This book places thermodynamics on a system-theoretic foundation so as to harmonize it with classical mechanics. Using the highest standards of exposition and rigor, the authors develop a novel formulation of thermodynamics that can be viewed as a moderate-sized system theory as compared to statistical thermodynamics. This middle-ground theory involves deterministic large-scale dynamical system models that bridge the gap between classical and statistical thermodynamics. The authors' theory is motivated by the fact that a discipline as cardinal as (...) thermodynamics--entrusted with some of the most perplexing secrets of our universe--demands far more than physical mathematics as its underpinning. Even though many great physicists, such as Archimedes, Newton, and Lagrange, have humbled us with their mathematically seamless eurekas over the centuries, this book suggests that a great many physicists and engineers who have developed the theory of thermodynamics seem to have forgotten that mathematics, when used rigorously, is the irrefutable pathway to truth. This book uses system theoretic ideas to bring coherence, clarity, and precision to an extremely important and poorly understood classical area of science. (shrink)

Roughly speaking, classical statistical physics is the branch of theoretical physics that aims to account for the thermal behaviour of macroscopic bodies in terms of a classical mechanical model of their microscopic constituents, with the help of probabilistic assumptions. In the last century and a half, a fair number of approaches have been developed to meet this aim. This study of their foundations assesses their coherence and analyzes the motivations for their basic assumptions, and the interpretations of (...) their central concepts. The most outstanding foundational problems are the explanation of time-asymmetry in thermal behaviour, the relative autonomy of thermal phenomena from their microscopic underpinning, and the meaning of probability. A more or less historic survey is given of the work of Maxwell, Boltzmann and Gibbs in statistical physics, and the problems and objections to which their work gave rise. Next, we review some modern approaches to (i) equilibrium statistical mechanics, such as ergodic theory and the theory of the thermodynamic limit; and to (ii) non-equilibrium statistical mechanics as provided by Lanford's work on the Boltzmann equation, the so-called Bogolyubov-Born-Green-Kirkwood-Yvon approach, and stochastic approaches such as `coarse-graining' and the `open systems' approach. In all cases, we focus on the subtle interplay between probabilistic assumptions, dynamical assumptions, initial conditions and other ingredients used in these approaches. (shrink)

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures (...) is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures. (shrink)

In the last years, the surprising bosonic behavior that a many-fermion system may acquire has raised interest because of theoretical and practical reasons. This trans-statistical behavior is usually considered to be the result of approximation modeling methods generally employed by physicists when faced with complexity. In this paper, we take a tensor product structure and an ontology of properties approach and provide two versions of a toy model in order to argue that trans-statistical behavior allows for a realistic (...) interpretation. (shrink)

We provide the construction of a de Broglie–Bohm model of the N-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the classical (...) case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time. (shrink)

The connection between quantum mechanics and classical statistical mechanics has motivated in the past the representation of the Schrödinger quantum-wave equation in terms of “projections” onto the quantum configuration space of suitable phase-space asymptotic kinetic models. This feature has suggested the search of a possible exact super-dimensional classical dynamical system, denoted as Schrödinger CDS, which uniquely determines the time-evolution of the underlying quantum state describing a set of N like and mutually interacting quantum particles. In this paper the (...) realization of the same CDS in terms of a coupled set of Hamiltonian systems is established. These are respectively associated with a quantum-hydrodynamic CDS advancing in time the quantum fluid velocity and a further one the RD-CDS, describing the relative dynamics with respect to the quantum fluid. (shrink)

