Panmicropsychism is the view that the fundamental physical ingredients of our universe are also its fundamental phenomenal ingredients. Since there is only a limited number of fundamental physical ingredients, panmicropsychism seems to imply that there exists only a small set (palette) of basic phenomenal qualities. How does this limited palette of basic phenomenal qualities give rise to our rich set of experiences? This is known as ‘the palette problem’. One class of solutions to this problem, large-palette solutions, simply denies that (...) the palette is limited. These solutions assume that all types of phenomenal qualities (color, sound, odor, taste, etc., and presumably also types not experienced by humans) were created fully formed at the birth of our universe. On this view, brains evoke conscious experiences by sampling primordial, preexisting phenomenal spaces. My main claim in this paper is that, by analogy with the mathematical description of the fundamental physical ingredients of our universe, which exhibits simplicity, symmetry, and beauty, panmicropsychists should expect the mathematical description of the fundamental phenomenal ingredients of our universe to exhibit similar features. The goal of this paper is to exemplify this claim using what is arguably the simplest of all types of phenomenal qualities—color. Specifically, I utilize phenomenological data on color to construct the maximally symmetric mathematical description of phenomenal color space. I then show that this mathematical description is isomorphic to the mathematical description of two-state quantum systems in a mixed state. Based on this isomorphism, I suggest that color may be the phenomenal dual aspect of two-state quantum systems. (shrink)

A geometric approach to quantum mechanics with unitary evolution and non-unitary collapse processes is developed. In this approach the Schrödinger evolution of a quantum system is a geodesic motion on the space of states of the system furnished with an appropriate Riemannian metric. The measuring device is modeled by a perturbation of the metric. The process of measurement is identified with a geodesic motion of state of the system in the perturbed metric. Under the assumption of random (...) fluctuations of the perturbed metric, the Born rule for probabilities of collapse is derived. The approach is applied to a two-level quantum system to obtain a simple geometric interpretation of quantum commutators, the uncertainty principle and Planck’s constant. In light of this, a lucid analysis of the double-slit experiment with collapse and an experiment on a pair of entangled particles is presented. (shrink)

We develop the theory of symmetry for a two-level quantum system in oder to illustrate the main ideas of the general theory of symmetry in quantum theory. It is based on the diffeomorphism of the two-dimensional sphere S 2 onto the space of states ℂP 1 and the isomorphism between the groups Pℳ(2) and SO 3 (ℝ). In particular, rotational invariance leads to the appearance of the spin1/2 in a natural way.

A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be attributed to individual quantum systems without violating standard quantum mechanics, which are called intrinsic. The intrinsic properties are classified into structural and conditional. A systematic and self-consistent account is given. Much more statements become meaningful than any (...) version of Copenhagen interpretation would allow. A new approach to classical properties and measurement problem is suggested. A quantum definition of classical states is proposed. (shrink)

In a recent paper, a “distance” function, $\cal D$ , was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a “distance”, D, which measures the distance between either pure or impure classical and quantum states. We also compare the new distance formula with the previous formula, when the latter is applicable. To illustrate these distances, we have used 2 × 2 matrix examples and two-dimensional vectors (...) for simplicity and clarity. Several specific examples are calculated. (shrink)

In a previous article it was shown that in general quantum states represent perspectives on the potentialities of quantum systems, rather than the potentialities themselves. In the present paper the following questions are investigated in the context of this result: (1) How do quantum states which undergo collapse transform under pure translations? (2) Under what conditions do quantum states represent the potentialities themselves? Two alternatives are presented in response to the first question: (1) Quantum (...) states are scalars under translations. (2) The collapse of a quantum state propagates between frames of reference at the speed of light. The advantages and disadvantages of the two alternatives are discussed. The response to the second question is shown to depend on the chosen alternative. In addition, the second alternative is shown to lead to a consistent view of quantum states as “potential perspectives on potentialities.”. (shrink)

