It has been shown that the orbits of motion for a wide class of non-relativistic Hamiltonian systems can be described as geodesic flows on a manifold and an associated dual by means of a conformal map. This method can be applied to a four dimensional manifold of orbits in spacetime associated with a relativistic system. We show that a relativistic Hamiltonian which generates Einstein geodesics, with the addition of a world scalar field, can be put into correspondence (...) in this way with another Hamiltonian with conformally modified metric. Such a construction could account for part of the requirements of Bekenstein for achieving the MOND theory of Milgrom in the post-Newtonian limit. The constraints on the MOND theory imposed by the galactic rotation curves, through this correspondence, would then imply constraints on the structure of the world scalar field. We then use the fact that a Hamiltonian with vector gauge fields results, through such a conformal map, in a Kaluza-Klein type theory, and indicate how the TeVeS structure of Bekenstein and Saunders can be put into this framework. We exhibit a class of infinitesimal gauge transformations on the gauge fields ${\mathcal{U}}_{\mu}(x)$ which preserve the Bekenstein-Sanders condition ${\mathcal{U}}_{\mu}{\mathcal{U}}^{\mu}=-1$ . The underlying quantum structure giving rise to these gauge fields is a Hilbert bundle, and the gauge transformations induce a non-commutative behavior to the fields, i.e. they become of Yang-Mills type. Working in the infinitesimal gauge neighborhood of the initial Abelian theory we show that in the Abelian limit the Yang-Mills field equations provide residual nonlinear terms which may avoid the caustic singularity found by Contaldi et al. (shrink)

Wegner’s method of flow equations offers a useful tool for diagonalizing a given Hamiltonian and is widely used in various branches of quantum physics. Here, generalizing this method, a condition is derived, under which the corresponding flow of a quantum state becomes geodesic in a submanifold of the projective Hilbert space, independently of specific initial conditions. This implies the geometric optimality of the present method as an algorithm of generating stationary states. The result is illustrated by analyzing some physical (...) examples. (shrink)

The extension of quantum mechanics to a general functional space (“rigged Hilbert space”), which incorporates time-symmetry breaking, is applied to construct extract dynamical models of entropy production and entropy flow. They are illustrated by using a simple conservative Hamiltonian system for multilevel atoms coupled to a time-dependent external force. The external force destroys the monotonicity of the ℋ-function evolution. This leads to a model of the entropy flow that allows a steady nonequilibrium structure of the emitted field around the (...) unstable particles. (shrink)

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show that the Schrödinger equation for a nonrelativistic spinless particle is a classical equation which is equivalent to Hamilton’s equations. Our discussion is quite general, and incorporates time-dependent systems. This gives us the opportunity of discussing the group of Hamiltonian canonical transformations which is a non-linear variant of the usual symplectic group.

In the usual procedure of deriving equilibrium thermodynamics from classical statistical mechanics, Gibbsian fine-grained entropy is taken as the analogue of thermodynamical entropy. However, it is well known that the fine-grained entropy remains constant under the Hamiltonian flow. In this paper it is argued that we need not search for alternatives for fine-grained entropy, nor do we have to reject Hamiltonian dynamics, in order to solve the problem of the constancy of fine-grained entropy and, more generally, to account (...) for the non-equilibrium part of the laws of thermodynamics. Rather, we have to weaken the requirement that equilibrium be identified with a stationary probability distribution. (shrink)

Analytical models describing the motion of colloidal particles in given force fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker–Planck equations, a global description based on path integration is reviewed. A new result is presented, showing that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference (...) between the flux-based and the force-based Rayleigh dissipation functions. In fact, the Fokker–Planck equation can be interpreted as the Hamilton–Jacobi equation resulting from such minumum principle. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker–Planck and the Langevin equations. (shrink)