Astronomical observations of redshifts and the cosmic background radiation show that there is a local frame of reference relative to which the solar system has a well-defined velocity. Also, in cosmology the cosmological principle implies the existence of cosmic time and unique local reference frames at all spacetime points. On the other hand, in a fundamental postulate, the theory of special relativity excludes the possibility of the velocity of the Earth from entering into theories of local physics.The theory put (...) forward in this paper resolves this conflict between local physics and cosmology. The theory retains the essential ingredient of the mathematical structure of special relativity, namely covariance under the Lorentz symmetry group, but changes radically the interpretation of the physical significance of the Lorentz transformation. The theory is based on the postulate that in free space the fundamental interactions in physics are propagated with constant velocity with respect to the local rest frame. In Minkowski spacetime the local rest frame of reference defines a unique time axis and consequently a unique three-dimensional spatial hyperplane. One particularly important result of this is that the theory includes the classical notion of simultaneity. From the fundamental postulate it follows that the equations of local physics, when expressed in terms of the rest frame coordinate system, must be covariant under the Lorentz symmetry group. By the identification of the local rest frame with the (unique) cosmological local reference frame the two theories become mutually consistent.The effects of the motion of the Earth on laboratory experiments are discussed. It is pointed out that existing experimental data do not discriminate between the present theory and that of special relativity: a proposal for an experimental test is made. (shrink)

The idea that quantum randomness can be reduced to randomness of classical fields (fluctuating at time and space scales which are essentially finer than scales approachable in modern quantum experiments) is rather old. Various models have been proposed, e.g., stochastic electrodynamics or the semiclassical model. Recently a new model, so called prequantum classical statistical field theory (PCSFT), was developed. By this model a “quantum system” is just a label for (so to say “prequantum”) classical random field. Quantum averages can (...) be represented as classical field averages. Correlations between observables on subsystems of a composite system can be as well represented as classical correlations. In particular, it can be done for entangled systems. Creation of such classical field representation demystifies quantum entanglement. In this paper we show that quantum dynamics (given by Schrödinger’s equation) of entangled systems can be represented as the stochastic dynamics of classical random fields. The “effect of entanglement” is produced by classical correlations which were present at the initial moment of time, cf. views of Albert Einstein. (shrink)

This thesis describes a method to control rare events in non-equilibrium systems by applying physical forces to those systems but without relying on numerical simulation techniques, such as copying rare events. In order to study this method, the book draws on the mathematical structure of equilibrium statistical mechanics, which connects large deviation functions with experimentally measureable thermodynamic functions. Referring to this specific structure as the "phenomenological structure for the large deviation principle", the author subsequently extends it to (...) time-series statistics that can be used to describe non-equilibrium physics. The book features pedagogical explanations and also shows many open problems to which the proposed method can be applied only to a limited extent. Beyond highlighting these challenging problems as a point of departure, it especially offers an effective means of description for rare events, which could become the next paradigm of non-equilibrium statistical mechanics. (shrink)

Speculations about the role of consciousness in physical systems are frequently observed in the literature concerned with the interpretation of quantum mechanics. While only three experimental investigations can be found on this topic in physics journals, more than 800 relevant experiments have been reported in the literature of parapsychology. A well-defined body of empirical evidence from this domain was reviewed using meta-analytic techniques to assess methodological quality and overall effect size. Results showed effects conforming to chance expectation in (...) control conditions and unequivocal non-chance effects in experimental conditions. This quantitative literature review agrees with the findings of two earlier reviews, suggesting the existence of some form of consciousness-related anomaly in random physical systems. (shrink)

Particle motion in stochastic space, i.e., space whose coordinates consist of small, regular stochastic parts, is considered. A free particle in this space resembles a Brownian particle the motion of which is characterized by a dispersionD dependent on the universal length l. It is shown that in the first approximation in the parameter l the particle motion in an external force field is described by equations coincident in form with equations of stochastic mechanics due to Nelson, Kershow, and de la (...) Pena-Auerbach. A method is proposed for the relativization of the scheme used to describe the processes in the stochastic space; by using this method, the equations of particle motion can be written in a covariant form. (shrink)

Quantum frameworks for modeling competitive ecological systems and self-organizing structures have been investigated under multiple perspectives yielded by quantum mechanics. These comprise the description of the phase-space prey–predator competition dynamics in the framework of the Weyl–Wigner quantum mechanics. In this case, from the classical dynamics described by the Lotka–Volterra (LV) Hamiltonian, quantum states convoluted by statistical gaussian ensembles can be analytically evaluated. Quantum modifications on the patterns of equilibrium and stability of the prey–predator dynamics can then be identified. (...) These include quantum distortions over the equilibrium point drivers of the LV dynamics which are quantified through the Wigner current fluxes obtained from an onset Hamiltonian background. In addition, for gaussian ensembles highly localized around the equilibrium point, stability properties are shown to be affected by emergent topological quantum domains which, in some cases, could lead either to extinction and revival scenarios or to the perpetual coexistence of both prey and predator agents identified as quantum observables in microscopic systems. Conclusively, quantum and gaussian statistical driving parameters are shown to affect the stability criteria and the time evolution pattern for such microbiological-like communities. (shrink)

