The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other (η) expressing the quantum groups as “deformation” of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the η-deformation. This suggests that the strong invariance condition is a possible origin of the (...) class='Hi'>quantum groups. (shrink)

The concept of classical r matrices is developed from a purely canonical standpoint. The final purpose of this work is to bring about a synthesis between recent developments in the theory of integrable systems and the general theory of quantization as a deformation of classical mechanics. The concept of quantization algebra is here dominant; in integrable systems this is the set of dynamical variables that appear in the Lax pair. The nature of this algebra, a solvable Lie algebra in such (...) models as the Sine-Gordon and Toda field theories but semisimple in the case of spin systems, provides a useful scheme for the classification of integrable models. A completely different classification is obtained by the nature of the r matrix employed; there are three kinds: rational, trigonometric, and elliptic. All cases are studied in detail, with numerous examples. Some of the problems connected with quantization are discussed. (shrink)

Quantum cellular automata and quantum walks provide a framework for the foundations of quantum field theory, since the equations of motion of free relativistic quantum fields can be derived as the small wave-vector limit of quantum automata and walks starting from very general principles. The intrinsic discreteness of this framework is reconciled with the continuous Lorentz symmetry by reformulating the notion of inertial reference frame in terms of the constants of motion of the quantum (...) walk dynamics. In particular, among the symmetries of the quantum walk which recovers the Weyl equation—the so called Weyl walk—one finds a non linear realisation of the Poincaré group, which recovers the usual linear representation in the small wave-vector limit. In this paper we characterise the full symmetry group of the Weyl walk which is shown to be a non linear realization of a group which is the semidirect product of the Poincaré group and the group of dilations. (shrink)

This axiomatization is based on the observation that ifG is the group of automorphisms of the states (induced, e.g., by suitable evolutions), then we can define a spherical function by mapping each element ofG to the matrix of its transition probabilities. Starting from five physically conservative axioms, we utilize the correspondence between spherical functions and representations to apply the structure theory for compact Lie groups and their orbits in representation spaces to arrive at the standard complex Hilbert space structure (...) of quantum mechanics. (shrink)

Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum (...) measurements in this framework. (shrink)

This philosophical anthropology tries to explore the basic categories of man’s being in the worlds using a special quantum meta-ontology that is introduced in the book. Quantum understanding of space and time, consciousness, or empirical/nonempirical reality elicits new questions relating to philosophical concerns such as subjectivity, free will, mind, perception, experience, dialectic, or agency. The authors have developed an inspiring theoretical framework transcending the boundaries of particular disciplines, e.g. quantum philosophy, metaphysics of consciousness, philosophy of mind, phenomenology (...) of space and time, and ontological relativity. (shrink)

Analogies between classical statistical mechanics and quantum field theory played a pivotal role in the development of renormalization group methods for application in the two theories. This paper focuses on the analogies that informed the application of RG methods in QFT by Kenneth Wilson and collaborators in the early 1970's. The central task that is accomplished is the identification and analysis of the analogical mappings employed. The conclusion is that the analogies in this case study are formal analogies, and (...) not physical analogies. That is, the analogical mappings relate elements of the models that play formally analogous roles and that have substantially different physical interpretations. Unlike other cases of the use of analogies in physics, the analogical mappings do not preserve causal structure. The conclusion that the analogies in this case are purely formal carries important implications for the interpretation of QFT, and poses challenges for philosophical accounts of analogical reasoning and arguments in defence of scientific realism. Analysis of the interpretation of the cutoffs is presented as an illustrative example of how physical disanalogies block the exportation of physical interpretations from from statistical mechanics to QFT. A final implication is that the application of RG methods in QFT supports non-causal explanations, but in a different manner than in statistical mechanics. (shrink)

We sketch a group-theoretical framework, based on the Heisenberg–Weyl group, encompassing both quantum and classical statistical descriptions of unconstrained, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-to-classical transition. We briefly discuss the structure of observables and dynamics within our framework.

