits of physics together in physics. The first consequence is the loss of determinism in experimental measurements of physical properties when the dynamics on the timescale too short to be measured causally determines the physical properties that are measured. Hence HPD: exactly how the initial state of the physical properties propagates to the final state is hidden due to the interactions used in experiments being too slow to record the dynamic process. This compliments Bell's hidden variable approach and it isn't covered by it. Bell approaches from experimental results and back to underlying physics. HPD approaches from underlying physics to experimental results. The two differ on the exact usage of the terms local, causal and deterministic. Implicitly assuming that their usage is the same is an error - an error that is one of the major things HPD finds. HPD is the same general idea as Bell - something unknown that is hidden, but it is dynamically hidden for a physical reason.

          Now we look at the maths of QT to see just how it mathematically gets strong correlations - i.e. cos(theta) and not linear correlations, as hidden variable physics cannot give cos() correlations. The standard interpretation of QT is implicitly based on a Hilbert space view of a Platonic realm of static spin states, but for this maths to represent physics the spin states cannot be static in physical space. A spin singlet state is a superposition of (u)(d) and (d)(u) for particles (1)(2). But each of these states is just denoting the eigenstate of spin component in one direction for a dynamic state of spin. In this dynamic spin singlet state the eigenstate orientation of each particle changes. This is a dynamic spin state where the spin orientation changes but the tip of the orientation spinor is constrained to lie on the surface of a spatial 2-sphere. This is the essential bit of dynamics: for the maths of QT spin to represent physics - which it must do because it successfully predicts physics experiments - then the QT spin state of a particle (as always discretely measured as a particle in its rest frame when it impacts a screen) must be a dynamics state in physics space, otherwise it violate the physics of relativity.

          At this point NO assumptions made - just following the physics and NOT implicitly making assumptions about QT maths. The critical point is that the QT integral is implicitly describing spin dynamics for a spin singlet state, or it violate relativity for physical space.

          Do you have any disputes with the physics above? HPD then looks at alternative hidden dynamics that could lead to the same integral result as QT for experimental measurements. The point of HPD is then to follow the physics and find the consequences: loss of determinism, and causal dynamics appears to give experimental results which look non-local - HPD allows us to make conclusions about this, which Bell does not.

          Regards,

          Michael

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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