In the present article, I propose to give a positive characterization of ontological emergence from a relational perspective that, in opposition both to atomism and to holism, defends that the existence-conditions, the identity and the behavior or causal role of any emergent entity are to be conceived, and explained, as constructed by diverse systems of qualitatively transformative relations. I argue that from this relational perspective, the notion of emergence can be seen as ontologically and epistemologically coherent and significant. Finally, I (...) try to show in what sense, and to what extent, the Nonlinear Quantum Physics, as developed by Croca and his team, expresses such a relational and emergentist view of physical reality. (shrink)

A (to our knowledge) novel Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson’s fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final (...) formulation of Quantum Gravity. (shrink)

This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has (...) the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws. (shrink)

A general solution is obtained for a model of a nonlinear quantum theory for gravitating particles proposed by H. Efinger. The solution procedure is easily generalized to space-time or stochastic formulations.

Quantum theory is one of the most fascinating and successful constructs in the intellectual history of mankind. Nonetheless, the theory has very shaky philosophical foundations. This book contains thoughtful discussions by eminent researchers of a spate of experimental techniques newly developed to test some of the stranger predictions of quantum physics. The advances considered include recent experiments in quantum optics, electron and ion interferometry, photon down conversion in nonlinear crystals, single trapped ions interacting with laser (...) beams, atom-field coupling in micromaser cavities, quantum computation, quantum cryptography, decoherence and macroscopic quantum effects, the quantum state diffusion model, quantum gravity, the quantum mechanics of cosmology and quantum non-locality along with the continuing debate surrounding the interpretation of quantum mechanics. -/- Audience: The book is intended for physicists, philosophers of science, mathematicians, graduate students and those interested in the foundations of quantum theory. (shrink)

We discuss Einstein's ideas on the need for a theory that is both objective and local and also his suggestion for realizing such a theory through nonlinear field equations. We go on to analyze the nonlocality implied by the quantum theory, especially in terms of the experiment of Einstein, Podolsky, and Rosen. We then suggest an objective local field model along Einstein's lines, which might explain quantum nonlocality as a coordination of the properties of pulse-like solutions of (...) the nonlinear equations that would represent particles. Finally, we discuss the implications of our model for Bell's inequality. (shrink)

This paper explores the possibility that linear dynamical maps might be used to describe the energy-conserving, entropy-increasing motions which occur in closed thermodynamic systems as they approach canonical thermal equilibrium. ForN-level quantum systems withN>2, we prove that no such maps exist which are independent of the initial state.

The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to (...) provide a solid functional analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics. (shrink)

In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP) where particles are represented as bunched fields or solitons guided by a base (weaker) wave. DSP evolved as the famous de Broglie-Bohm pilot wave interpretation (PWI) also known as Bohmian mechanics but the general idea to use solitons guided by a base wave to reproduce the dynamics of the PWI was abandoned. Here we propose a nonlinear scalar field (...) theory able to reproduce the PWI for the Schrödinger and Klein–Gordon guiding waves. Our model relies on a relativistic ‘phase harmony’ condition locking the phases of the solitonic particle and the guiding wave. We also discuss an extension of the theory for the N particles cases in presence of entanglement and external (classical) electromagnectic fields. (shrink)

The relationship between quantum collapse and consciousness is reconsidered under the assumption that quantum collapse is an objective dynamical process. We argue that the conscious observer can have a distinct role from the physical measuring device during the process of quantum collapse owing to the intrinsic nature of consciousness; the conscious observer can know whether he is in a definite state or a quantum superposition of definite states, while the physical measuring device cannot “know”. As a (...) result, the consciousness observer can distinguish the definite states and their quantum superposition, while the physical measuring device without consciousness cannot do. This provides a possible quantum physical method to distinguish man and machine. The new result also implies that consciousness has causal efficacies in the physical world when considering the existence of quantum collapse. Accordingly consciousness is not reducible or emergent, but a new fundamental property of matter. This may establish a quantum basis for panpsychism, and make it be a promising solution to the hard problem of consciousness. Furthermore, it is suggested that a unified theory of matter and consciousness includes two parts: one is the psychophysical principle or corresponding principle between conscious content and matter state, and the other is the complete quantum evolution of matter state, which includes the definite nonlinear evolution element introduced by consciousness and relating to conscious content. Lastly, some experimental schemes are presented to test the proposed quantum theory of consciousness. (shrink)

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.

