The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's version or in Bohm's version, does (...) not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

In the work of the late Belgian philosopher, logician and freethinker Leo Apostel (1924–1995) the concept of ‘world view’ is extensively developed. From the diverse research of Apostel, I gather and examine the constituents of a world view and their relationships. I propose to understand it as a pluralist and open, rationalised ontology of the ‘world whole’, comprising knowledge systems, valuative ethical systems and concomitant action guiding systems, to a large extent reflecting insight in the exact sciences. The prolific and (...) scattered opus of Apostel renders my account of encompassing world views approximate and incomplete. It merely outlines the intrinsically unfinished project and presents a recent development. This development mainly involves our approach to the phenomenon of emergence from a quantum theoretical perspective. (shrink)

The aim of this article is to analyse the relation between the second law of thermodynamics and the so-called arrow of time. For this purpose, a number of different aspects in this arrow of time are distinguished, in particular those of time-reversal (non-)invariance and of (ir)reversibility. Next I review versions of the second law in the work of Carnot, Clausius, Kelvin, Planck, Gibbs, Caratheodory and Lieb and Yngvason, and investigate their connection with these aspects of the arrow of time. It (...) is shown that this connection varies a great deal along with these formulations of the second law. According to the famous formulation by Planck, the second law expresses the irreversibility of natural processes. But in many other formulations irreversibility or even time-reversal non-invariance plays no role. I therefore argue for the view that the second law has nothing to do with the arrow of time. (shrink)

Sumantra Ghoshal’s condemnation of “bad management theories” that were “destroying good management practices” has not lost any of its salience, after a decade. Management theories anchored in agency theory (and neo-classical economics generally) continue to abet the financialization of society and undermine the functioning of business. An alternative approach (drawn from a more classic institutional, new ecological, and refocused ethical approaches) is reviewed.

Poststructuralism and complexity are plural and diverse modes of thought that share a common subscription to the `anteriority of radical relationality'. They nonetheless subscribe to a different ethic of life because they address the anteriority of radical relationality in different ways. Complexity remains strategic in its bid to become a power-knowledge of the laws of becoming. It derives that strategic ethic from its scientific interest in the implicate order of non-linearity that is said to subvert Newtonian science. Poststructuralism is poetic. (...) It derives its poetic ethic from Heidegger and from the reworking of orphic and tragic sensibilities to radical relationality with the radically non-relational. Observing that all poetry is complexity avant la lettre, the article illustrates these points with the Odyssey and concludes that while complexity is ultimately concerned with fitness, poststructuralism is preoccupied with justice. (shrink)

In this paper, a very close relationship between Prigogine's notions of irreversibility and the implicate order is brought out. Certain of Prigogine's basic assumptions with regard to irreversible processes are also shown to be the equivalent of the introduction of nilpotent operators in the algebra underlying the implicate order.

The logic of a physical system consists of the elementary observables of the system. We show that for chaotic systems the logic is not any more the classical Boolean lattice but a kind of fuzzy logic which we characterize for a class of chaotic maps. Among other interesting properties the fuzzy logic of chaos does not allow for infinite combinations of propositions. This fact reflects the instability of dynamics and it is shared also by quantum systems with diagonal singularity. We (...) also generalize the fuzzy implication to a probabilistic implication following the hint of von Neumann. In this way we can evaluate the probability of the validity of the logical inference. (shrink)

We examine, in the context of the Einstein-Podolsky-Rosen-Bohm gedankenexperiment, problems associated with state reduction and with nonlocal influences according to different interpretations of quantum mechanics, when attempts are made to apply these interpretations in the relativistic domain. We begin by considering the significance of retrodiction within four different interpretations of quantum mechanics, and show that three of these interpretations, if applied in a relativistic context, can lead to ambiguities in their description of a process. We consider ways of dealing with (...) these ambiguities, in particular focussing on the “preferred frame” hypothesis. We then re-examine an argument involving nonlocal measurements which claimed that the preferred frame hypothesis is not tenable, and show that this argument does not in fact necessitate a rejection of the preferred frame. We then suggest that, to avoid confusion, the preferred frame could be extended to cover unitary interactions as well as state reductions. We conclude with a brief examination of a proposal that state reduction should take effect across the backward light cone of a measurement event. (shrink)

