Table of contents

Preface

The International Association for Relativistic Dynamics was organized in February 1998 in Houston, Texas, with John R. Fanchi as president. Although the subject of relativistic dynamics has been explored, from both classical and quantum mechanical points of view, since the work of Einstein and Dirac, its most striking development has been in the framework of quantum field theory. The very accurate calculations of spectral and scattering properties, for example, of the anomalous magnetic moment of the electron and the Lamb shift in quantum electrodynamics, and many qualitative features of the strong and electroweak interactions, demonstrate the very great power of description achieved in this framework. Yet, many fundamental questions remain to be clarified, such as the structure of classical relativistic dynamical theories on the level of Hamilton and Lagrange in Minkowski space as well as on the curved manifolds of general relativity. There, moreover, remain the important questions of the covariant classical description of systems at high energy for which particle production effects are not large, such as discussed in Synge's book, The Relativistic Gas, and in Balescu's book on relativistic statistical mechanics, and the development of a consistent single and many body relativistic quantum theory. In recent years, highly accurate telescopes and advanced facilities for computation have brought a high level of interest in cosmological problems, such as the structure of galaxies (dark matter) and the apparently anomalous expansion of the universe (dark energy). Some of the papers reported here deal with these problems, as well as other fundamental related issues.

It was for this purpose, to bring together researchers from a wide variety of fields, such as particle physics, astrophysics, cosmology, foundations of relativity theory, and mathematical physics, with a common interest in relativistic dynamics, to investigate fundamental questions of this type, that this Association was founded. The second meeting took place in 2000 at Bar Ilan University in Israel, the third, in 2002, at Howard University in Washington, D.C., and the fourth, in 2004, in Saas Fee, Switzerland. Subsequent meeting took place in 2006 at the University of Connecticut Storrs, in 2008 at Aristotle University of Thessalonica, in 2010 at National Dong Hwa University, Hualien, Taiwan, in 2012 at the Galileo Galilei Institute for Theoretical Physics (GGI) in Florence, in 2014 as the University of Connecticut Storrs, Connecticut, in 2016 at Jožef Stefan Institute in Ljubljana, Slovenia, and in 2018 in Mérida, Yucatán, Mexico, under the sponsorship of the Instituto Politécnic Nacional. The 2020 meeting, planned for Czech Technical University in Prague, was successfully held online at the height of the Covid-19 pandemic, and the physical meeting in Prague was delayed to 2022.

The 2022 meeting forms the basis for the Proceedings that are recorded in this issue of the Journal of Physics: Conference Series. Along with the work of some of the founding and newer but already much engaged members of the Association, we were fortunate to have lecturers from application areas that provided strong challenges for further developments in quantum field theory, cosmological problems, and in the dynamics of systems subject to accelerations and the effects of general relativity. Topics treated in this issue include studies in general relativity and astrophysics, relativistic dynamics and electrodynamics, quantum theory and particles, and foundations of relativistic dynamics.

This first physical meeting of the Covid-19 era took place 6 - 9 June at Czech Technical University in Prague, as originally planned for 2020. The meeting was divided into seven plenary sessions over four days. As a result of continued travel restrictions in some areas, a small number of talks were delivered by videoconferencing. The papers presented in this volume represent extensions and refinements to the conference talks, building on feedback and discussions associated with the lectures. We once again express our gratitude to Czech Technical University, and especially the local conference chair Petr Jizba, for their generous hospitality.

List of Scientific Advisory Committee, International Organizing Committee and Editorial Board of the proceedings, Dedication are available in this Pdf.

All papers published in this volume have been reviewed through processes administered by the Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

• Type of peer review: Single Anonymous

• Conference submission management system: Morressier

• Number of submissions received: 33

• Number of submissions sent for review: 28

• Number of submissions accepted: 26

• Acceptance Rate (Submissions Accepted / Submissions Received × 100): 78.8

• Average number of reviews per paper: 2

• Total number of reviewers involved: 7

• Contact person for queries:

Name: Martin Land

Email: martin@hac.ac.il

Affiliation: Hadassah Academic College

About 40 years ago, since no viable candidate for "dark matter" was discovered, M. Milgrom and J.Bekenstein introduced a non-covariant modification of gravitational theory (MOND) to account for the anomalous rotation curves of galaxies. Bekenstein and Sanders then developed a relativistically covariant form of the theory, called TeVeS, involving scalar and tensor fields, which accounts well for the rotation curves as well for the observed lensing of background radiation around galaxies without the introduction of "dark matter". The dynamical behavior of a particle in such a gravitational theory has been recently discussed by Horwitz, Gershon and Schiffer. In this paper we study the dynamics of the N ≥ 2 particle problem in the framework of the TeVeS theory.