Quantum uncertainty relations have deep-rooted significance in the formalism of quantum mechanics. Heisenberg’s uncertainty relations attracted a renewed interest for its applications in quantum information science. Following the discovery of the Heisenberg uncertainty principle, Robertson derived a general form of Heisenberg’s uncertainty relations for a pair of arbitrary observables represented by Hermitian operators. In the present work, we discover a temporal version of the Heisenberg–Robertson uncertainty relations for the measurement of two observables at two different times, where the dynamical (...) uncertainties crucially depend on the time evolution of the observables. The uncertainties not only depend on the choice of observables but also depend on the times at which the physical observables are measured. The time correlated two-time commutator dictates the trade-off between the dynamical uncertainties. We demonstrate the dynamics of these uncertainty relations for a spin-1/2 quantum system and for a quantum harmonic oscillator. We also present the dynamical uncertainty relation in terms of entropies, where the temporal entropic uncertainties are restricted by a time-dependent complementarity factor. The temporal uncertainty relations explored in this work can be experimentally verified with the present quantum technology. (shrink)

Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first principles whether this claim is true: if we assume only that the time-evolution operator is linear, then does the stronger requirement that it be unitary follow from the other axioms of quantum mechanics? The answer is subtle. We discuss two mathematically distinct but physically (...) equivalent formulations of the axioms of quantum mechanics, and consider generalizing each to postulate only that time evolution is linear. Within one formulation, the unitarity of time evolution follows logically from the other axioms – but within the other formulation, it does not. Allowing the time-evolution operator to be (a priori) arbitrarily linear does not change the physical observables in one formulation of quantum mechanics, but changes the other formulation to a distinct (internally consistent) physical theory that allows new phenomenology like (e.g.) faster-than-light communication. Therefore, the unitarity of time evolution is arguably better thought of as a logically independent and experimentally falsifiable axiom of quantum mechanics, not as a tautological consequence of the other axioms. (shrink)

Physics underlies all complexity, including our own existence: how is this possible? How can our own lives emerge from interactions of electrons, protons, and neutrons? This book considers the interaction of physical and non-physical causation in complex systems such as living beings, and in particular in the human brain, relating this to the emergence of higher levels of complexity with real causal powers. In particular it explores the idea of top-down causation, which is the key effect allowing the (...) emergence of true complexity and also enables the causal efficacy of non-physical entities, including the value of money, social conventions, and ethical choices. (shrink)

One can interpret the Dirac equation either as giving the dynamics for a classical field or a quantum wave function. Here I examine whether Maxwell’s equations, which are standardly interpreted as giving the dynamics for the classical electromagnetic field, can alternatively be interpreted as giving the dynamics for the photon’s quantum wave function. I explain why this quantum interpretation would only be viable if the electromagnetic field were sufficiently weak, then motivate a particular approach to introducing a wave function for (...) the photon :1914–1919, 1957). This wave function ultimately turns out to be unsatisfactory because the probabilities derived from it do not always transform properly under Lorentz transformations. The fact that such a quantum interpretation of Maxwell’s equations is unsatisfactory suggests that the electromagnetic field is more fundamental than the photon. (shrink)

The operation of fundamental forces in quantum field theory is explicated here as the exchange of particles, consistently with the standard methodology of particle physics. The particles involved are seen to bear little relation to any classical particle but, rather, comprise unified collections of compresent, conserved quantities indicated by propagators. The exchange particles, which supervene upon quantum fields, are neither more fundamental than fields nor replace them as has often previously been assumed in models of exchange forces. It is (...) argued that this explication of quantum field-theoretic exchange forces definitively improves upon its predecessors. (shrink)