In this paper, we present a non-geometrodynamic quantum Yang–Mills theory of gravity based on the homogeneous Lorentz group within the general framework of the Poincare gauge theories. The obstacles of this treatment are that first, on the one hand, the gauge group that is available for this purpose is non-compact. On the other hand, Yang–Mills theories with non-compact groups are rarely healthy, and only a few instances exist in the literature. Second, it is not clear how the direct (...) observations of space–time waves can be explained when space–time has no dynamics. We show that the theory is unitary and is renormalizable to the one-loop perturbation. Although in our proposal, gravity is not associated with any elementary particle analogous to the graviton, classical helicity-two space–time waves are explained. Five essential exact solutions to the field equations of our proposal are presented as well. We also discuss a few experimental tests that can falsify the presented Yang–Mills theory. (shrink)

In this paper I investigate, within the framework of realistic interpretations of the wave function in nonrelativistic quantum mechanics, the mathematical and physical nature of the wave function. I argue against the view that mathematically the wave function is a two-component scalar field on configuration space. First, I review how this view makes quantum mechanics non- Galilei invariant and yields the wrong classical limit. Moreover, I argue that interpreting the wave function as a ray, in agreement many physicists, (...) Galilei invariance is preserved. In addition, I discuss how the wave function behaves more similarly to a gauge potential than to a field. Finally I show how this favors a nomological rather than an ontological view of the wave function. (shrink)

The relation of the conformal group to various earlier proposed relativistic quantum mechanical dynamical groups (and other related groups) is studied in the framework of projective geometry, by explicitly constructing the contractions of the six-dimensional coordinate transformations. Five-dimensional realizations are then derived. An attempt is made to improve our physical insight through geometry.

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory, but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

The renormalization group has been characterized as merely a coarse-graining procedure that does not illuminate the microscopic content of quantum field theory but merely gets us from that content, as given by axiomatic QFT, to macroscopic predictions. I argue that in the constructive field theory tradition, RG techniques do illuminate the microscopic dynamics of a QFT, which are not automatically given by axiomatic QFT. RG techniques in constructive field theory are also rigorous, so one cannot object to their foundational (...) import on grounds of lack of rigor. (shrink)

In this paper, I shall discuss the heuristic role of symmetry in the mathematical formulation of quantum mechanics. I shall first set out the scene in terms of Bas van Fraassen’s elegant presentation of how symmetry principles can be used as problem-solving devices (see van Fraassen [1989] and [1991]). I will then examine in what ways Hermann Weyl and John von Neumann have used symmetry principles in their work as a crucial problem-solving tool. Finally, I shall explore one consequence (...) of this situation to recent debates about structural realism (SR) and empiricism in physics (Worrall [1989], Ladyman [1998], and French [1999]). (shrink)

Research and engineering in the quantum domain involve long chains of activity involving theory development, hypothesis formation, experimentation, device prototyping, device testing, and many more. At each stage multiple paths become possible, and of the paths pursued, the majority will lead nowhere. Our quantum metascience approach provides a strategy which enables all stakeholders to gain an overview of those developments along these tracks, that are relevant to their specific concerns. It provides a controlled vocabulary, built out of terms (...) that are designed to be maximally comprehensible to all groups of stakeholders and across all the sub-fields of the quantum domain. (shrink)

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain (...) class of level sets defined by Fermi for the purpose of representing geometrically quantum states. (shrink)

An explicit expression of the “Wigner operator” is derived, such that the Wigner function of a quantum state is equal to the expectation value of this operator with respect to the same state. This Wigner operator leads to a representation-independent procedure for establishing the correspondence between the inhomogeneous symplectic group applicable to linear canonical transformations in classical mechanics and the Weyl-metaplectic group governing the symmetry of unitary transformations in quantum mechanics.

The relevance of symmetry to today's physics is a widely acknowledged fact. A significant part of recent physical inquiry – especially the physics concerned with investigating the fundamentalbuilding blocks of nature – is grounded on symmetry principles andtheir many and far-reaching consequences. But where these symmetries come from and what their real meaning is are open questions, at the center of a developing debate among physicists and philosophers of science. To tackle the problems arising in considering the symmetry issue is (...) the main purpose of this paper. Starting with briefly recalling the bases for the discussion – how symmetry enters and operates in physics, its special effectiveness in the quantum domain and the many relevant functions it performs (Sections 1–3), the paper then focus on the general interpretative questions that arise and the sorts of answers that have been given (Section 4). (shrink)