The purpose of this paper is to present a parametrized relativistic quantum theory (pRQT) in curved spacetime. The formulation of pRQT in curved spacetime is developed and applied to free particle motion in flat and curved spacetime. It provides a theory for calculating probability amplitudes in curved spacetime. Unlike other formulations of parametrized relativistic dynamics (pRD), this work assumes that the metric tensor does not depend on the invariant evolution parameter.

Quantum equations for massless particles of any spin and for massive spin one-half particles are considered in curved space-times. It is demonstrated that in stationary axially symmetric space-times the angular wave functions up to a normalization function are the same as in a Minkowski space-time. The radial wave functions satisfy second order nonhomogeneous differential equations with three nonhomogeneous terms which depend in a unique form on the ratio of time to space curvatures. For a Dirac spin one-half particle, in addition to these three terms a fourth term which depends on the particle rest mass is added.

Recently, Bizyaev et. al. (2021) conducted the first modeling of rotation curves for 153 ultra-faint, edge-on galaxies using the 3.5 m telescope at the Apache Point Observatory. These models derived high resolution rotation curves for 20 galaxies of various sizes and spiral morphologies, making new estimates of the optical scale lengths. Using the derived models, in this work we make the first fits to the rotation curves using alternative gravity, namely conformal gravity, Modified Newtonian Dynamics (MOND) and more. A robust analysis is shown including the derived rotation curve fits to the alternative gravity models, along with how the models account for empirical phenomena such as the Baryonic Tully Fisher relation and the Radial Acceleration Rule. This data is not only modern, but unique in that certain galaxies are shown to be able to be fit by standard gravity alone without dark matter.

The missing mass problem has been with us since the 1970s, as Newtonian gravity using baryonic mass cannot account for various observations. We investigate the viability of retardation theory, an alternative to the Dark Matter paradigm (DM) which does not seek to modify the General Principal of Relativity but to improve solutions within it by exploring its weak field approximation to solve the said problem in a galactic context. This work presents eleven rotation curves calculated using Retardation Theory. The calculated rotation curves are compared with observed rotation curves and with those calculated using MOND. Values for the change in mass flux to mass ratio are extracted from the fitting process as a free fitting parameter. Those quantities are interpreted here and in previous works using given galactic processes. Retardation Theory was able to successfully reproduce rotation curves and a preliminary correlation with star birthrate index is seen, suggesting a possible link between galactic winds and observed rotation curves. Retardation Theory shows promising results within current observations. More research is needed to elucidate the suggested mechanism and the processes which contribute to it. Galactic mass outflows carried by galactic winds may affect rotation curves.

The 4+1 formalism in general relativity expresses the Einstein equations as a manifestly covariant initial value problem, resulting in a pair of first order evolution equations for the metric γ_μv and intrinsic curvature K_μv of spacetime geometry (μ, v = 0, 1, 2, 3). This approach extends the Stueckelberg-Horwitz-Piron (SHP) framework, a covariant approach to canonical particle mechanics and field theory employing a Lorentz scalar Hamiltonian K and an external chronological parameter τ. The SHP Hamiltonian generates τ-evolution of spacetime events x^μ (τ) or ψ (x, τ) in an a priori unconstrained phase space; standard relativistic dynamics can be recovered a posteriori by imposing symmetries that express the usual mass shell constraint for individual particles and fields as conservation laws. As a guide to posing field equations for the evolving metric, we generalize the structure of SHP electrodynamics, with particular attention to O(3,1) covariance. Thus, the 4+1 method first defines a 5D pseudo-spacetime as a direct product of spacetime geometry and chronological evolution, poses 5D field equations whose symmetry must be broken to 4D, and then implements the implied 4+1 foliation to obtain evolution equations. In this paper, we sharpen and clarify the interpretation of this decomposition by introducing a fixed orthonormal quintrad frame and a 5D vielbein field that by construction respects the preferred 4+1 foliation. We show that for any diagonal metric, this procedure enables the evolution equation for the metric to be replaced by an evolution equation for the vielbein field itself, simplifying calculation of the spin connection and curvature.