This memoir consists of two parts, of which the first deals with the foundations of the theory of the struggle for existence, and begins with the introduction of the important concept of quantity of life, besides that of population. The fundamental equations are then established for the case where the individuals of a biological association mutually devour each other, the reasoning being based on the principle of encounters and on the fundamental hypothesis of the existence of equivalents of the individuals (...) constituting the different species which form the association.Having now obtained the equations which determine the rates of change of the numbers of individuals and of the quantities of life of the species, the memoir proceeds to find the equations relating to the stationary state, by establishing theorems which are afterwards applied for the purpose of obtaining the three general laws of the fluctuations. This investigation of the equilibrium state is then followed by the determination of the integrals of the fluctuation equations, and the deduction from these of their most important consequences.The second part of the memoir contains the enumeration and demonstration of the general laws of the struggle for existence, which flow from the discussion of the principles and the integrals obtained in the first part. In this way there is established a new sort of dynamics, demographic dynamics, which, though substantially different from the dynamics of material systems, is developed from an analogous point of view.The second part begins with the principle of the conservation of demographic energy, according to which there are two sorts of energy, one actual and one potential, which transform mutually the one into the other. This principle is the analogue of the principle of conservation of mechanical energy. It is followed by the enunciation of the three laws relating to the biological fluctuations, the experimental verification of which has been investigated by several naturalists. The success which has attended their efforts is well known.Everybody knows the importance ofHamilton's principle in mechanics and in all the domains of physical science. An analogous variation principle can be found in biology, and from it one can deduce the fluctuation equations in the canonical Hamiltonian form and also in the form of a Jacobian partial differential equation. Their integrals in involution from the subject next studied, and in this way are found cases where the integration is reducible to quadratures.Hamilton's principle leads to the principle of least action . There exists also in biology a closely related principle, which may be called the principle of least vital action. Its analytical form is such that it requires the existence of a true minimum, a state of affairs which does not always hold good in the analogous case in mechanics.Die Abhandlung besteht aus zwei Teilen: Der erste ist den Grundlagen der Theorie des Kampfes ums Dasein gewidmet. Man beginnt damit, neben der Bevölkerung die Menge des Lebens einzuführen, welche eine sehr wichtige Rolle spielt. Man geht dann dazu über, die Grundgleichungen für den Fall aufzustellen, in welchem die Individuen einer biologischen Assoziation sich gegenseitig auffressen. Man wendet das Prinzip der Begegnungen an und stützt sich auf die Grundhypothese der Existenz von Individuenäquivalenten der verschiedenen Arten, welche die Assoziation bilden.Wenn man die Gleichungen, welche die Variationen der Individuenzahlen und der Lebensmengen der Arten liefern, gefunden hat, so schreitet man zu den statischen oder Gleichgewichtsgleichungen fort und findet so die Theoreme, die man alsdann benutzt, um die drei allgemeinen Gesetze der Fluktuationen zu erhalten.Nach dem Studium des Gleichgewichtes geht man dazu über, die verschiedenen Integrale der Fluktuationengleichungen zu finden und zieht endlich aus ihnen die wichtigsten Folgerungen.Im zweiten Teile werden die allgemeinen Gesetze des Kampfes ums Dasein, welche aus der Diskussion der Prinzipien und der im ersten Teil gewonnenen Integrale stammen, ausgesprochen und bewiesen. Man baut so eine neue Dynamik auf: die demographische Dynamik, welche, obschon sie wesentlich verschieden von derjenigen der materiellen Systeme ist, sich nach einem analogen Gesichtspunkt entwickelt.Man beginnt in diesem zweiten Teil mit dem Prinzip der Erhaltung der demographischen Energie, nach welchem zwei Energien, die aktuelle und die potentielle, sich ineinander verwandeln. Wir haben hier eine Analogie zum Prinzip der Erhaltung der mechanischen Energie. Dann werden die drei Gesetze der biologischen Fluktuationen formuliert. Für sie haben verschiedene Naturforscher experimentelle Bestätigungen gesucht. Man kennt den Erfolg ihrer Bemühungen.Alle Welt kennt die Bedeutung des Prinzips vonHamilton in der Mechanik und in allen Gebieten der Physik. Man kann ein dem Variationskalkül analoges Prinzip in der Biologie finden. Aus ihm kann man die Fluktuationsgleichungen in der kanonischen Form vonHamilton und in der Gestalt einer Gleichung mit partiellen Differentialquotienten vonJacobi herleiten. Ihre Integrale bilden den Gegenstand der folgenden Studien. Man findet Fälle, in denen die Integration sich auf Quadraturen reduziert.Das Prinzip vonHamilton zieht das Prinzip der kleinsten Wirkung oder das Prinzip vonMaupertuis nach sich. Auch in der Biologie gibt es ein mit dem vorgenannten zusammenhängendes Prinzip, welches man das Prinzip der kleinsten vitalen Wirkung nennen kann. Seine analytische Form ist derart, dass es sich um ein wahres Minimum handelt, das im analogen Fall in der Mechanik nicht immer zutrifft. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy, Psychiatry, & Psychology 12.3 (2005) 229-234 [Access article in PDF] Nonlinear Dynamics at the Cutting Edge of Modernity: A Postmodern View Gordon Globus Keywords nonlinear dynamics, modernity, postmodernity, quantum brain theory, free will, self-organization, autopoiesis, autorhoesis Although nonlinear dynamical conceptu-alizations have been applied to psychia-try for over 20 years,1 they have not had significant impact on the field. Unfortunately Heinrichs' very thoughtful contribution to the discussion is unlikely (...) to move such disinterest. Pragmatically successful paradigms in the phase of Kuhnian "normal science" are highly resistant to change. There is no crisis that besets triumphalist biological psychiatry that might lead to clinical or scientific revolution. At the same time, as I suggest at the end of this commentary, the ideas of nonlinear dynamics may not be revolutionary enough, remaining staunchly within the framework of modernity.In what follows I discuss four issues related to Heinrichs' article. First, I try to enrich his presentation of nonlinear dynamics by bringing in the role of self-organization in the evolution of nonlinear dynamical brain systems and by making the nonlinear dynamics "tunable." Second, I discuss whether Heinrichs succeeds in avoiding the dualism of the biopsychosocial model that he criticizes. Third, I look at the issue of "free will," which Heinrichs would understandably like to avoid. Finally, I mention a new form of dynamics, namely thermofield dynamics, which I think is more promising than nonlinear dynamics. Self-Organizing Self-Tuning Nonlinear Dynamical Systems In the case of psychiatry, we are not considering nonlinear dynamical systems like the weather or an ecosystem, but the brain's neural networks in terms of nonlinear dynamics with all its chaos. There is a principle of such systems of neural networks that Heinrichs does not bring out, although it is extremely important for them. These systems are self-organizing under a Hamiltonian principle of "least energy." To use Hopfield and Tank's (1986) terms, nonlinear dynamical neural networks self-organize toward attractors that minimize the "computational energy" of the system, or for Smolensky (1988), self-organize toward "harmony," or for Globus (1995, 2003), in a Heideggerian vein, self-organize to maximize "belonging-together." In this elaborated framework, rational deliberation is one constraint among many on a self-organizing nonlinear dynamical process. [End Page 229]Heinrichs brings out beautifully the nonlinear dynamical way of thinking clinically. This is not the dynamics of mechanistic psychodynamics, which features psychological forces in vectorial conflict—id versus superego and their compromises—but a flowing evolution of states in which small changes in initial state may have large effects (nonlinearity) on the state trajectory. To live a life is often to feel surprise, which nonlinear dynamics with its chaotic regimes well portrays.But there is a way that classical Freud and nonlinear dynamical neural networks do come together—in the "economics," discharges and conservations of libidinal energy, expenditures and credits in Derrida's (1978) accounting. Heinrichs does not mention this similarity. The economic principles differ between Freud's late nineteenth-century thermodynamics and Heinrichs' late twentieth-century nonlinear dynamics, it is true, but it is all economics.Freud called this economic functioning the "pleasure principle" in which "libido" seeks to discharge its instinctual energy store, reducing the level of instinctual tension. This "primary process" proceeds to an attractor by the quickest, most direct way possible, whereas the "secondary process" defers reduction in instinctual tension, subjecting the primary process to thought. Self-organizing directly to the attractor is the primary process with which the secondary process interferes, introducing deferral.The economy of nonlinear dynamics pictures a "landscape," a variegated topography with peaks and valleys. Each point on the topography represents a state. Peak points are repellors—for example, states in which the phobic object is approached—and the lowest points of the valleys are attractors—for example, obsessions and compulsions. The path of occupied states self-organizes away from repellors and toward attractors. This topography is an energy landscape. Its dynamics spontaneously tends—"self-organizes"—toward least energy/high-constraint satisfaction. Freud's pleasure principle is just the Hamiltonian least energy... (shrink)