To answer foundational questions in physics, physicists turn more and more to abstract advanced mathematics, even though its physical significance may not be immediately clear. What if we started to borrow ideas and approaches, with appropriate modifications, from the foundations of mathematics? In this paper we explore this route. In reverse mathematics one starts from theorems and finds the minimum set of axioms required for their derivation. In reverse physics we want to start from laws or more specific (...) results, and find the physical concepts and starting points that recover them. We want to understand what physical results are implied by which physical assumptions. As an example of the technique, we will see six different characterizations of classical mechanics, show that the uncertainty principle depends only on the entropy bound on pure states and recast the third law of thermodynamics in terms of the entropy of an empty system. We believe the approach can provide greater insights into both current and new physical theories, put the physical concepts at the forefront of the discussion and provide a more unified view of physics by highlighting common patterns and ideas across different physical theories. (shrink)

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to (...) the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical. (shrink)

The causal closure of physics is usually discussed in a context free way. Here I discuss it in the context of engineering systems and biology, where strong emergence takes place due to a combination of upwards emergence and downwards causation. Firstly, I show that causal closure is strictly limited in terms of spatial interactions because these are cases that are of necessity strongly interacting with the environment. Effective Spatial Closure holds ceteris parabus, and can be violated by Black (...) Swan Events. Secondly, I show that causal closure in the hierarchy of emergence is a strictly interlevel affair, and in the cases of engineering and biology encompasses all levels from the social level to the particle physics level. However Effective Causal Closure can usefully be defined for a restricted set of levels, and one can experimentally determine Effective Theories that hold at each level. This does not however imply those effective theories are causally complete by themselves. In particular, the particle physics level is not causally complete by itself in the contexts of solid state physics, digital computers, or biology. Furthermore Inextricably Intertwined Levels occur in all these contexts. (shrink)

The paper presents an extension of the metaphysics of self-subsisting structures set out in a companion paper to the realm of non-relativistic quantum physics. The discussion is centered around a Pure Shape Dynamics model representing a relational implementation of a de Broglie-Bohm N-body system. An interpretation of this model in terms of self-subsisting structures is proposed and assessed against the background of the debate on the metaphysics of quantum physics, with a particular emphasis on the nature of the (...) wave function. The analysis shows that elaborating an appropriate Leibnizian/Machian metaphysics of the quantum world requires a substantial revision of the notion of world-building relation. (shrink)

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. Thisintrinsic timeis associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of (...) the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in its companion work (Gradenigo, Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant, 2021). (shrink)

There are various concepts of states in physics. Sometimes they are not formulated precisely. This leads to many misunderstandings. We try to give rigorous definitions for classical states, statistical states, and hidden states and to describe the relations between these various concepts.

We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein’s general relativity in a non-Riemannian Finsler space. This approach is based on the geometrization of quantum mechanics proposed in Tavernelli and combines quantum and gravitational effects into a global curvature of the Finsler space induced by the quantum potential associated to the matter quantum fields. In order to make this theory compatible with general relativity, the quantum effects are described in (...) the framework of quantum field theory, where a covariant definition of ‘simultaneity’ for many-body systems is introduced through the definition of a suited foliation of space-time. As in Einstein’s gravitation theory, the particle dynamics is finally described by means of a geodesic equation in a curved space-time manifold. (shrink)