Finsler's geometry usually describes an extension of Riemmann's geometry into a direction-dependent geometric structure. Historically, the well-known Riemann's quartic length element example served as the inspiration for this construction. Surprisingly, the covariant Fresnel equation—a fundamental dispersion relation in solid-state electrodynamics—emerges as the exact same quartic expression. As a result, Riemann's quartic length expression can be regarded of as a mathematical representation of a well-known physical phenomenon. In this study, we offer numerous Riemann's quartic examples that show Finsler's geometry, even in the situation of a positive definite Euclidean signature space, is too restrictive for many applications. The strong axioms of Finsler's geometry are violated in a substantially greater number of distinctive subsets for the spaces having an indefinite (Minkowski) signature. We suggest a weaker characterization of Finsler's structure based on explicitly calculated two-dimensional examples. In tangential vector space, this concept permits singular subsets. Only open subsets of a manifold's tangent bundle are required to satisfy the strong axioms of Finsler's geometry. We demonstrate the distinctive unique subsets of the Riemann's quartic in two dimensions and briefly discuss their possible physical origins.

In previous publications, it was argued that because energy and matter are aligned in the thin increment of present time for an observer, spacetime should and must have surface tension. In this paper, we review how to apply 4-dimensional continuum mechanics with imaginary time coordinates to derive a mechanical model of spacetime with surface tension. Then, to continue model development, we discuss the concept of preferred curvature from the physical chemistry of surfaces and attempt to apply those concepts to spacetime geometry. We show how the model exhibits quantum fluctuations at the Plank scale and components resembling dark matter and dark energy at the cosmic scale.

The clock hypothesis in relativity states that the rate of time as measured by any clock is determined by its Minkowskian proper-time, regardless of the nature of its motion; in particular independent of its acceleration, depending only on its instantaneous velocity. However, a unique proper-time may be assigned to an accelerating clock, as to any physical system, only in the limit of being point-like. But clocks, by their very nature, must be spatially extended systems, to allow an internal periodical mechanism. Therefore the question, How does the internal structure of the clock affect the clock hypothesis?

The simplest model to examine the clock hypothesis is the so-called 'light clock', consisting of two mirrors with a light signal reflected between them. So far, such examinations were carried out mainly in the limits of point-like clocks and/or constant acceleration. Here the clock hypothesis is theoretically examined for spatially extended linearly accelerated light-clocks, parallel and vertical relative to the direction of motion, with arbitrarily varying accelerations. Using the rapidity of the clock as its evolution parameter, a Lorentz covariant analysis is neatly performed. Taking into account the spatial extension of the clock, differences between externally measured Minkowskian proper-times and the time-scale determined by the internal periodical mechanism of the clock are computed.

Although these differences are practically very minute – of order aL/c² for characteristic acceleration a and spatial dimension L of the clock – theoretically they cannot be ignored. They indicate inherent inconsistency between the externally measured proper-time – the physical time-line which consists of moments-of-time – and the intrinsically defined age – the internal time-line, consisting of durations, intervals-of-time.

Neutrino oscillation observations are used to compare two competing theories of 3-flavor neutrino oscillations. The two theories considered here are the standard model of neutrino oscillations, and parametrized Relativistic Quantum Theory (pRQT). pRQT is a manifestly covariant quantum theory with invariant evolution parameter. Recent data and a neutrino mass model from each theory are used to calculate neutrino masses. The models yield significantly different predictions of neutrino masses.

In a long series of works the author has demonstrated that the model named the spin-charge-family theory offers the explanation for all in the standard model assumed properties of the fermion and boson fields, as well as for many of their so far observed properties if the space-time is ≥ (13 + 1) while fermions interact with gravity only. In this talk, I briefly report on the so far achievements of the theory. The main contribution demonstrates the offer of the Clifford odd and even objects for the description of the internal spaces of fermion (Clifford odd) and boson (Clifford even) fields, which is opening up a new understanding of the second quantization postulates for the fermion and boson fields: The "basis vectors" determined by the Clifford odd objects demonstrate all the properties of the internal space of fermions and transfer their anti-commutativity to their creation and annihilation operators, while the "basis vectors" determined by the Clifford even objects demonstrate all the properties of the internal space of boson fields and transfer their commutativity to their creation and annihilation operators. The toy model with d = (5 + 1) illustrates the statements.