In recent papers the authors have discussed the dynamical properties of “large Poincaré systems” (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. We show that this Poincaré “catastrophe” can be eliminated by a natural time ordering of the dynamical states. We obtain then a dynamical theory (...) which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that this time ordering can be performed in an “extended” Hilbert space. In general, we need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space. (shrink)

We present a simple first step toward a relativistically covariant generalization of the Bohm-Bub hidden-variable theory. The model is applicable to spin measurement on a single Dirac particle and describes the collapse of the state vector to a spin-up or spin-down state. The essential postulate is that the hidden-variable vector transforms in the same way as the state vector under a Lorentz transformation. This yields a covariant collapse equation, which reduces to the ordinary Bohm-Bub equation for an observer stationary with (...) respect to the particle and shows a time dilated collapse for a moving observer. The model yields the correct quantum transition probabilities for all observers. (shrink)

This is the third and final paper of a series bringing a philosophical investigation to matters of design and innovation. With the others examining: first, the urges to reconsider innovation from a creative, specifically design, direction ; and second, the type of dynamic innovation that may be thus reconsidered ; this paper will investigate a way of constructing this type of design-driven innovation. It will begin by looking at the networks that can be created to deliver a dynamic, continually innovative (...) innovation and will start by considering two concepts of network: the open and the closed. While there seems to be an easy distinction to be made between open and closed, and its mapping onto similarly convenient ideas of good and bad, I hope to show that this is not the case. The complexity of networked forms of organisation demand that we bring to them a complexity of thought that comes from philosophy. Nevertheless, such an account will also need to engage with discourses from other disciplinary areas: notably organisational theory, innovation management and design. The outcome is of importance to thinking the organisational structures in which innovation is managed. (shrink)

This short comment confirms Longo’s observation about the importance of symmetries for understanding space and time, but raises the additional issue of the transition from reversible to irreversible transformations.

Crane envisions the speculative conjecture that intelligent civilizations might want and be able to produce black holes in the very far future. He implicitly suggests two main purposes of this enterprise: (i) energy production and (ii) universe production. We discuss those two options. The commentary is obviously highly speculative and should be read accordingly.

(1993). Reconciling physics and the order‐producing universe: Evolutionary competence and the new vision of the second law. World Futures: Vol. 36, Evolutionary Consciousness, pp. 165-179.

The paper explores the basis for decision?making and policy with regard to the Environment. Clearly these should be based on knowledge of possible consequences and accompanying risk assessments involving the linked behaviour of the many interacting human actors within a socio?economic system and the ecological, and physical systems in which they are embedded. The paper describes the Complex Systems approach to these problems, showing the kind of models that are required in order to obtain whatever limited knowledge is possible about (...) the co?evolution of the human and environmental systems involved. Several practical examples are described and the models briefly presented. These are shown as examples of what should be required for the creation of the necessary basis for making policy and decision explorations with an integrated view of the system as a whole, instead of separate parts studied in detail by experts of specific disciplines. This provides a framework for making real use of the ?knowledge? of disciplinary experts, and linking their narrow views to the overall, practical consequences in the real world of possible policy options. (shrink)

(1997). What is a possible ontological and epistemological framework for a true universal ‘information science'?: The suggestion of a cybersemiotics. World Futures: Vol. 49, The Quest for a Unified Theory of Information, pp. 287-308.

