On the digraph of a unitary matrix

Given a matrix M of size n, a digraph D on n vertices is said to be the digraph of M, when M_{ij} is different from 0 if and only if (v_{i},v_{j}) is an arc of D. We give a necessary condition, called strong quadrangularity, for a digraph to be the digraph of a unitary matrix. With the use of such a condition, we show that a line digraph, LD, is the digraph of a unitary matrix if and only if D is Eulerian. It follows that, if D is strongly connected and LD is the digraph of a unitary matrix then LD is Hamiltonian. We conclude with some elementary observations. Among the motivations of this paper are coined quantum random walks, and, more generally, discrete quantum evolution on digraphs.Comment: 6 page

The Vacuum Fluctuation Theorem: Exact Schroedinger Equation via Nonequilibrium Thermodynamics

By assuming that a particle of energy hbar.omega is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow), the exact Schroedinger equation is derived, both for conservative and nonconservative systems. Thereby, only universal properties of oscillators and nonequilibrium thermostatting are used, such that a maximal model independence of the hypothesised sub-quantum physics is guaranteed. It is claimed that this represents the shortest derivation of the Schroedinger equation from (modern) classical physics in the literature, and the only exact one, too. Moreover, a "vacuum fluctuation theorem" is presented, with particular emphasis on possible applications for a better understanding of quantum mechanical nonlocal effects.Comment: 39 pages; sign error in equ. (3.2.29) now correcte

Emergent Quantum Mechanics: David Bohm Centennial Perspectives

Emergent quantum mechanics (EmQM) explores the possibility of an ontology for quantum mechanics. The resurgence of interest in realist approaches to quantum mechanics challenges the standard textbook view, which represents an operationalist approach. The possibility of an ontological, i.e., realist, quantum mechanics was first introduced with the original de Broglie–Bohm theory, which has also been developed in another context as Bohmian mechanics. This Editorial introduces a Special Issue featuring contributions which were invited as part of the David Bohm Centennial symposium of the EmQM conference series (www.emqm17.org). Questions directing the EmQM research agenda are: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent in ontological quantum mechanics? The Special Issue also includes research examining ontological propositions that are not based on the Bohm-type nonlocality. These include, for example, local, yet time-symmetric, ontologies, such as quantum models based upon retrocausality. This Editorial provides topical overviews of thirty-one contributions which are organized into seven categories to provide orientation

Continuum: A history of repression – with a special focus on quantum theoryv

Identifying »continuum« as a key concept in history, the author establishes a physicist’s view of this term, with a generally broader scope. However, when focusing on quantum physics, he produces a strong criticism both of basic theory building in quantum theory and in the historiography of this very field of scientific research. This criticism involves the fatal distinctions between the concepts of the digital and the analogue, respectively, the maintenance of a strictly reductionist, or »atomistic«, approach – as opposed to possible, more general and systemic view-points, and, consequently, the preference of research purely focussing on the particle-like rather than both the particle- and the wave-like »behaviours« on the quantum-level. It is argued that the dominant pattern of interpretation, the orthodox Kopenhagen inter- pretation, includes a highly metaphysical dimension, thereby hindering the solution of puzzles provided by quantum theory. The article pleads for a re-thinking, and re-working of the de Broglie-Bohm interpretation of quantum phenomena, which draws on a ›hidden variables‹ approach in full agreement with present experimental evidence. Furthermore, the dominance of the Kopenhagen interpretation is kept up not only by means of lobbying but also by means of historiography of science. The last chapter offers alternative viewpoints, avoiding the reductionism of the orthodox school, pleading for a more complex, multi-faceted view, and including both wave and particle aspects on an equal footing.Identifying »continuum« as a key concept in history, the author establishes a physicist’s view of this term, with a generally broader scope. However, when focusing on quantum physics, he produces a strong criticism both of basic theory building in quantum theory and in the historiography of this very field of scientific research. This criticism involves the fatal distinctions between the concepts of the digital and the analogue, respectively, the maintenance of a strictly reductionist, or »atomistic«, approach – as opposed to possible, more general and systemic view-points, and, consequently, the preference of research purely focussing on the particle-like rather than both the particle- and the wave-like »behaviours« on the quantum-level. It is argued that the dominant pattern of interpretation, the orthodox Kopenhagen inter- pretation, includes a highly metaphysical dimension, thereby hindering the solution of puzzles provided by quantum theory. The article pleads for a re-thinking, and re-working of the de Broglie-Bohm interpretation of quantum phenomena, which draws on a ›hidden variables‹ approach in full agreement with present experimental evidence. Furthermore, the dominance of the Kopenhagen interpretation is kept up not only by means of lobbying but also by means of historiography of science. The last chapter offers alternative viewpoints, avoiding the reductionism of the orthodox school, pleading for a more complex, multi-faceted view, and including both wave and particle aspects on an equal footing