Maxwell's equations and quantum electrodynamics are valid for any value of the permittivity ₀ of the vacuum; therefore, something additional is required to establish the value of ₀. A fundamental postulate of physics is that the properties of a physical system are determined by its structure. Since ₀ is an electromagnetic property of the vacuum, it should be possible to calculate ₀ using Maxwell's equations and quantum electrodynamics to describe the interaction of photons with the quantum vacuum. The feature of the quantum vacuum that allows for such interactions is the presence of vacuum fluctuations that appear as particle-antiparticle pairs. To minimize the violation of energy conservation and conserve angular momentum, the pair appears with zero center-of-mass momentum in the most tightly bound state that has zero angular momentum. Because vacuum fluctuations each appear as a bound state, the permittivity of the vacuum can be calculated somewhat similarly to the way that the permittivity of a dielectric is calculated, yielding ₀ ≃ (6μ_o/π)(8e²/ħ)² = 9.10 × 10⁻¹²C/(Vm), which is 2.8% larger than the experimental value. Formulas for the speed of light in the vacuum and the fine-structure constant follow immediately from the formula for ₀.

One of the key points of Pauli's proof of the spin-statistics theorem is the principle of microcausality, which essentially states "that all physical quantities at finite distance exterior to the light cone (for$|{x}_{o}^{^{\prime} }-{x}_{o}^{^{\prime\prime} }|\lt |x^{\prime} -x^{\prime\prime} |$) are commutable". Indeed, Pauli was aware that if it were not valid then neither was his version of the spin-statistics theorem. In this presentation, we explore the relationship between entanglement and microcausality and point out that in the case of spin-singlet states, microcausality does not apply. Consequenly, we revise the spin statistics theorem to incorporate entanglement and to suggest some refinements to the axiomatic structure of quantum mechanics. Ironically, singlet states are SL(2,C) invariant as is the Minkowski metric of special relativity, although the singlet state is often used to convey "spooky action at a distance" as if it were in violation of special relativity, which it is not. We also pose the question whether the paradoxes associated with "entanglement" can be understood as a special case of Gödel's theorem.

We discuss the extension of the Goldstone and Englert-Brout-Higgs mechanisms to non-Hermitian Hamiltonians that possess an antilinear PT symmetry. We study a model due to Alexandre, Ellis, Millington and Seynaeve and show that for the spontaneous breakdown of a continuous global symmetry we obtain a massless Goldstone boson in all three of the antilinear symmetry realizations: eigenvalues real, eigenvalues in complex conjugate pairs, and eigenvalues real but eigenvectors incomplete. In this last case we show that it is possible for the Goldstone boson mode to be a zero-norm state. For the breakdown of a continuous local symmetry the gauge boson acquires a non-zero mass by the Englert-Brout-Higgs mechanism in all realizations of the antilinear symmetry, except the one where the Goldstone boson itself has zero norm, in which case, and despite the fact that the continuous local symmetry has been spontaneously broken, the gauge boson remains massless.

This paper reviews research on the foundations of quantum electrodynamics (QED). We show that there are three definitions of the proper time that follow from Einstein's theory. The first definition is used to prove that the universe has a unique clock (Newton-Horwitz-Fanchi time) available to all observers. This clock is used to briefly discuss the mathematical foundations for Feynman's time ordered operator calculus. We use this calculus to solve the first and second conjectures of Dyson for QED: that the renormalized perturbation series is asymptotic and, that the ultra-violet divergence is caused by a violation of the time-energy uncertainly relationship. The second definition gives Minkowski's version of Einstein's theory and its problems are briefly reviewed. The third definition gives the dual Newton, dual Maxwell and dual quantum theories. The theory is dual in that, for a set of n particles, every observer has two unique sets of global variables (X, t) and (X, τ) to study the system, where X is the canonical center of mass. Using (X, t) time is relative with speed c, while in (X, τ), time is unique with relative speed b. The dual Maxwell theory contains a longitudinal (dissipative) term in the E field wave equation, which appears instantaneously with acceleration and we predict that radiation from a cyclotron will not produce photoelectrons. It is shown that this term gives an effective mass for the photon. A major outcome is the dual unification of Newtonian mechanics and classical electrodynamics with Einstein's theory and without the need for point particles or a self-energy divergency. This means that a second quantized version will not produce a self-energy or infrared divergency. These results along with the proof of Dyson's second conjecture resolves all the problems with QED. The dual Dirac theory provides a new formula for the anomalous magnetic moment of a charged particle, which can give exact values for the electron, muon and proton g-factors.