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state (...) to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes. (shrink)

The common cause principle states that common causes produce correlations amongst their effects, but that common effects do not produce correlations amongst their causes. I claim that this principle, as explicated in terms of probabilistic relations, is false in classical statistical mechanics. Indeterminism in the form of stationary Markov processes rather than quantum mechanics is found to be a possible saviour of the principle. In addition I argue that if causation is to be explicated in terms of probabilities, then it (...) should be done in terms of probabilistic relations which are invariant under changes of initial distributions. Such relations can also give rise to an asymmetric cause-effect relationship which always runs forwards in time. (shrink)

Entropy and information are both emerging as currencies of interdisciplinary dialogue, most recently in evolutionary theory. If this dialogue is to be fruitful, there must be general agreement about the meaning of these terms. That this is not presently the case owes principally to the supposition of many information theorists that information theory has succeeded in generalizing the entropy concept. The present paper will consider the merits of the generalization thesis, and make some suggestions for restricting both entropy and information (...) to specific arenas of discourse. (shrink)

During the last two decades the role of quantitative genetics in evolutionary theory has expanded considerably. Quantitative genetic-based models addressing long term phenotypic evolution, evolution in multiple environments (phenotypic plasticity) and evolution of ontogenies (developmental trajectories) have been proposed. Yet, the mathematical foundations of quantitative genetics were laid with a very different set of problems in mind (mostly the prediction of short term responses to artificial selection), and at a time in which any details of the genetic machinery were virtually (...) unknown. In this paper we discuss what a model is in population biology, and what kind of model we need in order to address the complexities of phenotypic evolution. We review the assumptions of quantitative genetics and its most recent accomplishments, together with the limitations that such assumptions impose on the modelling of some aspects of phenotypic evolution. We also discuss three alternative appr oaches to the theoretical description of evolutionary trajectories (nonlinear dynamics, complexity theory and optimization theory), and their respective advantages and limitations. We conclude by calling for a new theoretical synthesis, including quantitative genetics and not necessarily limited to the other approaches here discussed. (shrink)

This article explores the affinities and parallels between Foucault's Nietzschean view of history and models of complexity developed in the physical sciences in the twentieth century. It claims that Foucault's rejection of structuralism and Marxism can be explained as a consequence of his own approach which posits a radical ontology whereby the conception of the totality or whole is reconfigured as an always open, relatively borderless system of infinite interconnections, possibilities and developments. His rejection of Hegelianism, as well as of (...) other enlightenment philosophies, can be understood at one level as a direct response to his rejection of the mechanical atomist, and organicist epistemological world views, based upon a Newtonian conception of a closed universe operating upon the basis of a small number of invariable and universal laws, by which all could be predicted and explained. The idea of a fully determined, closed universe is replaced; and in a way parallel to complexity theories, Foucault's own approach emphasises notions such as self‐organisation and dissipative structures; time as an irreversible, existential dimension; a world of finite resources but with infinite possibilities for articulation, or re‐investment; and characterised by the principles of openness, indeterminism, unpredictability, and uncertainty. The implications of Foucault's type of approach are then explored in relation to identity, creativity, and the uniqueness of the person. The article suggests that within a complexity theory approach many of the old conundrums concerning determinism and creativity, social constructionism and uniqueness, can be overcome. (shrink)

Main principles of the complex nonlinear thinking which are based on the notions of the modern theory of evolution and self-organization of complex systems called also synergetics are under discussion in this article. The principles are transdisciplinary, holistic, and oriented to a human being. The notions of system complexity, nonlinearity of evolution, creative chaos, space-time definiteness of structure-attractors of evolution, resonant influences, nonlinear and soft management are here of great importance. In this connection, a prominent contribution made to system analysis (...) and to a necessary reform of education and thinking by Edgar Morin is considered. (shrink)