Models of the EPR-Bohm experiment usually consider just two times, an initial time, and the time of measurement. Within such analyses, it has been argued that locality is equivalent to determinism, given the strict correlations of quantum mechanics. However, an analysis based on such models is only a preliminary to an analysis based on a complete dynamical model. The latter analysis is carried out, and it is shown that, given certain definitions of locality and determinism for completely dynamical models, (...) locality implies, but is not implied by, determinism. Further, it is suggested that a local deterministic model has not been ruled out by Bell's theorem. It is suggested that such a model could naturally deny the independence of initial complete states from the settings of the apparatuses (a crucial assumption in the derivation of Bell's inequality). (shrink)

An effective formalism is developed to handle decaying two-state systems. Herewith, observables of such systems can be described by a single operator in the Heisenberg picture. This allows for using the usual framework in quantum information theory and, hence, to enlighten the quantum features of such systems compared to non-decaying systems. We apply it to systems in high energy physics, i.e. to oscillating meson–antimeson systems. In particular, we discuss the entropic Heisenberg (...) uncertainty relation for observables measured at different times at accelerator facilities including the effect of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{CP}$\end{document} violation, i.e. the imbalance of matter and antimatter. An operator-form of Bell inequalities for systems in high energy physics is presented, i.e. a Bell-witness operator, which allows for simple analysis of unstable systems. (shrink)

A theorem is derived that enables a systematic enumeration of all the linear superoperators ℒ (associated with a two-level quantum system) that generate, via the law of motion ℒρ= $\dot \rho$ , mappings ρ(0) → ρ(t) restricted to the domain of statistical operators. Such dynamical evolutions include the usual Hamiltonian motion as a special case, but they also encompass more general motions, which are noncyclic and feature a destination state ρ(t → ∞) that is in some cases independent (...) of ρ(0). (shrink)

The statistical properties of a single quantum object and an ensemble of independent such objects are considered in detail for two-level systems. Computer simulations of dynamic zero-point quantum fluctuations for a single quantum object are reported and compared with analytic solutions for the ensemble case.

A pair of spin-j particles, prepared in a singlet state, move away from each other and are examined by two distant observers. If the latter are able to discriminate between the2j+1 values of a component ofJ, there are pairs of observables whose correlation strongly violates Bell's inequality, for arbitrarily large j. However, if neighboring values are lumped together because of limited instrumental resolution, the observable correlations tend to those predicted by classical mechanics.

A novel photon-based proton model is developed. A proton’s ground state is assumed to be coherent to the degree that all of its mass-energy precipitates into a single uncharged spherical structure. A quantum vortex, initiated by the strong force, but sustained in the proton’s ground state by the circular Unruh effect and a spherical Rindler horizon, is proposed to confine the proton’s mass-energy in its ground state. A direct connection between the circular Unruh effect, the zitterbewegung (...) effect, spin, and general relativity is proposed. Such a structure acts as an uncharged zitterbewegung fermion, and may explain neutrino mass. A ground-state proton’s central zitterbewegung fermion is assumed to be surrounded by a halo of charge shells of both signs. Virtual photon standing waves are assumed to synchronize the inner shell with the central zitterbewegung fermion. The charge shells are proposed to be associated with isospin and proton g-factor. There are only two model inputs—proton mass and quantized electronic charge—and just one adjustable parameter. The adjustable parameter, reduced only by about 0.4% from an initial estimate, provides the proton’s experimentally determined magnetic moment to arbitrary precision. The resulting modeled proton charge radius agrees very well with the 2018 CODATA value. Magnetic moment and charge radius are calculated algebraically in a manner easily understood by undergraduate physics students. This proposed ground-state proton model could be considered a low-energy approximation to a full quantum chromodynamical proton model. (shrink)

Identifying the physiological processes in the central nervous system that underlie our conscious experiences has been at the forefront of cognitive neuroscience. While the principles of classical physics were long found to be unaccommodating for a causally effective consciousness, the inherent indeterminism of quantum physics, together with its characteristic dichotomy between quantum states and quantum observables, provides a fertile ground for the physical modeling of consciousness. Here, we utilize the Schrödinger equation, together with the Planck-Einstein relation between (...) energy and frequency, in order to determine the appropriate quantum dynamical timescale of conscious processes. Furthermore, with the help of a simple two-qubit toy model we illustrate the importance of non-zero interaction Hamiltonian for the generation of quantum entanglement and manifestation of observable correlations between different measurement outcomes. Employing a quantitative measure of entanglement based on Schmidt decomposition, we show that quantum evolution governed only by internal Hamiltonians for the individual quantum subsystems preserves quantum coherence of separable initial quantum states, but eliminates the possibility of any interaction and quantum entanglement. The presence of non-zero interaction Hamiltonian, however, allows for decoherence of the individual quantum subsystems along with their mutual interaction and quantum entanglement. The presented results show that quantum coherence of individual subsystems cannot be used for cognitive binding because it is a physical mechanism that leads to separability and non-interaction. In contrast, quantum interactions with their associated decoherence of individual subsystems are instrumental for dynamical changes in the quantum entanglement of the composite quantum state vector and manifested correlations of different observable outcomes. Thus, fast decoherence timescales could assist cognitive binding through quantum entanglement across extensive neural networks in the brain cortex. (shrink)