Rob Clifton was one of the most brilliant and productive researchers in the foundations and philosophy of quantum theory, who died tragically at the age of 38. Jeremy Butterfield and Hans Halvorson collect fourteen of his finest papers here, drawn from the latter part of his career (1995-2002), all of which combine exciting philosophical discussion with rigorous mathematical results. Many of these papers break wholly new ground, either conceptually or technically. Others resolve a vague controversy intoa precise technical problem, (...) which is then solved; still others solve an open problem that had been in the air for soem time. All of them show scientific and philosophical creativity of a high order, genuinely among the very best work in the field. The papers are grouped into four Parts. First come four papers about the modal interpretation of quantum mechanics. Part II comprises three papers on the foundations of algebraic quantum field theory, with an emphasis on entanglement and nonlocality. The two papers in Part III concern the concept of a particle in relativistic quantum theories. One paper analyses localization; the other analyses the Unruh effect (Rindler quanta) using the algebraic approach to quantum theory. Finally, Part IV contains striking new results about such central issues as complementarity, Bohr's reply to the EPR argument, and no hidden variables theorems; and ends with a philosophical survey of the field of quantum information. The volume includes a full bibliography of Clifton's publications. Quantum Entanglements offers inspiration and substantial reward to graduates and professionals in the foundations of physics, with a background in philosophy, physics, or mathematics. (shrink)

Quantum Field Theory (QFT) is the mathematical and conceptual framework for contemporary elementary particle physics. In a rather informal sense QFT is the extension of quantum mechanics (QM), dealing with particles, over to fields, i.e. systems with an infinite number of degrees of freedom. (See the entry on quantum mechanics.) In the last few years QFT has become a more widely discussed topic in philosophy of science, with questions ranging from methodology and semantics to ontology. QFT taken (...) seriously in its metaphysical implications seems to give a picture of the world which is at variance with central classical conceptions of particles and fields, and even with some features of QM. -/- The following sketches how QFT describes fundamental physics and what the status of QFT is among other theories of physics. Since there is a strong emphasis on those aspects of the theory that are particularly important for interpretive inquiries, it does not replace an introduction to QFT as such. One main group of target readers are philosophers who want to get a first impression of some issues that may be of interest for their own work, another target group are physicists who are interested in a philosophical view upon QFT. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical particles (...) as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of operator algebras, category theory, etc.. Given the rigor and generality of AQFT, it is a particularly apt tool for studying the foundations of QFT. This paper is a survey of AQFT, with an orientation towards foundational topics. In addition to covering the basics of (...) the theory, we discuss issues related to nonlocality, the particle concept, the field concept, and inequivalent representations. We also provide a detailed account of the analysis of superselection rules by Doplicher, Haag, and Roberts (DHR); and we give an alternative proof of Doplicher and Robert's reconstruction of fields and gauge group from the category of physical representations of the observable algebra. The latter is based on unpublished ideas due to J. E. Roberts and the abstract duality theorem for symmetric tensor *-categories, a self-contained proof of which is given in the appendix. (shrink)

The notion of an instrument in the quantum theory of measurement is studied in the context of transformation valued linear maps on von Neumann algebras and their *-subalgebras. An extension theorem is proved which yields among other things characterizations of the Fourier transforms of instruments and their noncommutative analogues. As an application, an ergodic type theorem for a general class of transformation valued functions on a locally compact group is obtained.

Quantum B‐algebras are partially ordered algebras characterizing the residuated structure of a quantale. Examples arise in algebraic logic, non‐commutative arithmetic, and quantum theory. A quantum B‐algebra with trivial partial order is equivalent to a group. The paper introduces a corresponding analogue of quantale modules. It is proved that every quantum B‐module admits an injective envelope which is a quantale module. The injective envelope is constructed explicitly as a completion, a multi‐poset version of the completion of Dedekind (...) and MacNeille. (shrink)

After leading to a new axiomatic derivation of quantum theory, the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles, the automata theory is quantum ab-initio, and does not assume Lorentz (...) covariance and mechanical notions. Being discrete it can describe localized states and measurements, solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (shrink)

The idea that the quantum probabilities are best construed as the personal/subjective degrees of belief of Bayesian agents is an old one. In recent years the idea has been vigorously pursued by a group of physicists who fly the banner of quantum Bayesianism. The present paper aims to identify the prospects and problems of implementing QBism, and it critically assesses the claim that QBism provides a resolution of some of the long-standing foundations issues in quantum mechanics, including (...) the measurement problem and puzzles of nonlocality. (shrink)

The aim of this paper is to consider in what sense the modal-Hamiltonian interpretation of quantum mechanics satisfies the physical constraints imposed by the Galilean group. In particular, we show that the only apparent conflict, which follows from boost-transformations, can be overcome when the definition of quantum systems and subsystems is taken into account. On this basis, we apply the interpretation to different well-known models, in order to obtain concrete examples of the previous conceptual conclusions. Finally, we consider (...) the role played by the Casimir operators of the Galilean group in the interpretation. (shrink)