This paper examines the problem of founding irreversibility on reversible equations of motion from the point of view of the Brussels school's recent developments in the foundations of quantum statistical mechanics. A detailed critique of both their 'subdynamics' and 'transformation' theory is given. It is argued that the subdynamics approach involves a generalized form of 'coarse-graining' description, whereas, transformation theory cannot lead to truly irreversible processes pointing to a preferred direction of time. It is concluded that the Brussels school's conception (...) of microscopic temporal irreversibility, as such, is tacitly assumed at the macroscopic level. Finally a logical argument is provided which shows, independently of the mathematical formalism of the theory concerned, that statistical reasoning alone is not sufficient to explain the arrow of time. (shrink)

The problem of assessing the sustainability of human development is discussed in theoretical and practical terms.In Part I, two theoretical tools for describing the challenge of assessing sustainable development are introduced and briefly discussed: (i) the use of an energetic model to describe the dynamic interaction between the human and the biophysical compartment; (ii) basic concepts derived from the hierarchy theory applied to the development of human society. Sustainable and ethical development of human society requires the consideration of three hierarchical (...) levels: the biosphere, the societal and the individual level. Such a holistic assessment can be obtained by integrating scientific and ethical considerations. (shrink)

Proponents of two axioms of biological evolutionary theory have attempted to find justification by reference to nonequilibrium thermodynamics. One states that biological systems and their evolutionary diversification are physically improbable states and transitions, resulting from a selective process; the other asserts that there is an historically constrained inherent directionality in evolutionary dynamics, independent of natural selection, which exerts a self-organizing influence. The first, the Axiom of Improbability, is shown to be nonhistorical and thus, for a theory of change through time, (...) acausal. Its perception of the improbability of living states is at least partially an artifact of closed system thinking. The second, the Axiom of Historically Determined Inherent Directionality, is supported evidentially and has an explicit historical component. Historically constrained dynamic populations are inherently nonequilibrium systems. It is argued that living, evolving systems, when considered to be historically constrained nonequilibrium systems, do not appear improbable at all. Thus, the two axioms are not compatible. Instead, the Axiom of Improbability is considered to result from an unjustified attempt to extend the contingent proximal actions of natural selection into the area of historical, causal explanations. It is thus denied axiomatic status, and the effects of natural selection are subsumed as an additional level of constraint in an evolutionary theory derived from the Axiom of Historically Determined Inherent Directionality. (shrink)

Although the knowledge about biological systems has advanced exponentially in recent decades, it is surprising to realize that the very definition of Life keeps presenting theoretical challenges. Even if several lines of reasoning seek to identify the essence of life phenomenon, most of these thoughts contain fundamental problem in their basic conceptual structure. Most concepts fail to identify either necessary or sufficient features to define life. Here, we analyzed the main conceptual frameworks regarding theoretical aspects that have been supporting the (...) most accepted concepts of life, such as (i) the physical, (ii) the cellular and (iii) the molecular approaches. Based on an ontological analysis, we propose that Life should not be positioned under the ontological category of Matter. Yet, life should be better understood under the top-level ontology of “Process”. Exercising an epistemological approach, we propose that the essential characteristic that pervades each and every living being is the presence of organic codes. Therefore, we explore theories in biosemiotics and code biology in order to propose a clear concept of life as a macrocode composed by multiple inter-related coding layers. This way, as life is a sort of metaphysical process of encoding, the living beings became the molecular materialization of that process. From the proposed concept, we show that the evolutionary process is a fundamental characteristic for life’s maintenance but it is not necessary to define life, as many organisms are clearly alive but they do not participate in the evolutionary process (such as infertile hybrids). The current proposition opens a fertile field of debate in astrobiology, epistemology, biosemiotics, code biology and robotics. (shrink)