The generalized Brans–Dicke theory (GBD), as one of the modified gravitational theories, was proposed previously and some interesting properties were found in this theory. Here we investigate the traversable-wormhole physics for GBD theory. Firstly, we derive the gravitational field equation in the framework of GBD wormhole geometry. The traversable wormhole could be gained in this theory. Secondly, using the classical reconstruction technique we originally derive an Lagrangian function for describing gravity in GBD theory. And the derived Lagrangian function for (...) gravity could be satisfied with the requirement of the viable conditions, such as the local gravity tests and the cosmological constraints, etc. Thus, the viable model for cosmology, local gravity and traversable WH can be unified in a uniform Lagrangian quantity within the framework of GBD theory. Thirdly, given that the violation of the energy conditions (ECs) often induce some problems in theory, we explore the ECs of matter in the traversable wormhole. It is shown that the null EC, the weak EC and the dominated EC for the matter can be satisfied in the traversable-wormhole physics of GBD theory, which are different from the results given in GR. It seems that the theory of GBD owns the more logic technically and consistency formally than the theory of GR. Fourthly, some other properties of GBD traversable WH are explored, such as the total gravitational energy, the volume integral quantifier, the dynamical stability of the anisotropic matter, and the difference of the propagation of sound within the matter configuration. The results support the GBD to provide an interesting candidate for traversable WH. (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 fundamental problem on which Ilya Prigogine and the Brussels–Austin Group have focused can be stated briefly as follows. Our observations indicate that there is an arrow of time in our experience of the world (e.g., decay of unstable radioactive atoms like uranium, or the mixing of cream in coffee). Most of the fundamental equations of physics are time reversible, however, presenting an apparent conflict between our theoretical descriptions and experimental observations. Many have thought that the observed arrow of (...) time was either an artifact of our observations or due to very special initial conditions. An alternative approach, followed by the Brussels–Austin Group, is to consider the observed direction of time to be a basic physical phenomenon due to the dynamics of physical systems. This essay focuses mainly on recent developments in the Brussels–Austin Group after the mid-1980s. The fundamental concerns are the same as in their earlier approaches (subdynamics, similarity transformations), but the contemporary approach utilizes rigged Hilbert space (whereas the older approaches used Hilbert space). While the emphasis on nonequilibrium statistical mechanics remains the same, their more recent approach addresses the physical features of large Poincare systems, nonlinear dynamics and the mathematical tools necessary to analyze them. (shrink)

One of the basic observations of the classical world is that physical entities are real and can be distinguished from each other. However, within quantum theory, the idea of physical realism is not well established. A framework to analyse how observations in experiments can be described using some physical states of reality was recently developed, known as ontological models framework. Different principles when imposed on the ontological level give rise to different theories, the validity of which can be tested based (...) on the statistics generated by these theories. Using the ontological models framework, we formulate a novel notion of classicality termed ontic-distinguishability, which is based upon the physical principles that in classical theories extremal states are physical states of reality and every sharp measurement observes the state of the system perfectly. We construct a communication task in which the success probability is bounded from above for ontological models satisfying the notion of ontic-distinguishability. Contrary to previous notions of classicality which either required systems of dimension strictly greater than two or atleast three preparations, a violation of ontic-distinguishability can be observed using just a pair of qubits and a pair of incompatible measurements. We further show that violation of previously known notions of classicality such as preparation non-contextuality and Bell’s local causality is a violation of ontic-distinguishability. (shrink)

In earlier writings, I argued that neither of the two major physical cosmologies of the 20th century support divine creation, so that atheism has nothing to fear from the explanations required by these cosmologies. Yet theists ranging from Augustine, Aquinas, Descartes, and Leibniz to Richard Swinburne and Philip Quinn have maintained that, at every instant anew, the existence of the world requires divine creation ex nihilo as its cause. Indeed, according to some such theists, for any given moment t. God's (...) volition that the-world-should-exist-at-t supposedly brings about its actual existence at t. In an effort to reestablish the current viability of this doctrine of perpetual divine conservation. Philip Quinn argued (1993) that it is entirely compatible with physical energy conservation in the Big Bang cosmology, as well as with the physics of the steady-state theories. But I now contend that instead, there is a logical incompatibility on both counts. Besides, the stated tenet of divine conservation has an additional defect: It speciously purchases plausibility by trading on the multiply disanalogous volitional explanations of human actions. (shrink)

Contemporary debate over laws of nature centers around Humean supervenience, the thesis that everything supervenes on the distribution of non-nomic facts. The key ingredient of this thesis is the idea that nomic-like concepts—law, chance, causation, etc.—are expressible in terms of the regularities of non-nomic facts. Inherent to this idea is the tacit conviction that regularities, “constant conjunctions” of non-nomic facts do supervene on the distribution of non-nomic facts. This paper raises a challenge for this conviction. It will be pointed out (...) that the notion of regularity, understood as statistical correlation, has a necessary conceptual component not clearly identified before—I shall call this the “conjunctive relation” of the correlated events. On the other hand, it will be argued that there exists no unambiguous, non-circular way in which this relation could be determined. In this regard, the notion of correlation is similar to that of distant simultaneity where the necessary conceptual component is the one-way speed of light, whose value doesn’t seem to be determined by matters of facts. (shrink)