Two approaches toward the arrow of time for scattering processes have been proposed in rigged Hilbert space quantum mechanics. One, due to Arno Bohm, involves preparations and registrations in laboratory operations and results in two semigroups oriented in the forward direction of time. The other, employed by the Brussels-Austin group, is more general, involving excitations and de-excitations of systems, and apparently results in two semigroups oriented in opposite directions of time. It turns out that these two time arrows can (...) be related to each other via Wigner's extensions of the spacetime symmetry group. Furthermore, their are subtle differences in causality as well as the possibilities for the existence and creation of time-reversed states depending on which time arrow is chosen. (shrink)

Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the (...) ‘three-fold way’. It is perhaps easiest to see it in the study of irreducible unitary representations of groups on complex Hilbert spaces. These representations come in three kinds: those that are not isomorphic to their own dual (the truly ‘complex’ representations), those that are self-dual thanks to a symmetric bilinear pairing (which are ‘real’, in that they are the complexifications of representations on real Hilbert spaces), and those that are self-dual thanks to an antisymmetric bilinear pairing (which are ‘quaternionic’, in that they are the underlying complex representations of representations on quaternionic Hilbert spaces). This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics. More generally, Hilbert spaces of any one of the three kinds—real, complex and quaternionic—can be seen as Hilbert spaces of the other kinds, equipped with extra structure. (shrink)

The essential biological processes that sustain life are catalyzed by protein nano-engines, which maintain living systems in far-from-equilibrium ordered states. To investigate energetic processes in proteins, we have analyzed the system of generalized Davydov equations that govern the quantum dynamics of multiple amide I exciton quanta propagating along the hydrogen-bonded peptide groups in α-helices. Computational simulations have confirmed the generation of moving Davydov solitons by applied pulses of amide I energy for protein α-helices of varying length. The stability (...) and mobility of these solitons depended on the uniformity of dipole-dipole coupling between amide I oscillators, and the isotropy of the exciton-phonon interaction. Davydov solitons were also able to quantum tunnel through massive barriers, or to quantum interfere at collision sites. The results presented here support a nontrivial role of quantum effects in biological systems that lies beyond the mechanistic support of covalent bonds as binding agents of macromolecular structures. Quantum tunneling and interference of Davydov solitons provide catalytically active macromolecular protein complexes with a physical mechanism allowing highly efficient transport, delivery, and utilization of free energy, besides the evolutionary mandate of biological order that supports the existence of such genuine quantum phenomena, and may indeed demarcate the quantum boundaries of life. (shrink)

In quantum logics, the notions of strong and full order determination and unitality for states on orthomodular posets are well known. These notions are defined for hypergraphs and their state spaces in a consistent manner and the relations between them and to the notions defined for orthomodular posets are discussed. The state space of a hypergraph is a polytope. This polytope is a simplex if and only if every superposition of pure states is a mixture of these same pure (...) states. Isomorphic hypergraphs have convexly isomorphic state spaces. A class of hypergraphs is given whose group of automorphisms is group-isomorphic to the group of convex automorphisms of their state spaces. (shrink)

This paper traces the origins of Eugene Wigner's pioneering application of group theory to quantum physics to his early work in chemistry and crystallography. In the early 1920s, crystallography was the only discipline in which symmetry groups were routinely used. Wigner's early training in chemistry, and his work in crystallography with Herman Mark and Karl Weissenberg at the Kaiser Wilhelm institute for fiber research in Berlin exposed him to conceptual tools which were absent from the pedagogy available to (...) physicists for many years to come. This both enabled and pushed him to apply the group theoretic approach to quantum physics. It took many years for the approach first introduced by Wigner in the 1920s – and whose reception by the physicists was initially problematical – to assume the pivotal place it now holds in physical theory and education. This is but one example that attests to the historic contribution made by the periphery in initiating new types of thought-perspectives and scientific careers. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary (...) particle, neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical (...) model of the Lüders-von Neumann measurement process). It is shown how positive groups, automorphism groups, Lie algebras and statistical operators emerge from one major postulate—the non-existence of third-order interference [third-order interference and its impossibility in quantum mechanics were discovered by Sorkin (Mod Phys Lett A 9:3119–3127, 1994)]. This again underlines the power of the combination of the conditional probability calculus with the postulate that there is no third-order interference. In two earlier papers, its impact on contextuality and nonlocality had already been revealed. (shrink)