Applied Evolutionary Epistemology is a scientific-philosophical theory that defines evolution as the set of phenomena whereby units evolve at levels of ontological hierarchies by mechanisms and processes. This theory also provides a methodology to study evolution, namely, studying evolution involves identifying the units that evolve, the levels at which they evolve, and the mechanisms and processes whereby they evolve. Identifying units and levels of evolution in turn requires the development of ontological hierarchy theories, and examining mechanisms and processes necessitates theorizing (...) about causality. Together, hierarchy and causality theories explain how biorealities form and diversify with time. This paper analyzes how Applied EE redefines both hierarchy and causality theories in the light of the recent explosion of network approaches to causal reasoning associated with studies on reticulate and macroevolution. Causality theories have often been framed from within a rigid, ladder-like hierarchy theory where the rungs of the ladder represent the different levels, and the elements on the rungs represent the evolving units. Causality then is either defined reductionistically as an upward movement along the strands of a singular hierarchy, or holistically as a downward movement along that same hierarchy. Upward causation theories thereby analyze causal processes in time, i.e. over the course of natural history or phylogenetically, as Darwin and the founders of the Modern Synthesis intended. Downward causation theories analyze causal processes in space, ontogenetically or ecologically, as the current eco-evo-devo schools are evidencing. This work demonstrates how macroevolution and reticulate evolution theories add to the complexity by examining reticulate causal processes in space–time, and the interactional hierarchies that such studies bring forth introduce a new form of causation that is here called reticulate causation. Reticulate causation occurs between units and levels belonging to different as well as to the same ontological hierarchies. This article concludes that beyond recognizing the existence of multiple units, levels, and mechanisms or processes of evolution, also the existence of multiple kinds of evolutionary causation as well as the existence of multiple evolutionary hierarchies needs to be acknowledged. This furthermore implies that evolution is a pluralistic process divisible into different kinds. (shrink)

Because an unmeasured quantum system consists of information — neither tangible existence nor its complete absence — no property can be assigned a definite value, only a range of likely values should it be measured. The instantaneous transition from information to matter upon measurement establishes a gradient between being and not-being. A quantum system enters a determinate state in a particular moment until this moment is past, at which point the system resumes its default state as an evolving superposition of (...) potential values of properties, neither strictly being nor not-being. Like a “self-organized” chemical system that derives energy from breaking down environmental gradients, a quantum system derives information from breaking down the ontological gradient. An organism is a body in the context of energy and a mind in the context of information. (shrink)

Time as the key to a theory of everything became recently a renewed topic in scientific literature. Social constructivism applied to physics abandons the inevitable essentials of nature. It adopts uncertainty in the scope of the existential activity of scientific research. We have enlightened the deep role of social constructivism of the predetermined Newtonian time and space notions in natural sciences. Despite its incompatibility with determinism governing the Newtonian mechanics, randomness and entropy are inevitable when negative localized energy is transformed (...) into spatially dissipative heat. In sharp contrast to the Newtonian notion, social constructivism makes room for the temporal twin of cyclic conservation and pseudo-linearly structural evolution both reconciling mechanical order and thermodynamic chaos in Leibnizian space-time. In the broad scope of natural sciences this triad nature of time produces a multiple reality and gives appropriate answers on virtual physical paradoxes. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...) time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

We propose a new dynamical mechanism for information processing in mind and brain. We emphasize that a hermeneutic process is one of the key processes manifesting the functions of the brain and that it can be formulated as an itinerant motion in ultrahigh dimensional dynamical systems, which may give a new realm of the dynamic information processing. Our discussions are based on the notion of chaotic information processing and the observations of biological chaos.