We argue that Hamiltonian mechanics is more fundamental than Lagrangian mechanics. Our argument provides a non-metaphysical strategy for privileging one formulation of a theory over another: ceteris paribus, a more general formulation is more fundamental. We illustrate this criterion through a novel interpretation of classical mechanics, based on three physical conditions. Two of these conditions suffice for recovering Hamiltonian mechanics. A third condition is necessary for Lagrangian mechanics. Hence, Lagrangian systems are a proper subset of Hamiltonian systems. (...) Finally, we provide a geometric interpretation of the principle of stationary action and rebut arguments for privileging Lagrangian mechanics. (shrink)

I show how Sir William Rowan Hamilton’s philosophical commitments led him to a causal interpretation of classical mechanics. I argue that Hamilton’s metaphysics of causation was injected into his dynamics by way of a causal interpretation of force. I then detail how forces are indispensable to both Hamilton’s formulation of classical mechanics and what we now call Hamiltonian mechanics (i.e., the modern formulation). On this point, my efforts primarily consist of showing that the contemporary orthodox interpretation of potential energy (...) is the interpretation found in Hamilton’s work. Hamilton called the potential energy function the “force-function” because he believed that it represents forces at work in the world. Various non-historical arguments for this orthodox interpretation of potential energy are provided, and matters are concluded by showing that in classical Hamiltonian mechanics, facts about the potential energies of systems are grounded in facts about forces. Thus, if one can tolerate the view that forces are causes of motion, then Hamilton provides one with a road map for transporting causation into one of the most mathematically sophisticated formulations of classical mechanics, viz., Hamiltonian mechanics. (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)

Hamilton’s Rule, named after the evolutionary biologist Bill Hamilton, and the related concepts of inclusive fitness and kin selection, have been the bedrock of the study of social evolution for the past half century. In ’The Philosophy of Social Evolution’, Jonathan Birch provides a comprehensive introduction to the conceptual foundations of the Hamiltonian view of social evolution, and a passionate defence of its enduring value in face of the recent high profile criticism. In this review essay, I first outline (...) the version of Hamilton’s Rule defended by Birch, dubbed Hamilton’s Rule General, and its derivation. With this in place, I then navigate through the fierce disagreements that Hamilton’s Rule generates among social evolution researchers and evaluate Birch’s central argument of the book that HRG serves as an organizing framework for social evolution research under which we can compare and interpret more detailed causal models. I then spend the remainder of the review discussing what I take to be three of the most exciting implications of Hamilton’s thinking raised by Birch: the extension of Hamilton’s Rule to mobile genetic elements, maximization of inclusive fitness models and the idea of adaptation as organism design, and the relationship between Hamilton’s approaches to social behaviour and the gene’s-eye view of evolution. (shrink)