A previous model for treating electromagnetic nonlinear wave systems is examined in the context of wave mechanics. It is shown that nonlinear wave mechanics implies harmonic generation of new quasiparticle wave functions, which are absent in linear systems. The phenomenon is interpreted in terms of pair (and higher order ensembles) coherence of the interacting particles. The implications are far-reaching, and the present approach might contribute toward a common basis for diverse physical phenomena involving nonlinearity. An intimate relationship connecting (...) coherence, nonlocal interaction, and nonlinearity has been previously noticed in the physics of superconductivity. It is shown here that all these ingredients are consistently contained in the present formalism. The present theory may contribute to elucidate a controversial theory proposed by Panarella, who claims to have measured high-energy photons due to high-intensity laser radiation, which cannot be predicted on the basis of linear quantum theory. Panarella explains the new phenomena by stipulating a nonlinear intensity-dependent photon energy. It is argued here that nonlinearity, manifested in the presence of high intensity, may give rise to high- and low-energy photons, the so-called “effective” and “tired” photons, respectively. However, the present explanation does not involve ad hoc assumptions regarding the foundations of quantum theory. In analogy with the electrodynamic model, the present theory leads to particulate self-focusing in high-density streams of particles. Since such particulate beams are currently under consideration in connection with fusion reactions, this might be of future interest. (shrink)

In this paper, we investigate the numerical solution of the coupled fractional massive Thirring equation with the aid of He’s fractional complex transform. This study plays a significant aspect in the field of quantum physics, weakly nonlinear thrilling waves, and nonlinear optics. The main advantage of FCT is that it converts the fractional differential equation into its traditional parts and is also capable to handle the fractional order, whereas the homotopy perturbation method is employed to tackle (...) the nonlinear terms in the coupled fractional massive Thirring equation. An example is illustrated to present the efficiency and validity of the two-scale theory. The solutions are obtained in the form of series with simple and easy computations which confirm that the present approach is good in agreement and is easy to implement for such type of complex systems in science and engineering. (shrink)

The main purpose of this book is to introduce a broader audience to emergence by illustrating how discoveries in the physical sciences have informed the ways we think about it. In a nutshell, emergence asserts that non-reductive behavior arises at higher levels of organization and complexity. As physicist Philip Anderson put it, "more is different." Along the text's conversational tour through the terrain of quantum physics, phase transitions, nonlinear and statistical physics, networks and complexity, the author (...) highlights the various philosophical nuances that arise in encounters with emergence. The final part of the book zooms out to reflect on some larger lessons that emergence affords us. One of those larger lessons is the realization that the great diversity of theories and models, and the great variety of independent explanatory frameworks, will always be with us in the sciences and beyond. There is no "Theory of Everything" just around the corner waiting to be discovered. One of the main benefits of this book is that it will make a number of exciting scientific concepts that are not normally covered at this level accessible to a broader audience. The overall presentation, including the use of examples, analogies, metaphors, and biographical interludes, is geared for the educated non-specialist. (shrink)

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the (...) Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively. (shrink)

The shape of the spectral lines of an optically active system interacting with one or more strong radiation fields in the presence of a perturbing bath is studied. A method based on the statistics of the fluctuation of the interaction between the radiator and the perturbing environment (the model Markov microfield theory) is used. This method permits the foundations of line shape theory in modern statistical mechanics to be seen clearly. Multiphoton processes and homogeneous, inhomogeneous, and power broadening mechanisms are (...) included in the analysis. The correlations between radiative and collisional processes which arise in nonlinear spectroscopy are included explicitly. A discussion of the new information that is obtained from these correlations in nonlinear spectroscopy is also presented. Several model systems are presented as illustrative examples of the theory. (shrink)

We consider an integrable, nonlocal and nonlinear, Schrödinger equation as a model for building space–time patchings in inhomogeneous loop quantum cosmology. We briefly review exact solutions of the NNSE, specially those obtained through “geometric equivalence” methods. Furthemore, we argue that the integrability of the NNSE could be linked to consistency conditions derived from LQC, under the assumption that the patchwork dynamics behaves as an integrable many-body system.