Mainstream forms of psychiatric talk therapy and cognitive behavioral therapy (CBT) do not reliably generate lasting recovery for eating disorders. We discuss widespread assumptions regarding the nature of eating disorders as fundamentally psychological disorders and highlight the problems that underlie these notions, as well as related practical problems in the implementation of mainstream treatments. We then offer a theoretical and practical alternative: a dynamical systems model of eating disorders in which behavioral interventions are foregrounded as powerful mediators between (...) psychological and physical states. We go on to present empirical evidence for behavioral modification specifically of eating speed in the treatment of eating disorders, and a hypothesis accounting for the etiology and progression, as well as the effective treatment, of the full spectrum of eating problems. A dynamical systems approach mandates that in any dietary and lifestyle change as profound as recovery from an eating disorder, acknowledgment must be made of the full range of pragmatic (psychological, cultural, social, etc.) factors involved. However, normalizing eating speed may be necessary if not sufficient for the development of a reliable treatment for the full spectrum of eating disorders, in its role as a mediator in the complex feedback loops that connect the biology and the psychology with the behaviors of eating. (shrink)

Bohmian mechanics supplements the quantum wavefunction with deterministic particle trajectories, offering an alternate, dynamical language for quantum theory. However, the Bohmian wavefunction evolves independently of these trajectories, and is thus unaffected by the observable properties of the system. While this property is widely assumed necessary to ensure agreement with quantum mechanics, much work has recently been dedicated to understanding classical pilot-wave systems, which feature a two-way coupling between particle and wave. These systems—including the “walking droplet” system of (...) Couder and Fort (Couder and Fort (2006) Phys. Rev. Lett. 97:154101) and its various abstractions (Dagan and Bush (2020) CR Mecanique 348:555–571; Durey and Bush (2020) Front. Phys. 8:300; (2021) Chaos 31:033136; Darrow and Bush (2024) Symmetry 16:149)—allow us to investigate the limits of classical systems and offer a touchstone between quantum and classical dynamics. In this work, we present a general result that bridges Bohmian mechanics with this classical pilot-wave theory. Namely, Darrow and Bush ((2024) Symmetry 16:149) recently introduced a Lagrangian pilot-wave framework to study quantum-like behaviours in classical systems; with a particular choice of particle-wave coupling, they recover key dynamics hypothesised in de Broglie’s early double-solution theory (de Broglie (1970) Foundations Phys. 1:5–15). We here show that, with a different choice of coupling, their de Broglie-like system reduces exactly to single-particle Bohmian mechanics in the non-relativistic limit. Our result clarifies that, while multi-particle entanglement is impossible to replicate in general with local, classical theories, no such restriction exists for single-particle quantum mechanics. Moreover, connecting with the previous work of Darrow and Bush, our work demonstrates that de Broglie’s and Bohm’s theories can be connected naturally within a single Lagrangian framework. Finally, we present an application of the present work in developing a single-particle analogue for position measurement in a de Broglie-like setting. (shrink)

Contextual emergence was originally proposed as an inter-level relation between different levels of description to describe an epistemic notion of emergence in physics. Here, we discuss the ontic extension of this relation to different domains or levels of physical reality using the properties of temperature and molecular shape as detailed case studies. We emphasize the concepts of stability conditions and multiple realizability as key features of contextual emergence. Some broader implications contextual emergence has for the foundations of physics (...) and cognitive and neural sciences are given in the concluding discussion. Relevant facts about algebras of observables are found in the appendices along with an abstract definition of Kubo-Martin-Schwinger states. (shrink)

The concept of contextual emergence has been proposed as a non-reductive, yet well- defined relation between different levels of description of physical and other systems. It is illustrated for the transition from statistical mechanics to thermodynamical properties such as temperature. Stability conditions are shown to be crucial for a rigorous implementation of contingent contexts that are required to understand temperature as an emergent property. Are such stability conditions meaningful for contextual emergence beyond physics as well? An affirmative (...) example from cognitive neuroscience addresses the relation between neurobiological and mental levels of description. For a particular class of partitions of the underlying neurobiological phase space, so-called generating partitions, the emergent mental states are stable under the dynamics. In this case, mental descriptions are (i) faithful representations of the neurodynamics and (ii) compatible with one another. (shrink)