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. Attention to the gauge generator G of Rosenfeld, Anderson, Bergmann, Castellani et al., a specially _tuned sum_ of first-class constraints, facilitates seeing that a solitary first-class constraint in fact generates not a gauge transformation, but a bad physical change in (...) electromagnetism or General Relativity. The change spoils the Lagrangian constraints, Gauss's law or the Gauss-Codazzi relations describing embedding of space into space-time, in terms of the physically relevant velocities rather than auxiliary canonical momenta. But the resemblance between the gauge generator G and the Hamiltonian H leaves still unclear where objective change is in GR. Insistence on Hamiltonian-Lagrangian equivalence, a theme emphasized by Castellani, Sugano, Pons, Salisbury, Shepley and Sundermeyer among others, holds the key. Taking objective change to be ineliminable time dependence, one recalls that there is change in vacuum GR just in case there is no time-like vector field xi^a satisfying Killing's equation L_xi g_mn=0, because then there exists no coordinate system such that everything is independent of time. Throwing away the spatial dependence of GR for convenience, one finds explicitly that the time evolution from Hamilton's equations is real change just when there is no time-like Killing vector. The inclusion of a massive scalar field is simple. No obstruction is expected in including spatial dependence and coupling more general matter fields. Hence change is real and local even in the Hamiltonian formalism. The considerations here resolve the Earman-Maudlin standoff over change in Hamiltonian General Relativity: the Hamiltonian formalism is helpful, and, suitably reformed, it does not have absurd consequences for change and observables. Hence the classical problem of time is resolved. The Lagrangian-equivalent Hamiltonian analysis of change in General Relativity is compared to Belot and Earman's treatment. The more serious quantum problem of time, however, is not automatically resolved due to issues of quantum constraint imposition. (shrink)

Change and local spatial variation are missing in canonical General Relativity's observables as usually defined, an aspect of the problem of time. Definitions can be tested using equivalent formulations of a theory, non-gauge and gauge, because they must have equivalent observables and everything is observable in the non-gauge formulation. Taking an observable from the non-gauge formulation and finding the equivalent in the gauge formulation, one requires that the equivalent be an observable, thus constraining definitions. For massive photons, the de Broglie-Proca (...) non-gauge formulation observable A_{\mu} is equivalent to the Stueckelberg-Utiyama gauge formulation quantity A_{\mu} + \partial_{\mu} \phi, which must therefore be an observable. To achieve that result, observables must have 0 Poisson bracket not with each first-class constraint, but with the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first-class constraints, in accord with the Pons-Salisbury-Sundermeyer definition of observables. The definition for external gauge symmetries can be tested using massive gravity, where one can install gauge freedom by parametrization with clock fields X^A. The non-gauge observable g^{\mu\nu} has the gauge equivalent X^A,_{\mu} g^{\mu\nu} X^B,_{\nu}. The Poisson bracket of X^A,_{\mu} g^{\mu\nu} X^B,_{\nu} with G turns out to be not 0 but a Lie derivative. This non-zero Poisson bracket refines and systematizes Kuchař's proposal to relax the 0 Poisson bracket condition with the Hamiltonian constraint. Thus observables need covariance, not invariance, in relation to external gauge symmetries. The Lagrangian and Hamiltonian for massive gravity are those of General Relativity + \Lambda + 4 scalars, so the same definition of observables applies to General Relativity. Local fields such as g_{\mu\nu} are observables. Thus observables change. Requiring equivalent observables for equivalent theories also recovers Hamiltonian-Lagrangian equivalence. (shrink)

The flow construct has been influential within positive psychology, sport psychology, the science of consciousness, the philosophy of agency, and popular culture. In spite of its longstanding influence, it remains unclear [a] how the constituents of the flow state ‘hang together’—how they relate to each other causally and functionally—[b] in what sense flow is an ‘optimal experience,’ and [c] how best to describe the unique phenomenology of the flow state. As a result, difficulties persist for a clear understanding of the (...) flow state’s structure and function. After explicating the standard view of the flow construct, I articulate several basic questions regarding its nature and functional roles, and I argue that these questions are best answered by integrating flow within broader streams of research on the dynamics of thought, on cognitive control resource allocation, and on creative thought. (shrink)

Is change missing in Hamiltonian Einstein–Maxwell theory? Given the most common definition of observables, observables are constants of the motion and nonlocal. Unfortunately this definition also implies that the observables for massive electromagnetism with gauge freedom are inequivalent to those of massive electromagnetism without gauge freedom. The alternative Pons–Salisbury–Sundermeyer definition of observables, aiming for Hamiltonian–Lagrangian equivalence, uses the gauge generator G, a tuned sum of first-class constraints, rather than each first-class constraint separately, and implies equivalent observables for equivalent (...) massive electromagnetisms. For General Relativity, G generates 4-dimensional Lie derivatives for solutions. The Lie derivative compares different space-time points with the same coordinate value in different coordinate systems, like 1 a.m. summer time versus 1 a.m. standard time, so a vanishing Lie derivative implies constancy rather than covariance. Requiring equivalent observables for equivalent formulations of massive gravity confirms that G must generate the 4-dimensional Lie derivative for observables. These separate results indicate that observables are invariant under internal gauge symmetries but covariant under external gauge symmetries, but can this bifurcated definition work for mixed theories such as Einstein–Maxwell theory? Pons, Salisbury and Shepley have studied G for Einstein–Yang–Mills. For Einstein–Maxwell, both \ and \ are invariant under electromagnetic gauge transformations and covariant under 4-dimensional coordinate transformations. Using the bifurcated definition, these quantities count as observables, as one would expect on non-Hamiltonian grounds. (shrink)

This chapter contains sections titled: The Key: Losing Oneself Windsurfing Performance, Psychology, and Embedded Cognition Windsurfing and Flow.