A high-precision hypernuclear experiment has been performed at the Mainz Microtron (MAMI) to determine the hypertriton Λ binding energy via decay-pion spectroscopy. A key element of this measurement is an accurate calibration of the magnetic spectrometers with the MAMI beam. For such an absolute calibration with small statistical and systematic uncertainties the undulator light interference method will be applied. In this contribution the basic principle of this method is discussed and the analysis status of the measured synchrotron radiation spectra is presented.

The quantum electron spin structure and the photon dressed electron energy spectrum problem are reanalyzed in the framework of the Fock many-temporal parameter approach. There is analyzed the spin structure and its dependence on the symmetry properties of the related representations of the basic Clifford algebra, generated by creation-annihilation operators. The self-interaction phenomenon is discussed within the quantum renormalized Lorenz constraint on a suitably reduced Fock space. The electron energy spectrum is analyzed within the many-temporal Fock and Feynman proper time paradigms.

We have developed a linearized effective theory with quantum mechanical Gaussian wavepacket of a charged relativistic particle coupled to quantum electromagnetic fields at a scale well below the Schwinger limit. Using this effective theory, we study the quantum decoherence of single electrons at rest due to their interactions with electromagnetic vacuum. According to the existing data of electron interference experiments in electron microscopes, the values of the parameters in our effective theory are chosen. With these values, we find that weak decoherence by vacuum fluctuations may have blurred the interference pattern in Ref. [1].

While experimental physics progressed tremendously since the 1970s, the neutron model has remained essentially unchanged. Motivated by developments in both experiments and theory, which we briefly review in section 1, we propose that the initial neutron decay step is not the emission of an 80 GeV mass boson particle, but the emission of a much lighter lepton particle. On the basis of well-known neutron data, in section 2 we estimate that this new lepton's mass is 1.5 MeV.

Historically, investigations of deuteron photo-dissociation led nuclear scientists to assume that no electron-like particle is associated with neutron decay. We therefore re-examine these experiments in section 3. We demonstrate that deuteron photo-dissociation leads to 2p⁺ + e⁻ products at high photon energies. Our calculations show why a deuteron always breaks up into p + n particles at <3 MeV photon energy.

Sections 4 - 7 discuss the properties and interactions of the 1.5 MeV lepton particle. Numerous investigations, including our own experiments, demonstrate the presence of negative elementary charges within atomic nuclei. The emission or absorption of negative nuclear charges involves the emission or absorption of a new lepton particle, which always decays into an electron. Various mass measurement methods converge to the same result: the emitted or absorbed lepton is approximately three times heavier than an ordinary electron. Specifically, we measure its mass to be 1553.5 keV.

Our work demonstrates that, despite being a single particle, the neutron comprises a positive and a negative elementary charge. To make sense of the neutron structure, it is necessary to firstly understand the proton's and the newly discovered 1.5 MeV lepton's internal structures. In section 9, we apply our results to better understand the neutron's properties.

Otto Stern's 1933 measurement of the unexpectedly large proton magnetic moment indicated to most physicists that the proton is not a point particle. At that time, many physicists modeled elementary particles as point particles, and therefore Stern's discovery initiated the speculation that the proton might be a composite particle. In this work, we show that despite being an elementary particle, the proton is an extended particle. Our work is motivated by the experimental data, which we review in section 1.

By applying Occam's Razor principle, we identify a simple proton structure that explains the origin of its principal parameters. Our model uses only relativistic and electromagnetic concepts, highlighting the primary role of the electromagnetic potentials and of the magnetic flux quantum Φ_M = h/e. Unlike prior proton models, our methodology does not violate Maxwell's equation, Noether's theorem, or the Pauli exclusion principle.

Considering that the proton has an anapole (toroidal) magnetic moment, we propose that the proton is a spherical shaped charge that moves at the speed of light along a path that encloses a toroidal volume. A magnetic flux quantum Φ_M = h/e stabilizes the proton's charge trajectory. The two curvatures of the toroidal and poloidal current loops are determined by the magnetic forces associated with Φ_M. We compare our calculations against experimental data.