Theoretical methods for empirical state determination of entangled two-level systems are analyzed in relation to information theory. We show that hidden variable theories would lead to a Shannon index of correlation between the entangled subsystems which is larger than that predicted by quantum mechanics. Canonical representations which have maximal correlations are treated by the use of Schmidt and Hilbert-Schmidt decomposition of the entangled states, including especially the Bohm singlet state and the GHZ entangled states. We show (...) that quantum mechanics does not violate locality, but does violate realism. (shrink)

Given a quantum system with a very large number of degrees of freedom and a preferred tensor product factorization of the Hilbert space we describe how it can be approximated with a very low-dimensional field theory with geometric degrees of freedom. The geometric approximation procedure consists of three steps. The first step is to construct weighted graphs with vertices representing subsystems and edges representing mutual information between subsystems. The second step is to deform the adjacency matrices of the information (...) graphs to that of a low-dimensional lattice using the graph flow equations introduced in the paper. The third step is to define an emergent metric and to derive an effective description of the metric and possibly other degrees of freedom. To illustrate the procedure we analyze two information graph flows with geometric attractors and metric perturbations obeying a geometric flow equation. Our analysis also suggests a possible approach to quantum gravity in which the geometry emerges directly from a quantum state due to the flow of the information graphs. (shrink)

Two quantum Macro-states and their Macroscopic Quantum Superpositions (MQS) localized in two far apart, space-like separated sites can be non-locally correlated by any entangled couple of single-particles having interacted in the past. This novel “Macro-Macro” paradigm is investigated on the basis of a recent study on an entangled Micro-Macro system involving N≈105 particles. Crucial experimental issues as the violation of Bell’s inequalities by the Macro-Macro system are considered.

Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic (...) class='Hi'>quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions. (shrink)

This communication is part I of a series of papers which explore the theoretical possibility of generalizing quantum dynamics in such a way that the predicted motions of an isolated system would include the irreversible (entropy-increasing) state evolutions that seem essential if the second law of thermodynamics is ever to become a theorem of mechanics. In this first paper, the general mathematical framework for describing linear but not necessarily Hamiltonian mappings of the statistical operator is reviewed, with particular (...) attention to detailed representations of the Kossakowski conditions for the case of a two-level system. (shrink)

We develop here the general treatment arising from the Bethe-Salpeter equation for a two-particle bound system in which at least one of the particles is spinless. It is shown that a natural two-component formalism can be formulated for describing the propagators of scalar particles. This leads to a formulation of the Bethe-Salpeter equation in a form very reminiscent of the fermion-fermion case. It is also shown, that using this two-component formulation for spinless particles, the perturbation theory can be systematically developed (...) in a manner similar to that of fermions. Quantum electrodynamics for scalar particles is then developed in the two component formalism, and the problem of bound states, in which one of the constituent particles is spinless, is examined by means of the means of the Bethe-Salpeter equation. For this case, the Bethe-Salpeter equation is cast into a form which is convenient to perform a Foldy-Woutyhuysen transformation which we carry out, keeping the lowest-order relativistic corrections to the nonrelativistic equation. The results are compared with the corresponding fermion-fermion case. It is shown, as might have been expected, that the only spin-independent terms that occur for the fermion-fermion system which do not occur for bound scalar particle cases, is the zitterbewegung contribution. The relevance of the above considerations for systems that are essentially bound by electromagnetic interactions, such as kaonic hydrogen, is discussed. (shrink)