With many Hamiltonians one can naturally associate a |Ψ|2-distributed Markov process. For nonrelativistic quantum mechanics, this process is in fact deterministic, and is known as Bohmian mechanics. For the Hamiltonian of a quantum field theory, it is typically a jump process on the configuration space of a variable number of particles. We define these processes for regularized quantum field theories, thereby generalizing previous work of John S. Bell [3] and of ourselves [11]. We introduce a formula expressing the jump (...) rates in terms of the interaction Hamiltonian, and establish a condition for finiteness of the rates. (shrink)

In recent work, Peter Railton, Julia Annas, and David Velleman aim to reconcile the phenomenon of “flow”—broadly understood as describing the “unreflective” aspect of skilled action—with one or another familiar conception of agency. While there are important differences between their arguments, Railton, Annas, and Velleman all make, or are committed to, at least one similar pivotal claim. Each argues, directly or indirectly, that agents who perform skilled unreflective actions can, in principle, accurately answer “Anscombean” questions—”what” and “why” questions— about what (...) they do. I argue against this claim and explore the ramifications for theories of skilled action and agency. (shrink)

The Hamiltonian for the Einstein equations is constructed on an outgoing null cone with the help of the usual null tetrad used in the study of the asymptotical gravitational radiation field.

Dissipative systems are described by a Hamiltonian, combined with a “dynamical matrix” which generalizes the simplectic form of the equations of motion. Criteria for dissipation are given and the examples of a particle with friction and of the Lotka-Volterra model are presented. Quantization is first introduced by translating generalized Poisson brackets into commutators and anticommutators. Then a generalized Schrödinger equation expressed by a dynamical matrix is constructed and discussed.

In thirteenth-century philosophical psychology, it is commonly held that the powers of the soul, responsible for a living being’s various operations, “flow” from the soul’s essence. The phrase is used systematically by Albert the Great, who imports it from Avicenna. It suggests that the soul, considered as a separate substance, is ontologically distinct from its powers. This is how Albert understands Avicenna, and how modern interpreters understand both Avicenna and Albert. The aim of this paper is to call into question (...) such an understanding, as a reading of Avicenna and as a philosophical doctrine. It argues that an ontological distinction between the soul and its powers isn’t intended in Avicenna, and isn’t successfully established in Albert. It further argues that psychological emanation yields such a distinction only in Aquinas, where the soul is no longer considered a separate substance, but a material form. (shrink)

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two (...) reforms might use the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket, or is covariance sufficient? A graviton mass breaks the gauge symmetry, but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail. (shrink)

This collection of essays explores the metaphysical thesis that the living world is not made up of substantial particles or things, as has often been assumed, but is rather constituted by processes. The biological domain is organised as an interdependent hierarchy of processes, which are stabilised and actively maintained at different timescales. Even entities that intuitively appear to be paradigms of things, such as organisms, are actually better understood as processes. Unlike previous attempts to articulate processual views of biology, which (...) have tended to use Alfred North Whitehead’s panpsychist metaphysics as a foundation, this book takes a naturalistic approach to metaphysics. It submits that the main motivations for replacing an ontology of substances with one of processes are to be found in the empirical findings of science. Biology provides compelling reasons for thinking that the living realm is fundamentally dynamic, and that the existence of things is always conditional on the existence of processes. The phenomenon of life cries out for theories that prioritise processes over things, and it suggests that the central explanandum of biology is not change but rather stability, or more precisely, stability attained through constant change. This edited volume brings together philosophers of science and metaphysicians interested in exploring the consequences of a processual philosophy of biology. The contributors draw on an extremely wide range of biological case studies, and employ a process perspective to cast new light on a number of traditional philosophical problems, such as identity, persistence, and individuality. (shrink)