Why Things Develop: On the Self-Organization of Recursive »Probes « in Possibility Space

Development and dissolution are basic characteristics of a wide variety of systems. The latter include biological ones, but also non-living systems as, for example, geological onesand, of course, also social systems. As we have known for a long time, processes of decay in the physical and biological domains are governed by the law of entropy. However, processes related to the emergence of new structures, or of organizational forms, have become an issue of broad scientific investigation only during the last third of the twentieth century. Based on the studies of the phenomenon of self-organization (or emergence), new approaches to understanding the abstract machines behind structure generating and structure changing processes have emerged in recent years. This has led to the design of nonlinear models for general systems, which, among others, are also applicable to historical processes. (See, for example, M. de Landa, »A Thousand Years of Nonlinear History «. ) Some of the contemporary instruments used to simulate correspondingly complex systems on the computer are briefly reviewed, e. g., genetic algorithms and cellular automata. lt is shown that there is a solid foundation for explaining the emergence of an »arrow of time« in biological, and even in social systems. Here, decisive roles are attributed to a) the presence of recursive processes (replications, for example) and b) significant fluctuations around mean values. Such systems can often be characterized by the self-organization of recursive »probes« in the space of poten-tial forms of their organization. In sufficiently complex systems, the latter may emerge by means of their intrinsic dynamics, i. e., independent of any external control mechanisms.Development and dissolution are basic characteristics of a wide variety of systems. The latter include biological ones, but also non-living systems as, for example, geological onesand, of course, also social systems. As we have known for a long time, processes of decay in the physical and biological domains are governed by the law of entropy. However, processes related to the emergence of new structures, or of organizational forms, have become an issue of broad scientific investigation only during the last third of the twentieth century. Based on the studies of the phenomenon of self-organization (or emergence), new approaches to understanding the abstract machines behind structure generating and structure changing processes have emerged in recent years. This has led to the design of nonlinear models for general systems, which, among others, are also applicable to historical processes. (See, for example, M. de Landa, »A Thousand Years of Nonlinear History «. ) Some of the contemporary instruments used to simulate correspondingly complex systems on the computer are briefly reviewed, e. g., genetic algorithms and cellular automata. lt is shown that there is a solid foundation for explaining the emergence of an »arrow of time« in biological, and even in social systems. Here, decisive roles are attributed to a) the presence of recursive processes (replications, for example) and b) significant fluctuations around mean values. Such systems can often be characterized by the self-organization of recursive »probes« in the space of poten-tial forms of their organization. In sufficiently complex systems, the latter may emerge by means of their intrinsic dynamics, i. e., independent of any external control mechanisms

Sub-Quantum Thermodynamics as a Basis of Emergent Quantum Mechanics

This review presents results obtained from our group’s approach to model quantum mechanics with the aid of nonequilibrium thermodynamics. As has been shown, the exact Schrödinger equation can be derived by assuming that a particle of energy is actually a dissipative system maintained in a nonequilibrium steady state by a constant throughput of energy (heat flow). Here, also other typical quantum mechanical features are discussed and shown to be completely understandable within our approach, i.e., on the basis of the assumed sub-quantum thermodynamics. In particular, Planck’s relation for the energy of a particle, the Heisenberg uncertainty relations, the quantum mechanical superposition principle and Born’s rule, or the “dispersion of the Gaussian wave packet”, a.o., are all explained on the basis of purely classical physics