In the first half of this two-part article, we analyzed a cognitive psychology experiment where participants were asked to select pairs of directions that they considered to be the best example of Two Different Wind Directions, and showed that the data violate the CHSH version of Bell’s inequality, with same magnitude as in typical Bell-test experiments in physics. In this second part, we complete our analysis by presenting a symmetrized version of the experiment, still violating the CHSH inequality but now (...) also obeying the marginal law, for which we provide a full quantum modeling in Hilbert space, using a singlet state and suitably chosen product measurements. We also address some of the criticisms that have been recently directed at experiments of this kind, according to which they would not highlight the presence of genuine forms of entanglement. We explain that these criticisms are based on a view of entanglement that is too restrictive, thus unable to capture all possible ways physical and conceptual entities can connect and form systems behaving as a whole. We also provide an example of a mechanical model showing that the violations of the marginal law and Bell inequalities are generally to be associated with different mechanisms. (shrink)

The present paper discusses the problem of quantum-mechanical properties of a subject’s consciousness. The model of generalized economic measurements is used for the analysis. Two types of such measurements are analyzed – transactions and technologies. Algebraic ratios between the technology-type measurements allow making their analogy with slit experiments in physics. It has been shown that the description of results of such measurements is possible both in classical and in quantum formalism of calculation of probabilities. Thus, the quantum-mechanical (...) formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness. (shrink)

The analysis, with the use of two state vectors, of a quantum system, during the time interval between two measurements, leads to some amazing results, which seem to contradict our usual “quantum common sense.” We explore the questions of compatibility with the conventional quantum theory, uniqueness of pre- and post-selected ensembles, commutativity, simultaneity and reality of strong and weak values in the intermediate time, and the meaning of the weak value. Common criticisms are shown to be (...) unfounded. (shrink)

A two-body quantum correlation is calculated for a particle reflecting from a moving mirror. Correlated interference results when the incident and reflected particle substates and their associated mirror substates overlap. Using the Copenhagen interpretation of measurement, an asynchronous joint probability density, which is a function both of the different positions and different times at which the particle and mirror are measured, is derived assuming that no interaction occurs between each measurement. Measurement of the particle first, in the correlated interference (...) region, results in a splitting of the mirror substate into ones which have and have not reflected the particle. An analog of the interference from the Doppler effect for only measurements of the particle, in this two-body system, is shown to be a consequence of the asynchronous measurement. The simplification obtained for a microscopic particle reflecting from a mesoscopic or macroscopic mirror is used to illustrate asynchronous correlation interferometry. In this case, the small displacement between these mirror states can yield negligible environmental decoherence times. In addition, interference of these mirror states does not vanish in the limit of large mirror mass due to the small momentum exchange in reflecting a microscopic particle. (shrink)

We discuss foundational issues of quantum information biology —one of the most successful applications of the quantum formalism outside of physics. QIB provides a multi-scale model of information processing in bio-systems: from proteins and cells to cognitive and social systems. This theory has to be sharply distinguished from “traditional quantum biophysics”. The latter is about quantum bio-physical processes, e.g., in cells or brains. QIB models the dynamics of information states of bio-systems. We argue (...) that the information interpretation of quantum mechanics is the most natural interpretation of QIB. Biologically QIB is based on two principles: adaptivity; openness. These principles are mathematically represented in the framework of a novel formalism— quantum adaptive dynamics which, in particular, contains the standard theory of open quantum systems. (shrink)

Atomic states are rigorously characterized by the total orbital angular momentum and the total spin angular momentum, but chemists persist in the use of electron configurations based on one-electron quantum numbers and simplified rules for predicting ground state configurations. This practice is defended against two lines of criticism, and its use in teaching chemistry is encouraged with the claim that the inductive approach of Mendeleev and the deductive approach initiated by Schrödinger compose the consummate example of that interaction (...) of empirical and rational epistemologies that defines how chemists think. (shrink)

The relativistic Schrödinger theory (RST) for N-fermion systems is further elaborated with respect to three fundamental problems which must emerge in any relativistic theory of quantum matter: (i) emergence/suppression of exchange forces between identical/non-identical particles, (ii) self-interactions, (iii) non-relativistic approximation. These questions are studied in detail for two- and three-particle systems but the results do apply to a general N-particle system. As a concrete demonstration, the singlet and triplet configurations of the positronium groundstate are considered within the (...) RST framework, including a discussion of the corresponding hyperfine splitting. (shrink)