Humans are complex systems, ‘macro-entities’, whose existence, behaviour and consciousness stem out of the configurations of physical entities on the micro-level of the physical world. But an explanation of what humans do and think cannot be found through ‘tracking us back’, so to speak, to micro-particles. So, in explaining human behaviour, including linguistic behaviour on which this paper focuses, emergentism opens up a powerful opportunity to explain what it is exactly that emerged on that level, bearing in mind the end (...) product in the form of the intra- and inter-cultural diversity. Currently there is a gap in emergentism research. On one hand, there are discussions in philosophy of the emergent human reality; on the other, there are discussions of social, cultural, or individual variation of these emergent aspects of humanity in the fields of anthropology, sociology, linguistics or psychology. What I do in this paper is look for a way to ‘trace’ some such diversified emergents from what is universal about their ‘coming to being’, all the way through to their diversification. My chosen emergent is human time, my domain of inquiry is natural-language discourse, and the drive behind this project is to understand the link between ‘real’ time of spacetime on the micro-level from which we emerged and the human time devised by us, paying close attention to the overwhelming diversity in which temporal reference is expressed in human languages. The main question is, where does this diversity fit in? Does understanding of this diversity, as well as of what lurks under the surface of this diversity, aid the emergentism story? My contribution to this volume on ‘the nature of structure and the structure of nature’ thus takes the following take on the title. The structure of human communication is at the same time uniform, universal, and relative to culture, in that it is emergent as a human characteristic, and as such compatible with the micro-level correlates in some essential ways, but also free to fly in different directions that are specific to societies and cultures. I explore here the grey area between the micro-level and the linguistic reflections of time—the middle ground that is emergent itself but that tends to be by-passed by those who approach the question of human flowing time from either end: metaphysics and the philosophy of time on the one hand, and contrastive linguistics, anthropological linguistics and language documentation on the other. I illustrate the debate with examples from tensed and tenseless languages from different language families, entertaining the possibility of a conceptual universal pertaining to time as degrees of epistemic modality. Needless to say, putting the question in this way also sets out my (not unassailable) methodology. (shrink)

Change seems missing in Hamiltonian General Relativity's observables. The typical definition takes observables to have $0$ Poisson bracket with \emph{each} first-class constraint. Another definition aims to recover Lagrangian-equivalence: observables have $0$ Poisson bracket with the gauge generator $G$, a \emph{tuned sum} of first-class constraints. Empirically equivalent theories have equivalent observables. That platitude provides a test of definitions using de Broglie's massive electromagnetism. The non-gauge ``Proca'' formulation has no first-class constraints, so everything is observable. The gauge ``Stueckelberg'' formulation has first-class (...) constraints, so observables vary with the definition. Which satisfies the platitude? The team definition does; the individual definition does not. Subsequent work using the gravitational analog has shown that observables have not a 0 Poisson bracket, but a Lie derivative for the Poisson bracket with the gauge generator $G$. The same should hold for General Relativity, so observables change locally and correspond to 4-dimensional tensor calculus. Thus requiring equivalent observables for empirically equivalent formulations helps to address the problem of time. (shrink)

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription (...) rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (shrink)

In General Relativity in Hamiltonian form, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best, because the Hamiltonian is a sum of first-class constraints and a boundary term and thus supposedly generates gauge transformations. By construing change as essential time dependence, one can find change locally in vacuum GR in the Hamiltonian formulation just where it should be. But what if spinors are present? This paper is motivated by the tendency in space-time (...) philosophy tends to slight fermionic/spinorial matter, the tendency in Hamiltonian GR to misplace changes of time coordinate, and the tendency in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry along with the physically significant coordinate freedom. Spatial dependence is dropped in most of the paper, both restricting the physical situation and largely fixing the spatial coordinates. In the interest of including all and only the coordinate freedom, the Einstein-Dirac equation is investigated using the Schwinger time gauge and Kibble-Deser symmetric triad condition are employed as a \ version of the DeWitt-Ogievetsky-Polubarinov nonlinear group realization formalism that dispenses with a tetrad and local Lorentz gauge freedom. Change is the lack of a time-like stronger-than-Killing field for which the Lie derivative of the metric-spinor complex vanishes. An appropriate \-friendly form of the Rosenfeld-Anderson-Bergmann-Castellani gauge generator G, a tuned sum of first class-constraints, is shown to change the canonical Lagrangian by a total derivative, implying the preservation of Hamilton’s equations. Given the essential presence of second-class constraints with spinors and their lack of resemblance to a gauge theory, it is useful to have an explicit physically interesting example. This gauge generator implements changes of time coordinate for solutions of the equations of motion, showing that the gauge generator makes sense even with spinors. (shrink)

The aim of this paper is to introduce a new member of the family of the modal interpretations of quantum mechanics. In this modal-Hamiltonian interpretation, the Hamiltonian of the quantum system plays a decisive role in the property-ascription rule that selects the definite-valued observables whose possible values become actual. We show that this interpretation is effective for solving the measurement problem, both in its ideal and its non-ideal versions, and we argue for the physical relevance of the property-ascription (...) rule by applying it to well-known physical situations. Moreover, we explain how this interpretation supplies a description of the elemental categories of the ontology referred to by the theory, where quantum systems turn out to be bundles of possible properties. (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)

According to Dreyfus and Dreyfus, skilled coping in sport occurs when an athlete reaches an expert level and can execute a sport skill on ‘automatic-pilot’, in a state of ‘flow’. In this paper we reframe phenomenological accounts of sport that try to depict flow-states as part of an athlete’s competency framework. We do so from the point of view of post-structural and post-phenomenological scholars such as Jacques Derrida’s deconstructive work on sovereignty and Jean-Luc Nancy’s ontological vantage of ‘being-with’. This lens (...) pushes us to challenge phenomenological accounts of sport such as skilled coping and flow that, we argue, portray zombie-like performances as optimal. We suggest that such a phenomenological account of sport is not only impoverished as Breivik has argued, but also misses the very promising aspects of sport that can generate the possibility for creative and relational experiences. In making this claim we aim to reorient sport philosophy’s uptake of phenomenology towards a relat... (shrink)