This paper considers questions of continuity and change in education from the perspective of complexity theory, introducing the field to educationists who might not be familiar with it. Given a significant degree of complexity in a particular environment , new properties and behaviours, which are not necessarily contained in the essence of the constituent elements or able to be predicted from a knowledge of initial conditions, will emerge. These concepts of emergent phenomena from a critical mass, associated with notions of (...) lock‐in, path dependence, and inertial momentum, suggest that it is in the dynamic interactions and adaptive orientation of a system that new phenomena, new properties and behaviours, emerge. The focus thus shifts from a concern with decontextualised and universalised essence to contextualised and contingent complex wholes. This is where complexity theory seeks the levers of history. The paper posits the notion of inertial momentum as the conceptual link between the principle of emergent phenomena as developed principally in the natural sciences and the notion of socio‐historical change in human society. It is argued that educational and institutional change is less a consequence of effecting change in one particular factor or variable, and more a case of generating momentum in a new direction by attention to as many factors as possible. Complexity theory suggests, in other words, that what it might take to change a school's inertial momentum from an ethos of failure is massive and sustained intervention at every possible level until the phenomenon of learning excellence emerges from this new set of interactions among these new factors, and sustains itself autocatalytically. The paper concludes with a summary consideration of the conditions that contribute to the emergence of new properties and behaviours in a system. (shrink)

The cybernetic definition of a living individual proposed previously (Korzeniewski, 2001) is very abstract and therefore describes the essence of life in a very formal and general way. In the present article this definition is reformulated in order to determine clearly the relation between life in general and a living individual in particular, and it is further explained and defended. Next, the cybernetic definition of a living individual is confronted with the real world. It is demonstrated that numerous restrictions imposed (...) on the cybernetic definition of life by physical reality imply a number of particular properties of life that characterize present life on Earth, namely: (1) a living individual must be a dissipative structure (and therefore a low-entropy thermodynamic system out of the state of equilibrium); (2) spontaneously-originated life must be based on organic compounds; (3) evolutionarily stable self-dependent, free-living individuals must have some minimal level of complexity of structure and function; (4) a living individual must have a record of identity separated from an executive machinery; (5) the identity of living individuals must mutate and may evolve; (6) living individuals may collect and accumulate information in subsequent generations over very long periods of time; (7) the degree of complexity of a living individual reflects the degree of complexity of its environment (ecological niche) and (8) living individuals are capable of supple adaptation to varying environmental conditions. Thus, the cybernetic definition of a living individual, when confronted with the real physical world, generates most of the general properties of the present life on Earth. (shrink)

Many sophisticated essays and books have been written about the topic of consciousness. My own contributions date back some twenty-five years in an essay entitled 'Problems concerning the structure of consciousness' (Pribram 1976), and five years before that in delineating the difference between brain processes that are coordinate with awareness and those that are coordinate with habitual behavior (Pribram 1971a). I have been intrigued by what has been written since and take this occasion to reassess a few of the major (...) issues that have arisen. (shrink)

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

Constantin Caratheodory offered the first systematic and contradiction free formulation of thermodynamics on the basis of his mathematical work on Pfaff forms. Moreover, his work on measure theory provided the basis for later improved formulations of thermodynamics and physics of continua where extensive variables are measures and intensive variables are densities. Caratheodory was the first to see that measure theory and not topology is the natural tool to understand the difficulties (ergodicity, approach to equilibrium, irreversibility) in the Foundations of Statistical (...) Physics. He gave a measure-theoretic proof of Poincaré's recurrence theorem in 1919. This work paved the way for Birkhoff to identify later ergodicity as metric transitivity and for Koopman and von Neumann to introduce spectral analysis of dynamical systems in Hilbert spaces. Mixing provided an explanation of the approach to equilibrium but not of irreversibility. The recent extension of spectral theory of dynamical systems to locally convex spaces, achieved by the Brussels–Austin groups, gives new nontrivial time asymmetric spectral decompositions for unstable and/or non-integrable systems. In this way irreversibility is resolved in a natural way. (shrink)

Abstract.The basic laws of physics for particles and fields can be formulated in terms of variational principles. The initial development of a variational principle had distinct teleological implications. The formulation of physical laws in terms of variational principles is outlined with specific reference to classical and quantum mechanics and field theory. Because of time irreversibility no variational principle exists for thermodynamics. In order to obtain time irreversibility molecular trajectories must be abandoned in the lowest‐level description of complex multicomponent systems. A (...) more open set of possibilities results. I suggest that this may be more consistent with a modern teleology. (shrink)