There are strong indications that ancient Egyptian mythology contains knowledge of the nature of space up to higher dimensions and provides ontologic answers to the question about the creation of matter. This article examines the pentagonal interpretation of the myth of Isis and Osiris by comparing the iconographic details with recent findings from the art research project Quantum Cinema, where an interdisciplinary group of digital artists and scientists established a virtual space model for visualizing the usually non-perceivable processes in (...) the microcosm on a Planck scale. At this scale, quantum mechanics applied to space itself leads to a discrete amount of quantum states. For this research, a new geometrical tool proved invaluable: the epitahedron. The double heptahedron named epitahedron (E±), a 3D Penrose kites and darts representation, confines the dodecahedron in many ways and seems to be Plato’s fifth element. It is a 5D space cell, decorated with fragments of circles, which allows to visualize the permutations of symmetry elements within a discrete lattice (Z5). This higher-dimensional configuration is also the appropriate space to create a quantum-mechanical depiction of particles with inherent wave-like character by means of 3D animated geometry. Disguised in a mythological language the same subscendent space structure with the same golden polytope (E±) can be revealed: is this the origin of the concept of aether, the quintessence model which was a basic scientific task for the last 2500 years? (shrink)

Unitary, irreducible representations of the proper, orthochronous Lorentz group comprise the main series and the supplementary series. The main series is spanned by the complete set of eigenstates of the self-adjoint Casimir operator C 1=−(1/2)M μν M μν , where M μν are generators of Lorentz transformations. The supplementary series has no such interpretation; moreover it is spurious from the point of view of functional analysis as it does not enter into the integral representation of an arbitrary test function. The (...) author describes the physical context within which the supplementary series arises, nevertheless, in a natural way: it arises if we exponentiate a massless scalar quantum field living in three-dimensional de Sitter space-time and if the appropriate coupling constant is small enough. (shrink)

As quantum technologies (QT) advance, their potential impact on and relation with society has been developing into an important issue for exploration. In this paper, we investigate the topic of democratization in the context of QT, particularly quantum computing. The paper contains three main sections. First, we briefly introduce different theories of democracy (participatory, representative, and deliberative) and how the concept of democratization can be formulated with respect to whether democracy is taken as an intrinsic or instrumental value. (...) Second, we give an overview of how the concept of democratization is used in the QT field. Democratization is mainly adopted by companies working on quantum computing and used in a very narrow understanding of the concept. Third, we explore various narratives and counter-narratives concerning democratization in QT. Finally, we explore the general efforts of democratization in QT such as different forms of access, formation of grassroot communities and special interest groups, the emerging culture of manifesto writing, and how these can be located within the different theories of democracy. In conclusion, we argue that although the ongoing efforts in the democratization of QT are necessary steps towards the democratization of this set of emerging technologies, they should not be accepted as sufficient to argue that QT is a democratized field. We argue that more reflexivity and responsiveness regarding the narratives and actions adopted by the actors in the QT field and making the underlying assumptions of ongoing efforts on democratization of QT explicit, can result in a better technology for society. (shrink)

This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, (...) and loop quantum gravity. (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.

I pedagogically show that the momentum operator in quantum mechanics, in the position representation, commonly known to be a derivative with respect to a spatial x-coordinate, can be derived by identifying momentum as the generator of space translations.

This article seeks to clarify the relation between consciousness and quantum physics. It is argued that, in order to be consistent with quantum theory, one must never assert that conscious action has caused a given event to occur. Rather, consciousness must be identified with "measurement" or, more concretely, with an increase in the entropy of the probability distribution of possible events. It is suggested that the feeling of self-awareness may be associated with the exchange of entropy between (...) class='Hi'>groups of quantum systems which are so tightly coupled as to be, for all practical purposes, an indivisible unit. Such groups of systems may be understood to measure themselves. Two interpretations of the quantum theory of consciousness are distinguished: one in which consciousness is defined as quantum measurement; and one in which this measurement is hypothesized to correlate with a certain biological phenomenon called consciousness. (shrink)

. The deep structural properties of a quantum information theoretic approach to formal languages and universal computation, as well as those of the topology problem of defining the presentation of the Mapping Class Group of a smooth, compact manifold are shown to be grounded in the common categorical features of the two problems.