According to a scalar theory of gravity with a preferred frame, electromagnetism in the presence of a gravitational field implies that there is an additional energy tensor, which might contribute to dark matter. The expression of this tensor is determined by a mere scalar p, that depends on the EM field and (for a weak field) on the Newtonian gravitational field. We briefly recall why this tensor arises and how the EM field in a galaxy can be calculated. The data fields that enter the PDE for the scalar field p oscillate very quickly in space and time, as does the EM field. This prevents integration of that PDE at the relevant galactic scale. Therefore, a homogenization of that PDE has to be operated. We discuss in some detail three possible ways of applying the homogenization theory to that PDE: time, space, or spacetime homogenization. The second and third ways may lead to feasible, albeit heavy calculations.

We compare various formalisms for neutral particles. It is found that they contain unexplained contradictions. Next, we investigate the spin-1/2 and spin-1 cases in different bases. Next, we look for relations with the Majorana-like field operator. We show explicitly incompatibility of the Majorana anzatzen with the Dirac-like field operators in both the original Majorana theory and its generalizations. Several explicit examples are presented for higher spins too. It seems that the calculations in the helicity basis only give mathematically and physically reasonable results.

If we use the path integral approach, we can write quantum electrodynamics (QED) in a way that is manifestly relativistic. However the path integrals are confined to paths that are on mass-shell. What happens if we extend QED by computing the path integrals over all paths in energy momentum space, not only those on mass-shell? We use the requirement of covariance to do this in an unambiguous way. This gives a QED where the time/energy components appear in a way that is manifestly parallel to the space/momentum components: we have dispersion in time, entanglement in time, full equivalence of the Heisenberg uncertainty principle (HUP) in time to the HUP in space, and so on. Entanglement in time has the welcome side effect of eliminating the ultraviolet divergences. We recover standard QED in the long time limit. We predict effects at scales of attoseconds. With recent developments in attosecond physics and in quantum computing, these effects should be detectable. Since the predictions are unambiguous and testable the approach is falsifiable. Falsification would sharpen our understanding of the role of time in QED. Confirmation would have significant implications for attosecond physics, quantum computing and communications, and quantum gravity.

This article serves as a review of the mathematical tool of group contraction with an emphasis on physical applications. It was implicitly understood that some theories contain others as a special case (e.g., the relation between special relativity and Newtonian mechanics), but until the 1950s there was no firm mathematical grounding for such relations. We discuss the historical development of these concepts, their application to symmetry groups of space and time, and their relevance to the phenomenon of spontaneous symmetry breaking. Finally, we close by proposing a speculative chronology of space-time symmetries in the early universe.

The Bohigas-Giannoni-Schmit (BGS) conjecture states that the Hamiltonian of a microscopic analogue of a classical chaotic system can be modeled by a random matrix from a Gaussian ensemble. Here, this conjecture is considered in the context of a recently discovered geometric relationship between classical and quantum mechanics. Motivated by BGS, we conjecture that the Hamiltonian of a system whose classical counterpart performs a random walk can be modeled by a family of independent random matrices from the Gaussian unitary ensemble. By accepting this conjecture, we find a relationship between the process of observation in classical and quantum physics, derive irreversibility of observation and describe the boundary between the micro and macro worlds.