Neuroconstructivism: How the Brain Constructs Cognition proposes a unifying framework for the study of cognitive development that brings together (1) constructivism (which views development as the progressive elaboration of increasingly complex structures), (2) cognitive neuroscience (which aims to understand the neural mechanisms underlying behavior), and (3) computational modeling (which proposes formal and explicit specifications of information processing). The guiding principle of our approach is context dependence, within and (in contrast to Marr [1982]) between levels of organization. We propose that three (...) mechanisms guide the emergence of representations: competition, cooperation, and chronotopy; which themselves allow for two central processes: proactivity and progressive specialization. We suggest that the main outcome of development is partial representations, distributed across distinct functional circuits. This framework is derived by examining development at the level of single neurons, brain systems, and whole organisms. We use the terms encellment, embrainment, and embodiment to describe the higher-level contextual influences that act at each of these levels of organization. To illustrate these mechanisms in operation we provide case studies in early visual perception, infant habituation, phonological development, and object representations in infancy. Three further case studies are concerned with interactions between levels of explanation: social development, atypical development and within that, developmental dyslexia. We conclude that cognitive development arises from a dynamic, contextual change in embodied neural structures leading to partial representations across multiple brain regions and timescales, in response to proactively specified physical and social environment. (shrink)

The essence of the method of physics is inseparably connected with the problem of interplay between local and global properties of the universe. In the present paper we discuss this interplay as it is present in three major departments of contemporary physics: general relativity, quantum mechanics and some attempts at quantizing gravity (especially geometrodynamics and its recent successors in the form of various pregeometry conceptions). It turns out that all big interpretative issues involved in this problem point towards the necessity (...) of changing from the standard space-time geometry to some radically new, most probably non-local, generalization. We argue that the recent noncommutative geometry offers attractive possibilities, and gives us a conceptual insight into its algebraic foundations. Noncommutative spaces are, in general, non-local, and their applications to physics, known at present, seem very promising. One would expect that beneath the Planck threshold there reigns a "noncommutative pregeometry", and only when crossing this threshold does the usual space-time geometry emerges. (shrink)

Sciences are often regarded as providing the best, or, ideally, exact, knowledge of the world, especially in providing laws of nature. Ilya Prigogine, who was awarded the Nobel Prize for his theory of non-equilibrium chemical processes—this being also an important attempt to bridge the gap between exact and non-exact sciences [mentioned in the Presentation Speech by Professor Stig Claesson (nobelprize.org, The Nobel Prize in Chemistry 1977)]—has had this ideal in mind when trying to formulate a new kind of science. Philosophers (...) of science distinguish theory and reality, examining relations between these two. Nancy Cartwright’s distinction of fundamental and phenomenological laws, Rein Vihalemm’s conception of the peculiarity of the exact sciences, and Ronald Giere’s account of models in science and science as a set of models are deployed in this article to criticise the common view of science and analyse Ilya Prigogine’s view in particular. We will conclude that on a more abstract, philosophical level, Prigogine’s understanding of science doesn’t differ from the common understanding. (shrink)

Vacuum radiation causes a particle to make a random walk about its dynamical trajectory. In this random walk the root mean square change in spatial coordinate is proportional to t 1/2, and the fractional changes in momentum and energy are proportional to t −1/2, where t is time. Thus the exchange of energy and momentum between a particle and the vacuum tends to zero over time. At the end of a mean free path the fractional change in momentum of a (...) particle in a gas is very small. However, at the end of the mean free path each particle undergoes an interaction that magnifies the preceding change, and the net result is that the momentum distribution of the particles in a gas is randomized in a few collision times. In this way the random action of vacuum radiation and its subsequent magnification by molecular interaction produces entropy increase. This process justifies the assumption of molecular chaos used in the Boltzmann transport equation. (shrink)