The concept of quantum principle is introduced as a principle whose formulation is based on specific quantum ideas and notions. We consider three such principles, viz, those of quantizability, local gauge symmetry, and supersymmetry, and their role in the development of the quantum field theory (QFT). Concerning the first of these, we analyze the formal aspects and physical contents of the renormalization procedure in QFT and its relation to ultraviolet divergences and the renorm group. The quantizability principle (...) is formulated as an existence condition of a self-consistent quantum version with a given mechanism of the field interaction. It is shown that the consecutive (from a historical point of view) use of these quantum principles puts still larger limitations on possible forms of field interactions. (shrink)

We present a precise form of structural realism, called group structural realism , which identifies ‘structure’ in quantum theory with symmetry groups. However, working out the details of this view actually illuminates a major problem for structural realism; namely, a structure can itself have structure. This article argues that, once a precise characterization of structure is given, the ‘metaphysical hierarchy’ on which group structural realism rests is overly extravagant and ultimately unmotivated.

Although quantum mechanics can accurately predict the probability distribution of outcomes in an ensemble of identical systems, it cannot predict the result of an individual system. All the local and global hidden variable theories attempting to explain individual behavior have been proved invalid by experiments (violation of Bell’s inequality) and theory. As an alternative, Schrodinger and others have hypothesized existence of free will in every particle which causes randomness in individual results. However, these free will theories have failed to (...) quantitatively explain the quantum mechanical results. In this paper, we take the clue from quantum biology to get the explanation of quantum mechanical distribution. Recently it was reported that mutations (which are quantum processes) in DNA of E. coli bacteria instead of being random were biased in a direction such that the chance of survival of the bacteria is increased. Extrapolating it, we assume that all the particles including inanimate fundamental particles have a will and that is biased to satisfy the collective goals of the ensemble. Using this postulate, we mathematically derive the correct spin probability distribution without using quantum mechanical formalism (operators and Born’s rule) and exactly reproduce the quantum mechanical spin correlation in entangled pairs. Using our concept, we also mathematically derive the form of quantum mechanical wave function of free particle which is conventionally a postulate of quantum mechanics. Thus, we prove that the origin of quantum mechanical results lies in the will (or consciousness) of the objects biased by the collective goal of ensemble or universe. This biasing by the group on individuals can be called as “coherence” which directly represents the extent of life present in the ensemble. So, we can say that life originates out of establishment of coherence in a group of inanimate particles. (shrink)

This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems encountered in early attempts to construct a relativistic quantum theory. A relativistically covariant construction is given for which particle spins and angular (...) momenta can be combined through the usual rotation group Clebsch-Gordan coefficients. Solutions are defined for both the classical and quantum two body bound state and scattering problems. The recently developed quantum Lax-Phillips theory of semigroup evolution of resonant states is described. The experiment of Lindner and coworkers on interference in time is discussed showing how the property of coherence in time provides a simple understanding of the results. The full gauge invariance of the Stueckelberg-Schroedinger equation results in a 5D generalization of the usual gauge theories. A description of this structure and some of its consequences for both Abelian and non-Abelian fields are discussed. A review of the basic foundations of relativistic classical and quantum statistical mechanics is also given. The Bekenstein-Sanders construction for imbedding Milgrom's theory of modified spacetime structure into general relativity as an alternative to dark matter is also studied. (shrink)

One realist response to the pessimistic meta-induction distinguishes idle theoretical wheels from aspects of successful theories we can expect to persist and espouses realism about the latter. Implementing the response requires a strategy for identifying the distinguished aspects. The strategy I will call renormalization group realism has the virtue of directly engaging the gears of our best current physics—perturbative quantum field theories. I argue that the strategy, rather than disarming the skeptical possibilities evinced by the pessimistic meta-induction, forces them (...) to retreat a level. I also suggest that those skeptical possibilities continue to carry force. (shrink)

Let Uq be the quantum group associated to sl2 with char≠2 and qk not a root of unity. The article is devoted to the model-theoretic study of the quantum plane kq[x,y], considered as an -structure, where is the language of representations of Uq. It is proved that the lattice of definable k-subspaces of kq[x,y] is complemented. This is deduced from the same result for the Uq-module M, which is defined to be the direct sum of all finite dimensional (...) representations of Uq. It follows that the ring of definable scalars for the quantum plane is a von Neumann regular epimorphic ring extension of the quantum group Uq. (shrink)