The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system describing in terms of ray trajectories, for a stationary refractive medium, a very wide family of wave-like phenomena (including diffraction and interference) going much beyond the limits of the geometrical optics (“eikonal”) approximation, which is contained as a simple limiting case. Due to the fact, moreover, that the time independent Schrödinger equation is itself a Helmholtz-like equation, the same mathematics holding for a classical optical (...) beam turns out to apply to a quantum particle beam moving in a stationary force field, and leads to a system of Hamiltonian equations providing exact and deterministic particle trajectories and dynamical laws, and containing the laws of Classical Mechanics in the eikonal limit. (shrink)

One of the most pleasurable aspects of video games is their ability to induce immersive experiences. However, there appears to be a tentative conceptualization of what an immersive experience is. In this short review, we specifically focus on the terms of flow and immersion, as they are the most widely used and applied definitions in the video game literature, whilst their differences remain disputable. We critically review the concepts separately and proceed with a comparison on their proposed differences. We conclude (...) that immersion and flow do not substantially differ in current studies and that more evidence is needed to justify their separation. (shrink)

In this paper, we articulate a version of non-standard A-theory—which we call Flow Fragmentalism—in relation to its take on the issue of supervenience of truth on being. According to the Truth Supervenes on Being (TSB) Principle, the truth of past- and future-tensed propositions supervenes, respectively, on past and future facts. Since the standard presentist denies the existence of past and future entities and facts concerning them that do not obtain in the present, she seems to lack the resources to accept (...) both past and future-tensed truths and the TSB Principle. Contrariwise, positions in philosophy of time that accept an eternalist ontology (e.g., B-theory, moving spotlight, and Fine’s and Lipman’s versions of fragmentalism) allow for a “direct” supervenience base for past- and future-tensed truths. We argue that Flow Fragmentalism constitutes a middle ground, which retains most of the advantages of both views, and allows us to articulate a novel account of the passage of time. (shrink)

The main purpose of this study was to examine the relationship between flow experience and goal orientation theory, as well as, the differences in flow experience based on the orthogonal model of goal orientation theory. Two hundred and seventy eight athletes completed the Task and Ego Orientation Sport Questionnaire based on how they usually feel. The Flow State Scale was completed thirty minutes after an important competition, along with the challenge-skill ratings, based on how athletes felt during the particular competition. (...) The results indicated that the athletes’ task orientation may be the critical factor for attaining flow in competitive sport, feeling more skillful and estimating the upcoming competition as challenging, while ego orientated athletes lack these elements, which are important for them to get into flow. Additionally, the balance between athletes’ goal orientation preferences seems important for the formation of flow experience. (shrink)

Objective: Pulmonary complications could badly affect the recovery of neurological function and neurological prognosis of neurological critically ill patients. This study evaluated the effect of high-flow nasal cannula therapy on decreasing pulmonary complications in neurologically critically ill patients.Patients and Methods: The patients admitted to the intensive care unit with serious neurological disease and receiving oxygen therapy were retrospectively reviewed. Patients were divided into the HFNC group and the conventional oxygen therapy group. We analyzed the data within these two groups, including (...) patients’ baseline data, short-term outcomes of respiratory complications, general outcomes including hospital stay, ICU stay and mortality, and neurological functions. To analyze the relevant factors, we performed multivariable logistic regression analysis.Results: A total of 283 patients met the criteria, including 164 cases in the HFNC group and 119 cases in the COT group. The HFNC group had remarkably less mechanical ventilation requirement with lower phlegm viscosity. Even more, ICU stay and total hospital stay were significantly shortened in the HNFC group.Conclusion: HFNC decreased pulmonary complications in neurologically critically ill patients and improved recovery of neurological function and neurological prognosis. (shrink)

In Anti-Oedipus, Deleuze and Guattari claim that a general theory of society must be a generalised theory of flows. This is hardly a straightforward claim, and this paper attempts to examine the grounds for it. Why should socio-political theory be based on a theory of flows rather than, say, a theory of the social contract, or a theory of the State, or the questions of legitimation or revolution, or numerous other possible candidates? The concept of flow (and the (...) related notions of code and stock), I argue, is derived from contemporary economic theory, and most notably John Maynard Keynes. Deleuze and Guattari remained Marxists, not only because they held that contemporary political philosophy must inevitably be centred on the analysis of capitalism, but also because they held, following Marx himself, that the Marxist analysis of capital must constantly be transformed and adapted to new conditions. Thus, while certain aspects of Marx's analysis disappear from Capitalism and Schizophrenia, they are supplemented by the addition of new concepts adequate to the contemporary state of capitalism. The paper concludes, then, with an analysis of the role played by the concepts of flow, code and stock in Deleuze and Guattari's political philosophy. (shrink)