We discuss the torsion geometries as the universal dynamical setting for the five-fold symmetry and its relation to nonorientable surfaces of selfreference embodying a supradual logophysics, rooted in the Möbius strip and Klein Bottle. We frame the discussion in terms of image-schemas in cognitive semantics and their disruption stemming from supraduality and nonorientability. We present the relation with anholonomic phases, chaos and the brain-mind as an integrated dynamical system. We discuss nonorientability as the characteristic transcendental metapattern of resonant connection, pattern formation and recognition. We present the torsion geometry and nonorientability in psychophysics and the neurosciences. We discuss the homology of the torsion geometry of physical space or spacetime with that of the unconscious modelization by the brain-mind of the kinematics of objects in physical space and in the perception of music, elaborating on the Principle of Complementarity of cognitive psychology due to Shepard. We elaborate on the phenomenological construal of experience, the world as experience. We discuss the supraduality of the liminal states of consciousness and the basis of awareness in memory. We introduce the cognitive psychology foundations of memory on nonorientability and its relations to the short-memory space and its quantumlike nature, and the hyperbolicity of the psychophysics of vision. We discuss the chaotic behaviour of dynamical systems as a manifestation of supraduality as their nonorientability. We propose a basis for the source of consciousness, the Hard Problem, given by the principles of selfreference and hetero-reference which generate the Klein Bottle supradual logophysics. We present the supradual logophysics of neuron cytoskeletal structures, its relation to torsion, resonances, topological and geometrical phases and the microtubule dynamics in terms of nonlinear buckling patterns and nonorientability, and still the torsion geometry of the irreversible thermodynamical processes supporting interactions-at-a-distance. We discuss the primal relation of torsion, nonorientability and memory, particularly arising in the buckling of microtubules. We discuss the primal morphogenesis of the cell as a tensegrity structure, torsion and the indiscernibility of elastodynamics, electromagnetic and gravitational wavefronts as morphogenetic fields. We discuss nonorientability as the metaform pattern of connection and resonance, particularly of interaction-at-a-distance. We apply it to a topological allosteric effect mediated by electromagnetic fields. We discuss the topological chemistry paradigm, particularly of organic chemistry where conformation superposition is crucial, its relation to anaesthetics and its application to the ORC OR theory of Penrose and Hameroff for consciousness as arising from the collapse of the wave function which we relate to the multiconformation in the topological chemistry paradigm. We propose a model of continuous signal processing in digital terms which allows an optimal reconstruction -from digital to continuous-in terms of the Nyquist-Shannon theorem whose constraints on frequencies and bandwidths is naturally interpreted in the terms of the 2:1 harmonics of nonorientability in the Möbius strip or Klein Bottle. We discuss the non-dual logic of the tubulin code and the resonator nature of the neuronal cytoskeleton. We propose that the topological phases appearing in the cytoskeleton may correspond to the topological anholonomity, namely, nonorientability, as was elicited empirically by the Bandyopadhyay group, the existence of anholonomity corresponding to the 360° rotation characteristic of the topological anholonomity, Möbius strip. We propose the Matrix Logic representation of the Klein Bottle logic as the basis for microtubule computations, and discuss the relation to quantum computation, topological entanglement and the topological coherence/decoherence Klein Bottle cycle. We also relate it to holography, the brain's integration and Velmans' Reflexive Monism extended by Rapoport. We discuss the multiconformation orientable and nonorientable resonators electronic devices and antennas as classical-quantum realisations of microtubule coherent behaviour. We discuss the relation of life and consciousness and the topological nonorientable embodiment of memory. We introduce the dynamical reduction program for the collapse of the quantum state in terms of the torsion stochastic differential geometry of the quantum geometry of Quantum Mechanics as projective space, and particularly the stochastic extension of the Schroedinger equation to account for the coupling of quantum system and environment, say a measurement apparatus. Thus we identify a realisation of the dynamical reduction program which is based on the torsion geometry, yet supports an agent-free collapse of the quantum state, as an objective albeit random process due to quantum fluctuations. We shall discuss the present supradual logophysics in several aspects such as 1) microtubule structure and dynamics, 2) the orientable and nonorientable conformations of organic molecules, 3) the relation with anaesthetics and the altered states of consciousness and 4) confront them with the tenets of Penrose & Hameroff ORC OR theory for the origin of consciousness, not only the topological chemistry but their choice of a superposition of null torsion as in General Relativity, which renders a trivial selfreferentiality, with the topological chemistry multiconformations which requires non-null torsion. The nontrivial selfreferentiality is both proper to the mind and the torsion geometry, be that on the physical, chemical, perceptual or cognitive domains. All in all, we propose that consciousness is neither based on panpsychism nor the collapse of quantum states, nor exclusively on the control of superposition of conformations of organic chemistry, but rather on the torsion-nonorientable geometry-topology based on the principles of selfreference and hetero-reference, operating in all domains: that of meaning, the mental-anatomical-physiological domain, structural processes of matter energy and in-formation, be that physical, chemical, biological, cognitive and perception. We present a remarkable connection between them. Our approach rather than multidisciplinary will be transdisciplinary, a possibility supported on supraduality - transcending the dual-logic based logophysics-from which the theory will follow in a rather smooth way.