In the energy–momentum density expressions for a relativistic perfect fluid with a bulk motion, one comes across a couple of pressure-dependent terms, which though well known, are to an extent, lacking in their conceptual basis and the ensuing physical interpretation. In the expression for the energy density, the rest mass density along with the kinetic energy density of the fluid constituents due to their random motion, which contributes to the pressure as well, are already included. However, in a fluid with (...) a bulk motion, there are, in addition, a couple of explicit, pressure-dependent terms in the energy–momentum density, whose presence to an extent, is shrouded in mystery, especially from a physical perspective. We show here that one such pressure-dependent term appearing in the energy density, represents the work done by the fluid pressure against the Lorentz contraction during transition from the rest frame of the fluid to another frame in which the fluid has a bulk motion. This applies equally to the electromagnetic energy density of electrically charged systems in motion and explains in a natural manner an apparently paradoxical result that the field energy of a charged capacitor system decreases with an increase in the system velocity. The momentum density includes another pressure-dependent term, that represents an energy flow across the system, due to the opposite signs of work being done by pressure on two opposite sides of the moving fluid. From Maxwell’s stress tensor we demonstrate that in the expression for electromagnetic momentum of an electric charged particle, it is the presence of a similar pressure term, arising from electrical self-repulsion forces in the charged sphere, that yields a natural solution for the notorious, more than a century old but thought by many as still unresolved, 4/3 problem in the electromagnetic mass. (shrink)

Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques (...) proven to be the most useful in the behavioral sciences. The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics. The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them. (shrink)

In this work we develop a time-symmetric soliton theory for quantum particles inspired from works by de Broglie and Bohm. We consider explicitly a non-linear Klein–Gordon theory leading to monopolar oscillating solitons. We show that the theory is able to reproduce the main results of the pilot-wave interpretation for non interacting particles in a external electromagnetic field. In this regime, using the time symmetry of the theory, we are also able to explain quantum entanglement between several solitons and we reproduce (...) the famous pilot-wave nonlocality associated with the de Broglie-Bohm theory. (shrink)

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally indeterminate, (...) while also explaining the intuitive (and observed) asymmetry between the past—which can be remembered, at least partially—and the future—which is impossible to fully predict. (shrink)

Here, in our approximation of polaron theory, we examine the importance of introducing theT product, which turn out to be a very convenient theoretical approach for the calculation of thermodynamical averages.We focus attention on the investigation of the so-called linear polaron Hamiltonian and present in detail the calculation of the correlation function, spectral function, and Green function for such a linear system.It is shown that the linear polaron Hamiltonian provides an exactly solvable model of our system, and the result obtained (...) with this approach holds true for an arbitrary coupling constant which describes the strength of interaction between the electron and the lattice vibrations. Then, with the help of a variational technique, we show the possibility of reducing the real polaron Hamiltonian to a socalled trial or approximate linear model Hamiltonian.We also consider the exact calculation of free energy with a special technique that reduces calculations with the help of the T product, which, in our opinion, works much better and is easier than other analogous considerations, for example, the path-integral or Feynman-integral method.(1,2)Here we furthermore recall our own work,(4) where it was shown that the results of Refs. 7 and 8 concerning the impedance calculation in the polaron model may be obtained directly without the use of the path-integral method.The study of the polaron system's thermodynamics is carried out by us in the framework of the functional method. A calculation of the free energy and the momentum distribution function is proposed.Note also that the polaron systems with strong coupling(9) proved to be useful in different quantum field models in connection with the construction of dynamical models of composite particles. A rigorous solution of the special strong-coupling polaron problem, describing the interaction of a nonrelativistic particle with a quantum field, was given by Bogolubov.(3) The works of Tavkhelidze, Fedyanin, Khrustalev, and others(10–13) are dedicated to the further development and generalization of the Bogolubov method.Notice, too, that the electron-photon interaction effects play an important part in many problems of modern solid state theory (see, e.g., Refs. 7 and 14–19).The present paper summarizes a set of lectures delivered as a special course in the physics department of Moscow State University. (shrink)

Several authors have hypothesized that completely positive maps should provide the means for generalizing quantum dynamics. In a critical analysis of that proposal, we show that such maps are incompatible with the standard phenomenological theory of spin relaxation and that the theoretical argument which has been offered as justification for the hypothesis is fallacious.