In the early 1960s of the 20th century de Broglie was able to explain the cosmological observable red shift, without ad hoc assumptions. Starting from basic quantum considerations he developed his tired light model for the photon. This model explains in a single and beautiful causal way the cosmological redshift without need of assuming the Big Bang and consequently a beginning for the universe. Evidence coming from Earth sciences seems also to confirm these ideas and furthermore concrete proposal of (...) laboratorial scale experiments that can test the model are reviewed. (shrink)

If one starts from de Broglie's basic relativistic assumptions, i.e., that all particles have an intrinsic real internal vibration in their rest frame, i.e., hv 0 =m 0 c 2 ; that when they are at any one point in space-time the phase of this vibration cannot depend on the choice of the reference frame, then, one can show (following Mackinnon (1) ) that there exists a nondispersive wave packet of de Broglie's waves which can be assimilated to the (...) class='Hi'>nonlinear soliton wave U 0 introduced by him in his double solution model of wave mechanics. (2) Since de Broglie's linear pilot waves can be considered to be real waves propagating as collective motions on a covariant subquantum chaotic “aether,” (3) these new solition waves can be considered as describing the particle's immediate neighborhood, i.e., the aether's reaction to the particle's motion in the stochastic interpretation of quantum mechanics. The existence of such a physical aether (which provides a perfectly causal interpretation of the action-a-distance implied by the Einstein-Podolsky-Rosen experiments) can now be proved by establishing the reality of de Broglie's waves in realizable experiments. (shrink)

Replies are given to arguments advanced in this journal that claim to show that it is to nonlinear classical mechanics rather than quantum mechanics that one must look for the physical underpinnings of conscious ness..

Everett proposed resolving the quantum measurement problem by dropping the nonlinear collapse dynamics from quantum mechanics and taking what is left as a complete physical theory. If one takes such a proposal seriously, then the question becomes how much of the predictive and explanatory power of the standard theory can one recover without the collapse postulate and without adding anything else. Quantum mechanics without the collapse postulate has several suggestive properties, which we will consider in some (...) detail. While these properties are not enough to make it acceptable given the usual standards for a satisfactory physical theory, one might want to exploit these properties to cook up a satisfactory no-collapse formulation of quantum mechanics. In considering how this might work, we will see why any no-collapse theory must generally fail to satisfy at least one of two plausible-sounding conditions. (shrink)

This work is part of a program which has the aim to investigate which phenomena can be explained by nonlinear effects in classical mechanics and which ones require the new axioms of quantum mechanics. In this paper, we construct a nonlinear field equation which admits soliton solutions. These solitons exibit a dynamics which is similar to that of quantum particles.

A generalized Onsager reciprocity theorem emerges as an exact consequence of the structure of the nonlinear equation of motion of quantum thermodynamics and is valid for all the dissipative nonequilibrium states, close and far from stable thermodynamic equilibrium, of an isolated system composed of a single constituent of matter with a finite-dimensional Hilbert space. In addition, a dispersion-dissipation theorem results in a precise relation between the generalized dissipative conductivity that describes the mutual interrelation between dissipative rates of a (...) pair of observables and the codispersions of the same observables and the generators of the motion. These results are presented together with a review of quantum thermodynamic postulates and general results. (shrink)

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables ξ, a physical wave Ψ x (ξ) representing the proper characteristics of the particles, and a functional wave X [ Ψ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The (...) first study is undertaken in a special instance Ψ x (ξ) = ξ(x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed. (shrink)

Quantum physics is believed to be the fundamental theory underlying our understanding of the physical universe. However, it is based on concepts and principles that have always been difficult to understand and controversial in their interpretation. This book aims to explain these issues using a minimum of technical language and mathematics. After a brief introduction to the ideas of quantum physics, the problems of interpretation are identified and explained. The rest of the book surveys, describes and (...) criticises a range of suggestions that have been made with the aim of resolving these problems; these include the traditional, or 'Copenhagen' interpretation, the possible role of the conscious mind in measurement, and the postulate of parallel universes. This new edition has been revised throughout to take into account developments in this field over the past fifteen years, including the idea of 'consistent histories' to which a completely new chapter is devoted. (shrink)

A model of dissipative quantum dynamics (with a nonlinear friction term) is applied to systems periodic in time. The model is compared with the standard approaches based on the Floquet theorem. It is shown that for weak frictions the asymptotic states of the dynamics we propose are the periodic steady states which are usually postulated to be the states relevant for the statistical mechanics of time-periodic systems. A solution to the problem of nonuniqueness of the “quasienergies” is proposed. (...) The implication of a nonlinear evolution for Ludwig's axiomatization is briefly outlined. (shrink)