This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give (...) examples of simple states of a model system, the kicked top, which have the statistical properties of random states. Interestingly, examples of both kinds of randomness can be found in the same system. In studying the last two kinds of random state, we obtain new results concerning the application of information theory to quantum systems. (shrink)

It is well known that the non-orthogonality relation between the (pure) states of a quantum system is reflexive and symmetric, and the modal logic $$\mathbf {KTB}$$ is sound and complete with respect to the class of sets each equipped with a reflexive and symmetric binary relation. In this paper, we consider two properties of the non-orthogonality relation: Separation and Superposition. We find sound and complete modal axiomatizations for the classes of sets each equipped with a reflexive and symmetric relation (...) that satisfies each one of these two properties and both, respectively. We also show that the modal logics involved are decidable. (shrink)

In the literature there has been evidence that a kind of relational structure called a quantum Kripke frame captures the essential characteristics of the orthogonality relation between pure states of quantum systems, and thus is a good qualitative mathematical model of quantum systems. This paper adds another piece of evidence by providing a tensor-product construction of two finite-dimensional quantum Kripke frames. We prove that this construction is exactly the qualitative counterpart of the tensor-product construction (...) of two finite-dimensional Hilbert spaces over the complex numbers, and thus show that composition of quantum systems, especially the phenomenon of quantum entanglement, can be modelled in the framework of quantum Kripke frames. The assumptions used in our construction hint that we need complex numbers in quantum theory. Moreover, for this construction, we give a new and interesting characterization of linear maps of trace 0 in terms of the orthogonality relation. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to (...) the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)

Complex Systems Biology approaches are here considered from the viewpoint of Robert Rosen’s (M,R)-systems, Relational Biology and Quantum theory, as well as from the standpoint of computer modeling. Realizability and Entailment of (M,R)-systems are two key aspects that relate the abstract, mathematical world of organizational structure introduced by Rosen to the various physicochemical structures of complex biological systems. Their importance for understanding biological function and life itself, as well as for designing new strategies for treating (...) diseases such as cancers, is pointed out. The roles played by multiple metastable states in the “continuous uphill flow of Life” supported through internal bioenergetic processes that are coupled to essential inflows are also discussed in relation to dynamic realizations of (M,R)-systems. Furthermore, the roles played by the underlying, many-valued, quantum logics and symbolic computations for ultra-complex biological systems are also briefly discussed. (shrink)

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one (...) system. The first theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

Modal interpretations take quantum mechanics as a theory which assigns at all times definite values to magnitudes of quantum systems. In the case of single systems, modal interpretations manage to do so without falling prey to the Kochen and Specker no-go theorem, because they assign values only to a limited set of magnitudes. In this paper I present two further no-go theorems which prove that two modal interpretations become nevertheless problematic when applied to more than one (...) system. The first theorem proves that the modal interpretation proposed by Kochen and by Dieks cannot correlate the values simultaneously assigned to three systems. The second and new theorem proves that the atomic modal interpretation proposed by Bacciagaluppi and Dickson and by Dieks cannot correlate the values simultaneously and sequentially assigned to two systems if one assumes that these correlations are uniquely related to the dynamics of the state of the systems. (shrink)