This study examined Flow with Nature treatment, which is an integrative intervention based on eco and environmental psychology, psychotherapeutic theories and professional psychological practice. FWN is intended for depression rehabilitation with the help of social support, nature environments and FWN exercises. Exercises encourage sensing the environment, mindful awareness, psychological processing and focusing on the future. The FWN treatment proceeds in separate stages, which emphasise nature, group and FWN exercises differently. This study focused on the experiences of the participants in the (...) FWN treatment. Finnish adults who had been diagnosed with clinical depression took part in the FWN treatment and answered feedback questions. Answers were analysed using theory-based content analysis. Data were collected between spring 2019 and spring 2020. The majority of the participants were women and on average 44 years old. Content analysis revealed that the participant feedback answers were in agreement with the central theoretical themes of FWN. The participants emphasised the significance of nature, social support and exercises differently. Moreover, the significance of these ingredients differed according to the stages of treatment: in the horizon stage restorative and comprehensive nature experiences, in the growth stage social support and in the path stage environmental self-regulation were emphasised. These results are in accordance with the objectives of the stages and seem to support the phase-based rationale. The participants’ experiences of the key elements of the intervention, social support and nature environment were experienced mainly positively, which supports their inclusion in future intervention versions. In the future, FWN exercises should be developed to better enable participants’ possibilities for concentration and being present in the moment. Exercises should also be simplified to match the target group’s cognitive abilities. (shrink)

In this chapter I analyse group flow: a state in which performers report intense interpersonal absorption with the music and each other. I compare group flow to individual flow, and argue that the same essential structure can be discerned. I argue that group flow does not justify an anti-representationalist enactivist interpretation. However, I claim that the cognitive task in which the music is produced is irreducibly collective.

In this bold new study, Andrew J. Mason seeks both to shed light on the key issue of flux in Plato s work, and to show that there is also in Plato a notion of "flow" that needs to be distinguished from flux. Mason brings out the importance of this hitherto neglected distinction, and proposes on its basis a new way of understanding the development of Plato s thought. The opposition between the being of Forms and the becoming or flux (...) of sensibles has been fundamental to the understanding of Plato from Aristotle to the present day. One key concern of this volume is to clarify which kinds or levels of flux Plato accepts in sensibles. In addition, Mason argues that this traditional approach is unsatisfactory, as it leaves out the important notion of flow. Unlike flux, flow is a kind of motion that does not entail intrinsic change. It is also not restricted to the sensible, but covers motions of soul as well, including the circular motion of "nous" that is crucial in Plato s later thought, particularly his cosmology. In short, flow is not incompatible with being, and in this study Plato s development is presented, largely, as his arrival at this view, in correction of his earlier conflation of flux and flow in establishing the dichotomy between being and becoming. Mason s study offers fresh insights into many dialogues and difficult passages in Plato s oeuvre, and situates Plato s conception and usage of flow and flux in relation to earlier usage in the Greek poetic tradition and the Presocratic thinkers, particularly Heraclitus. The first study of its kind, "Flow and Flux" uncovers dimensions of Plato s thinking that may reshape the way his philosophy is understood.". (shrink)

It was recently suggested that the cosmological constant problem as viewed in a non-perturbative framework is intimately connected to the choice of time and a physical Hamiltonian. We develop this idea further by calculating the non-perturbative vacuum energy density as a function of the cosmological constant with multiple choices of time. We also include a spatial curvature of the universe and generalize this calculation beyond cosmology at a classical level. We show that vacuum energy density depends on the choice (...) of time, and in almost all time gauges, is a non-linear function of the cosmological constant. This non-linear relation is a calculation for the vacuum energy density given some arbitrary value of the cosmological constant. Hence, in this non-perturbative framework, certain conventional aspects of the cosmological constant problem do not arise. We also discuss why the conventional cosmological constant problem is not well-posed, and formulate and answer the question: “Does vacuum gravitate?”. (shrink)

I distinguish between empiricist and rationalist approaches to the idea of the flow of time. The former trace back the idea of the flow of time to the deliverances of our sensory or introspective capacities. According to the latter, the idea of the flow of time is integral to what it is to have a conscious point of view in the first place. I discuss some aspects of what I take to be Ismael’s version of a rationalist approach, which focuses (...) on the point of view of an agent. In particular, I raise some questions as to whether Ismael’s account does succeed in reconstructing the common-sense idea of the flow of time in the sense of Becoming, and where her account leaves us with respect to the ‘two times’ problem regarding the relationship between everyday thought about time and the scientific view of time. (shrink)

Pipe flow has been a challenge that gave rise to investigations on turbulence—long before turbulence was discerned as a research problem in its own right. The discharge of water from elevated reservoirs through long conduits such as for the fountains at Versailles suggested investigations about the resistance in relation to the different diameters and lengths of the pipes as well as the speed of flow. Despite numerous measurements of hydraulic engineers, the data could not be reproduced by a commonly accepted (...) formula, not to mention a theoretical derivation. The resistance of air flow in long pipes for the supply of blast furnaces or mine air appeared even more inaccessible to rational elaboration. In the nineteenth century, it became gradually clear that there were two modes of pipe flow, laminar and turbulent. While the former could be accommodated under the roof of hydrodynamic theory, the latter proved elusive. When the wealth of turbulent pipe flow data in smooth tubes was displayed as a function of the Reynolds number, the empirically observed friction factor served as a guide for the search of a fundamental law about turbulent skin friction. By 1930, a logarithmic “wall law” seemed to resolve this quest. Yet pipe flow has not been exhausted as a research subject. It still ranks high on the agenda of turbulence research—both the transition from laminar to turbulent flow and fully developed turbulence at very large Reynolds numbers. (shrink)