A corollary of Gleason's theorem asserts that if the lattice of propositions of a physical system is isomorphic to the lattice of subspaces of a Hilbert space of dimension greater than two, then there is no probability measure that assigns only the values 1 and 0 (truth and falsity, respectively) to each of the propositions. Belinfante outlined an elegant geometrical proof of this corollary but relied upon an unrigorous measure-theoretical statement. An amplified geometrical proof is given along Belinfante's lines, but (...) dispensing with measure theory. (shrink)

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)

In recent previous work, the authors proposed a new approach extending the framework of statistical mechanics to reparametrization-invariant systems with no additional gauges. In this paper, the approach is generalized to systems defined by more than one Hamiltonian constraint. We show how well-known features as the Ehrenfest–Tolman effect and the Jüttner distribution for the relativistic gas can be consistently recovered from a covariant approach in the multi-fingered framework. Eventually, the crucial role played by the interaction in the (...) definition of a global notion of equilibrium is discussed. (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)

The paper shows the standard definition of time at a distance to be beset with ambiguities that may be solved by making a fresh start taking its point of departure in the idea of a cosmic time as proposed by the British tradition of relativistic cosmology.

Dynamical systems promise to elucidate a notion of top–down causation without violating the causal closure of physical events. This approach is particularly useful for the problem of mental causation. Since dynamical systems seek out, appropriate, and replace physical substrata needed to continue their structural pattern, the system is autonomous with respect to its components, yet the components constitute closed causal chains. But how can systems have causal power over their substrates, if each component is sufficiently (...) caused by other components? Suppose every causal relation requires background conditions, without which it is insufficient. The dynamical system is structured with a tendency to change background conditions for causal relations anytime needed substrates for the pattern's maintenance are missing; under the changed background conditions, alternative causal relations become sufficient to maintain the pattern. The system controls the background conditions under which one or another causal relation can subserve the system's overall pattern, while the components remain causally closed under their given background conditions. (shrink)

In the following paper, the author will try to test the meaning of the transcendental approach in respect of the inner changes implied by the idea of quantum gravity. He will firstly describe the basic methodological Kant’s aim, viz. the grounding of a meta-science of physics as the a priori corpus of physical knowledge. After that, he will take into account the problematic physical and philosophical relationship between the theory of relativity and the quantum mechanics; in showing how the (...) elementary ontological and epistemological assumptions of experience result to be changed within them, he will also show the further modifications occurred in the development of the loop quantum gravity. He will particularly focus on the tough problem of the relationship space-matter, in order to settle the decisive question about the possibility of keeping a transcendental approach in the light of quantum gravity. He will positively answer by recalling Cassirer’s theory of the invariants of experience, although he will also add some problematic issues arising from the new physical context. (shrink)

In this work, ZZ transformation is combined with the Adomian decomposition method to solve the dynamical system of fractional order. The derivative of fractional order is represented in the Atangana–Baleanu derivative. The numerical examples are combined for their approximate-analytical solution. It is explored using graphs that indicate that the actual and approximation results are close to each other, demonstrating the method’s usefulness. Fractional-order solutions are the most in line with the dynamics of the targeted problems, and they provide an (...) endless number of options for an optimal mathematical model solution for a particular physical phenomenon. This analytical approach produces a series form solution that is quickly convergent to exact solutions. The acquired results suggest that the novel analytical solution technique is simple to use and very successful at assessing complicated problems that arise in related fields of research and technology. (shrink)

We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which (1) is consistent with our observations (a subjective fact about our ability to observe the system) and (2) obeys a Markov process (an objective fact about the system’s dynamics). We review the ideas of computational mechanics, (...) an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the “causal states” of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables. (shrink)