We present the Dirac and Laplacian operators on Clifford bundles over space–time, associated to metric compatible linear connections of Cartan–Weyl, with trace-torsion, Q. In the case of nondegenerate metrics, we obtain a theory of generalized Brownian motions whose drift is the metric conjugate of Q. We give the constitutive equations for Q. We find that it contains Maxwell’s equations, characterized by two potentials, an harmonic one which has a zero field (Bohm-Aharonov potential) and a coexact term that generalizes the Hertz (...) potential of Maxwell’s equations in Minkowski space.We develop the theory of the Hertz potential for a general Riemannian manifold. We study the invariant state for the theory, and determine the decomposition of Q in this state which has an invariant Born measure. In addition to the logarithmic potential derivative term, we have the previous Maxwellian potentials normalized by the invariant density. We characterize the time-evolution irreversibility of the Brownian motions generated by the Cartan–Weyl laplacians, in terms of these normalized Maxwell’s potentials. We prove the equivalence of the sourceless Maxwell equation on Minkowski space, and the Dirac-Hestenes equation for a Dirac-Hestenes spinor field written on Minkowski space provided with a Cartan–Weyl connection. If Q is characterized by the invariant state of the diffusion process generated on Euclidean space, then the Maxwell’s potentials appearing in Q can be seen alternatively as derived from the internal rotational degrees of freedom of the Dirac-Hestenes spinor field, yet the equivalence between Maxwell’s equation and Dirac-Hestenes equations is valid if we have that these potentials have only two components corresponding to the spin-plane. We present Lorentz-invariant diffusion representations for the Cartan–Weyl connections that sustain the equivalence of these equations, and furthermore, the diffusion of differential forms along these Brownian motions. We prove that the construction of the relativistic Brownian motion theory for the flat Minkowski metric, follows from the choices of the degenerate Clifford structure and the Oron and Horwitz relativistic Gaussian, instead of the Euclidean structure and the orthogonal invariant Gaussian. We further indicate the random Poincaré–Cartan invariants of phase-space provided with the canonical symplectic structure. We introduce the energy-form of the exact terms of Q and derive the relativistic quantum potential from the groundstate representation. We derive the field equations corresponding to these exact terms from an average on the invariant state Cartan scalar curvature, and find that the quantum potential can be identified with 1 / 12R(g), where R(g) is the metric scalar curvature. We establish a link between an anisotropic noise tensor and the genesis of a gravitational field in terms of the generalized Brownian motions. Thus, when we have a nontrivial curvature, we can identify the quantum nonlocal correlations with the gravitational field. We discuss the relations of this work with the heat kernel approach in quantum gravity. We finally present for the case of Q restricted to this exact term a supersymmetric system, in the classical sense due to E.Witten, and discuss the possible extensions to include the electromagnetic potential terms of Q. (shrink)

A mathematical rigorous definition of EPR states has been introduced by Arens and Varadarajan for finite dimensional systems, and extended by Werner to general systems. In the present paper we follow a definition of EPR states due to Werner. Then we show that an EPR state for incommensurable pairs is Bell correlated, and that the set of EPR states for incommensurable pairs is norm dense between two strictly space-like separated regions in algebraic quantum field theory.

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed (...) scattering and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (shrink)

The paper reviews the current situation regarding a new theory of brain dynamics put forward by the authors in an earlier publication. Motivation for the theory is discussed in terms of two issues: the long-standing problem of accounting for the stability and nonlocal properties of memory, and the experimental and theoretical evidence against the classical theory of brain action. It is shown that the new theory provides an explanation and a conceptually unifying framework for phenomena of brain action that resist (...) classical explanation. Further independent experiments provide strong additional support for the theory. The fact that this theory incorporates quantum mechanisms in an essential way is considered to be of wide scientific interest in view of the unique status of the brain in relation to the physical, biological, and mental orders in nature. (shrink)

I define sublaltices of quantum propositions that can be taken as having determinate (but perhaps unknown) truth values for a given quantum state, in the sense that sufficiently many two-valued maps satisfying a Boolean homomorphism condition exist on each determinate sublattice to generate a Kolmogorov probability space for the probabilities defined by the slate. I show that these sublattices are maximal, subject to certain constraints, from which it follows easily that they are unique. I discuss the relevance (...) of this result for the measurement problem, relating it to an early proposal by Jauch and Piron for defining a new notion of state for quantum systems, to a recent uniqueness proof by Clifton for the sublattice of propositions specified as determinate by modal interpretations of quantum mechanics that exploit the polar decompostion theorem, and to my own previous suggestions for interpreting quantum mechanics without the projection postulate. (shrink)

Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is a collection of 33 selected papers from the scientific contributions presented at the 16th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI), held at Ishikawa Prefecture Museum of Art in Kanazawa, Japan, from September 11th to 17th, 2011. The volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to (...) a wide range of problems in physics, chemistry, and biology. The breadth and depth of the scientific topics discussed during QSCP-XVI appears in the classification of the contributions in six parts: I. Fundamental Theory II. Molecular Processes III. Molecular Structure IV. Molecular Properties V. Condensed Matter VI. Biosystems. Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is written for advanced graduate students as well as for professionals in theoretical chemical physics and physical chemistry. The book covers current scientific topics in molecular, nano, material, and bio sciences and provides insights into methodological developments and applications of quantum theory in physics, chemistry, and biology that have become feasible at end of 2011. (shrink)

Quantum bit commitment is insecure in the standard non-relativistic quantum cryptographic framework, essentially because Alice can exploit quantum steering to defer making her commitment. Two assumptions in this framework are that: Alice knows the ensembles of evidence E corresponding to either commitment; and system E is quantum rather than classical. Here, we show how relaxing assumption or can render her malicious steering operation indeterminable or inexistent, respectively. Finally, we present a secure protocol that relaxes both assumptions (...) in a quantum teleportation setting. Without appeal to an ontological framework, we argue that the protocol’s security entails the reality of the quantum state, provided retrocausality is excluded. (shrink)

Weak measurements offer new insights into the behavior of quantum systems. Combined with post-selection, quantum mechanics predicts a range of new experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent pre- and post-selected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of post-selection and the choice of final (...) class='Hi'>state. The generalized law is illustrated for two interesting choices of post-selection. (shrink)

The concept of time-coarsened density matrix for open systems has frequently featured in equilibrium and non-equilibrium statistical mechanics, without being probed as to the detailed consequences of the time averaging procedure. In this work we introduce and prove the need for a selective and non-uniform time-sampling, whose form depends on the properties of the bath. It is also applicable when an open microscopic sub-system is coupled to another finite system. By use of a time-periodic minimal coupling model between these (...) two systems, we present detailed quantitative consequences of time coarsening, which include initial state independence of equilibration, deviations from long term averages, their environment size dependence and the approach to classicality, as measured by a Leggett–Garg type inequality. An interacting multiple qubit model affords comparison between the time integrating procedure and the more conventional environment tracing method. (shrink)

Abstract This paper argues that there are good reasons to adopt a non-reductive account of states when it comes to quantum mechanics. That is to say, it is argued that there are advantages to thinking about states as sui generis, as reducible to classes of values of quantities, when it comes to the quantum domain. One reason for holding this view is that it seems to improve the prospects for explanation. In more detail, it is argued that there (...) is an 'explanatory shortfall' in the quantum domain owing to the failure of value definiteness. To remedy this situation, two proposals are put forward about the nature of the quantum state: Proposal A, that the quantum state is the only first-order property of quantum systems, Proposal B, that the quantum state is one first-order property among many. These proposals seem equally good. (shrink)

The interpretation of quantum mechanics is discussed from the viewpoint of quantum logic (QL). QL is understood to concern the possible properties that can be ascribed to a physical system SYS. The micro-state of SYS at any given moment t is identified with the set of all properties actualized by SYS at time t. Minimal adequacy requirements are proposed for all interpretations of micro-states. A strict interpretation is defined to be one according to which the properties ascribable (...) to SYS are individuated by the projection operators on the associated Hilbert space. Two strict interpretations are examined. Kochen's interpretation is also discussed, and it is argued that it is not a strict interpretation. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the (...) quantum state in a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

The problem of time’s arrow is (roughly) to understand why macroscopic physical processes typically evolve in a specific direction (the one we call “the future”) even though the underlying laws of physics describing the individual microscopic systems are time-reversal invariant. The standard answer to this problem is given by Boltzmann’s explanation of the II law of thermodynamics: a classical system starting in a non-equilibrium state spontaneously (i.e. with a high level of probability) tends towards equilibrium, thus implementing an (...) irreversible process. However, this explanation has two drawbacks: 1. it needs a further assumption on the entropy of the initial state of the universe (past hypothesis); 2. microscopic systems (e.g. molecules in a box) should be represented as quantum states and not classical states. In this talk, I want to propose a different hypothesis to explain the origin of time’s arrow, based on quantum mechanics, specifically on decoherence theory. Differently from isolated systems, open quantum systems described by decoherence theory show irreversible behavior, as they evolve towards decoherence and von Neumann entropy increase. Is this behavior a sign of genuine irreversibility? And, if so, can this be linked to thermodynamic irreversibility? (shrink)