In Minkowski flat space-time, it is perceived that time inversion is unitary rather than antiunitary, with energy being a time vector changing sign under time inversion. The Dirac equation, in the case of electromagnetic interaction, is not invariant under unitary time inversion, giving rise to a “Klein paradox.” To render unitary time inversion invariance, a nonlinear wave equation is constructed, in which the “Klein paradox” disappears. In the case of Coulomb interaction, the revised nonlinear equation can be linearized (...) to give energy solutions for Hydrogen-like ions without singularity when nuclear number Z>137, showing a reversed energy order pending for experimental tests such as Zeeman effects. In non-relativistic limit, this nonlinear equation reduces to nonlinear Schrödinger equation with soliton-like solutions. Moreover, particle conjugation and electron-proton scattering with a nonsingular current-potential interaction are discussed. Finally the explicit form of gauge function is found, the uniqueness of Lorentz gauge is proven and the Lagrangian density of quantum electrodynamics (QED) is revised as well. The implementation of unitary time inversion leads to the ultimate derivation of nonlinear QED. (shrink)

Free and weakly interacting particles are described by a second-quantized nonlinear Schrödinger equation, or relativistic versions of it. They describe Gaussian random walks with collisions. By contrast, the fields of strongly interacting particles are governed by effective actions, whose extremum yields fractional field equations. Their particle orbits perform universal Lévy walks with heavy tails, in which rare events are much more frequent than in Gaussian random walks. Such rare events are observed in exceptionally strong windgusts, monster or rogue waves, (...) earthquakes, and financial crashes. While earthquakes may destroy entire cities, the latter have the potential of devastating entire economies. (shrink)

This paper focuses on the nonlinear self-interaction of gravitational waves and explores its impact on the spectrum of the resulting gravitational wave. While many authors primarily investigate the nonlinear effects within the framework of "gravitational memory," we take a different approach by conducting a comprehensive analysis of harmonic generation. Theoretical analysis indicates that higher harmonics do not possess suitable conditions for energy accumulation. However, our study presents intriguing evidence supporting the concept of "nonlinear gravitational memory": the conversion (...) and accumulation of gravitational wave energy into a persistent metric deformation in the background space (specifically referred here to as zero harmonics). In simpler terms, a wave leaves a lasting imprint on the background space, even after the gravitational pulse subsides. Furthermore, our study estimates the significance of this effect and demonstrates that it should not be disregarded. (shrink)

The nonlinear integro-differential equation, obtained from the coupled Maxwell-Dirac equations by eliminating the potential Aμ, is solved by iteration rather than perturbation. The energy shift is complex, the imaginary part giving the spontaneous emission. Both self-energy and vacuum polarization terms are obtained. All results, including renormalization terms, are finite.

We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous localization” (...) has been derived from the Schrödinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments. (shrink)

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are (...) the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed. (shrink)

This paper outlines the qualitative foundations of a “quasiclassical” theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such (...) concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of “quantizing” a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum “measurement problem”; in particular, it is suggested that the unpredictability of quantum phenomena may arise from “deterministic chaos” in the behavior of the background field. (shrink)

This paper exploits the modified simple equation and dynamical system schemes to integrate the Klein–Gordon model amid quadratic nonlinearity arising in nonlinear optics, quantum theories, and solid state physics. By implementing the modified simple equation technique, we develop some disguise adaptation of analytical solutions in terms of hyperbolic, exponential, and trigonometric functions with some special parameters. We apply the dynamical system to bifurcate the model and draw distinct phase portraits on unlike parametric constraints. Following each orbit of (...) all phase portraits, we originate bounded and unbounded solitary, periodic, and periodic rogue-type wave solutions of the KG model. These two schemes extract widespread classes of solitary, periodic, and periodic rogue-type wave solutions for the KG model jointly due to restrictions on parameters. We also analyze the effect of parameters on the obtained wave solutions and discuss why and when it changes its nature. We illustrate some dynamical features of the acquired solutions via the 3D, 2D, and contour graphics. (shrink)

We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is (...) not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof. (shrink)

The complex mechanisms by which nonlinear classical conservative systems undergo a transition from quasiperiodic to chaotic behavior are now fairly well understood. This transition is associated with a breakdown of quasi-constants of motion (KAM surfaces). There is growing evidence that similar mechanisms may govern the behavior of quantum systems. While K-type mixing behavior has not yet been found, there does appear to be a transition associated with the destruction of a quantum quasi-constant of motion (quantum KAM (...) states) which changes qualitatively the spectrum of quantum systems. (shrink)

Starting from a nonlinear relativistic Klein-Gordon equation derived from the stochastic interpretation of quantum mechanics (proposed by Bohm-Vigier, (1) Nelson, (2) de Broglie, (3) Guerra et al. (4) ), one can construct joint wave and particle, soliton-like solutions, which follow the average de Broglie-Bohm (5) real trajectories associated with linear solutions of the usual Schrödinger and Klein-Gordon equations.

A notion of quantum space-time is introduced, physically defined as the totality of all flows of quantum test particles in free fall. In quantum space-time the classical notion of deterministic inertial frames is replaced by that of stochastic frames marked by extended particles. The same particles are used both as markers of quantum space-time points as well as natural clocks, each species of quantum test particle thus providing a standard for space-time measurements. In the considered (...) flat-space case, the fluctuations in coordinate values with respect to stochastic frames are described by coordinate probability amplitudes related to irreducible stochastic phase space representations of the Poincaré group. Lagrangian field theory on quantum space-time is formulated. The ensuing equations of motion for interacting fields contain no singularities in their nonlinear terms, and therefore can be handled by methods borrowed from classical nonlinear analysis. (shrink)

The way, in which quantum information can unify quantum mechanics (and therefore the standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance (...) to the axiom of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the standard model. As the standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general. (shrink)

A generalization of Weinberg’s nonlinear quantum theory is used to model a reported violation of the predictions of orthodox quantum theory.

A theoretical physicist and feminist theorist, Karen Barad elaborates her theory of agential realism, a schema that is at once a new epistemology, ontology, and ethics.

Representation of quantum states by statistical ensembles on the quantum phase space in the Hamiltonian form of quantum mechanics is analyzed. Various mathematical properties and some physical interpretations of the equivalence classes of ensembles representing a mixed quantum state in the Hamiltonian formulation are examined. In particular, non-uniqueness of the quantum phase space probability density associated with the quantum mixed state, Liouville dynamics of the probability densities and the possibility to represent the reduced states (...) of bipartite systems by marginal distributions are discussed in detail. These considerations are used to study ensembles of hybrid quantum-classical systems. In particular, nonlinear evolution of a single hybrid system in a pure state and unequal evolutions of initially equivalent ensembles are discussed in the context of coupled hybrid systems. (shrink)

Department of History and Philosophy of Science. University of Cambridge, Free School Lane, Cambridge CB2 3RH This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends on what exactly (...) the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization *Some of the arguments inn this paper appeared in a thesis submited by one of us (S.F.) In partial fulfilment of the requirements for the PhD degree of the University of London, in 1984. entitled 'Identity and ‘Individuality in Classical and Quantum Physics’. (shrink)

Piercing incisively and deeply into the nature of the overlapping of the material andmental realms. Aage Petersen uncovers the reciprocal relations between quantum physics and theconcepts of metaphysics and epistemology, assessing the extent to which each has influenced theother. The author is eminently qualified to undertake this important work, which grew out of hisclose contact with Neils Bohr and his Copenhagen school during the years 1952-1962.Although themathematical formalism of quantum physics has long since been established, the (...) question of itsphysical interpretation is not yet closed, and the question of its philosophical interpretationremains in a formative state. The most widely accepted physical interpretation of the quantalformalism emerged from discussions between Bohr and Heisenberg in the winter of 1926-1927. ThisCopenhagen Interpretation centers around the relations of indeterminacy around the relations ofindeterminacy and the concept of complementarity, and was refined but not radically altered in theyears following, especially during the famous debate with Einstein on the completeness possible inthe description of events. The philosophical interpretation has proceeded along two principal lines:Bohr's emphasis on complementarity as a unifying concept, and Heisenberg's exploration of therelationship of quantum physics to the traditional categories of philosophy.To Bohr's mind, thecentral feature of human knowledge is the distinction between subject and object. The indeterminacyof the placing of the partition between instrument and system, which played so large a part inquantal description was, Bohr believed, an expression of the general relation between the knower andthe knowable. He thus sought to find relationships of complementarity in areas beyond quantumphysics.Quantum physics and traditional philosophy certainly relate enough to interact--even thoughthe effects of interaction may produce uncertain results. Heisenberg's view also emphasizes thatscience describes, not nature itself, but the interplay between nature and man, nature as affectedby man's method of questioning, thus denying the school of philosophical thought that began withDescartes' sharp separation of the World and the I.The author's investigation leads him as well tobelieve that complementarity is deeply linked to the basis of philosophy, but that the details ofthe relationship are so obscure that some other feature of quantum physics that makes amore directconnection with philosophy should be sought. He is led to choose the idea of correspondence as suchfeature. This idea played a key role in the development of the matrix version of the formalism andof the Copenhagen interpretation.Mathematically, the idea of correspondence was seen to imply thatquantal formalisms should emerge as generalizations of classical entities, that matrix mechanics wasa generalization of classical Hamiltonian mechanics. It is in this possibility of treating thetraditional categories of philosophy as limits of a more general scheme, or as analogies of a deeperorder, that the fruitfulness of the correspondence idea lies. (shrink)