In this brief paper, starting from recent works, we analyze from conceptual point of view this basic question: can be the nature of quantum entangled states interpreted ontologically or epistemologically? According some works, the degrees of freedom of quantum systems permit us to establish a possible classification between factorizables and entangled states. We suggest, that the "choice" of degree of freedom, even if mathematically justified introduces epistemic element, not only in the systems but also in their (...) classification. We retain, instead, that there are not two classes of quantum states, entangled and factorizables, but only a single classes of states: the entangled states. In fact, the factorizable states become entangled for a different choice of their degrees of freedom. In the same way, there are not partitions of quantum system which have an ontological superior status with respect to any other. For all these reasons, both mathematical tools utilized are responsible of improper classification of quantum systems. Finally, we argue that we cannot speak about a classification of quantum systems: all the quantum states exhibit a unique objective nature, they are all entangled states. (shrink)

Traditional philosophical discourse draws a distinction between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated and unrelated. In addition, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, all kinds of measurement-related problems force us to consider both our knowledge of the states and observables of a system (epistemic perspective) and its states and observables independent of such knowledge (ontic perspective). This applies to (...) class='Hi'>quantum systems in particular. (shrink)

Despite the progress made in studying the observable exteriors of conscious processes, which are reflected in the neural correlates of consciousness (NCC), there are still no satisfactory answers to two closely related core questions. These are the question of the origin of the subjective, phenomenal aspects of consciousness, and the question of the causal mechanisms underlying the generation of specific phenomenal states. In this article, we address these questions using a novel variant of cosmopsychism, a holistic form of panpsychism relying (...) on the central idea that the universe is imbued with a ubiquitous field of consciousness (UFC). This field is understood as a foundational dual-aspect component of the cosmos, the extrinsic appearance of which is physical in nature and the intrinsic manifestation of which is phenomenological in nature. We argue that this approach brings a new perspective into play, according to which the organizational characteristics of the NCC are indicative of the brain’s interaction with and modulation of the UFC. Key insights from modern physics suggest that the modulation mechanism is identical with the fundamental mechanism underlying quantum systems, resulting in the conclusion that a coherently oscillating neural cell assembly acquires phenomenal properties by tapping into the universal pool of phenomenal nuances predetermined by the UFC, or more specifically, by entering into a temporary liaison with the UFC and extracting a subset of phenomenal tones from the phenomenal color palette inherent in the basic structure of the UFC. This hypothesis is supported by a substantial body of empirical evidence. (shrink)

El presente artículo busca ofrecer un análisis conceptual de la noción de información, a partir del modo en que es definida por las teorías formales de Claude Shannon y de Benjamin Schumacher. Contra la postura según la cual existen dos tipos de información de naturalezas diferentes, una información clásica y una información cuántica, aquí argumentamos que no hay razones suficientes para sostener la existencia de la información cuántica como un nuevo tipo sustancialmente distinto de información. Afirmamos así que existe un (...) único tipo de información que puede ser codificado de diversas maneras, en particular, mediante sistemas clásicos o sistemas cuánticos. Esta posición nos conducirá a concebir un concepto unificado y abstracto de información, en un contexto donde la teoría de Shannon resulta neutral e independiente de las teorías físicas utilizadas para describir las partes involucradas en el proceso de transmitir información, y la teoría de Schumacher no define un nuevo tipo de entidad informacional, sino una manera alternativa de codificar la información mediante estados cuánticos. The aim of this article is to offer a conceptual analysis of the notion of information, on the basis of the way in which it is defined by the theories of Claude Shannon and of Benjamin Schumacher. Against the position according to which there are two kinds of information of different natures, a classical information and a quantum information, here we argue that there are not sufficient reasons to maintain the existence of quantum information as a new and substantially different kind of information. So we claim that there is only one kind of information, which can be encoded in different ways, in particular, by means of classical or quantum systems. This position will lead us to conceive an unified and abstract concept of information in a context where Shannon's theory is neutral and independent from the physical theories used to describe the stages involved in the process of transmitting information, and Schumacher's theory does not define a new kind of informational entity, but a alternative way of coding information by means of quantum states. (shrink)