Showing papers in "International Journal of Theoretical Physics in 1995"
TL;DR: In this article, a quantum machine is proposed to explain the quantum structure as a consequence of a real change of state of an entity under the influence of a measurement and a lack of knowledge about a deeper deterministic reality of the measurement process.
Abstract: We explain quantum structure as due to two effects: (a) a real change of state of the entity under the influence of the measurement and (b) a lack of knowledge about a deeper deterministic reality of the measurement process. We present a quantum machine, with which we can illustrate in a simple way how the quantum structure arises as a consequence of the two mentioned effects. We introduce a parameter e that measures the size of the lack of knowledge of the measurement process, and by varying this parameter, we describe a continuous evolution from a quantum structure (maximal lack of knowledge) to a classical structure (zero lack of knowledge). We show that for intermediate values of e we find a new type of structure that is neither quantum nor classical. We apply the model to situations of lack of knowledge about the measurement process appearing in other aspects of reality. Specifically, we investigate the quantumlike structures that appear in the situation of psychological decision processes, where the subject is influenced during the testing and forms some opinions during the testing process. Our conclusion is that in the light of this explanation, the quantum probabilities are epistemic and not ontological, which means that quantum mechanics is compatible with a determinism of the whole.
66 citations
TL;DR: In this paper, the Boolean D-poset is defined and it is shown that every subset of a D-POSet is a compatible set, which is the same as the definition of a set.
Abstract: In this paper the Boolean D-poset is defined and it is showed that every subset of a Boolean D-poset is a compatible set.
56 citations
TL;DR: In this paper, an overview of the theory and phenomenology of truly neutral particles based on the papers of Majorana, Racah, Furry, McLennan, and Case is presented.
Abstract: The first part of this article presents an overview of the theory and phenomenology of truly neutral particles based on the papers of Majorana, Racah, Furry, McLennan, and Case. The recent development of the construct undertaken by Ahluwalia could be relevant for the explanation of the present experimental situation in neutrino physics and astrophysics. Then the new fundamental wave equations for self-/anti-self-conjugate type II spinors proposed by Ahluwalia are recast into covariant form. The connection with Foldy-Nigam-Bargmann-Wightman-Wigner (FNBWW)-type quantum field theory is found. Possible applications to the problem of neutrino oscillations are discussed.
52 citations
TL;DR: Locally anisotropic gauge theories for semisimple and non-semisimple groups are examined in this article, where a gauge approach to generalized Lagrange gravity based on local linear and affine structural groups is proposed.
Abstract: Locally anisotropic gauge theories for semisimple and nonsemisimple groups are examined A gauge approach to generalized Lagrange gravity based on local linear and affine structural groups is proposed
47 citations
TL;DR: The theory of effect algebras, and its connection with partially ordered abelian groups, have been studied extensively in the literature as discussed by the authors, and a list of important open problems, appropriate research projects and unresolved philosophical issues engendered by the developing theory is given.
Abstract: An account is given of the recent development of the theory of effect algebras, their connection with partially ordered abelian groups, and their use for the mathematical representation of fuzzy or unsharp events. We submit an annotated list of important open problems, appropriate research projects, and unresolved philosophical issues engendered by the developing theory.
38 citations
TL;DR: In this article, a procedure of classical extension of a theory is worked out on the basis of a natural generalization of the notion of observable, the states of the extended theory being the probability measures on the pure state of the original one.
Abstract: A procedure of classical extension of a theory is worked out on the basis of a natural generalization of the notion of observable, the states of the extended theory being the probability measures on the pure states of the original one. Such a classical extension applies to quantum theory, and the qualifying features of quantum observables are preserved in the extended model.
38 citations
TL;DR: The quantum logics are all examples of sharp logics as discussed by the authors, and both the logical and the semantic version of the noncontradiction principle hold: any contradiction α ⋏ ¬ α is always false; α and its negation cannot both be true.
Abstract: The quantum logics we have studied so far are all examples of sharp logics Both the logical and the semantic version of the noncontradiction principle hold:
any contradiction α ⋏ ¬α is always false;1
a sentence α and its negation ¬α cannot both be true
36 citations
TL;DR: In this article, it was shown that these partial Boolean algebras have no common extension (as a partial Boolean subalgebra of the properties of the total system) that is embeddable in a Boolean algebra.
Abstract: According to the modal interpretation of quantum mechanics, subsystems of a quantum mechanical system have definite properties, the set of definite properties forming a partial Boolean algebra. It is shown that these partial Boolean algebras have no common extension (as a partial Boolean subalgebra of the properties of the total system) that is embeddable in a Boolean algebra. One has thus either to restrict the rules to preferred subsystems (Healey), or to advocate a shift in metaphysics (Dieks).
34 citations
TL;DR: The propositional system of a general class of discrete deterministic systems is formally characterized in this paper, and it is shown that any finite prime orthomodular lattice allowing two-valued states can be represented by an automaton logic.
Abstract: The propositional system of a general class of discrete deterministic systems is formally characterized. We find that any finite prime orthomodular lattice allowing two-valued states can be represented by an automaton logic.
33 citations
TL;DR: In this paper, an expression for the overall mass of the universe in terms of the constants of nature and the parameters describing the elementary particles was derived using only microphysical arguments, and the link between cosmology and the microscopic world was highlighted in the spirit of Dirac's large number hypothesis.
Abstract: Using solely microphysical arguments, we arrive at an expression for the overall mass of the universe in terms of the constants of nature and the parameters describing the elementary particles. The link between cosmology and the microscopic world is thus highlighted in the spirit of Dirac's large number hypothesis.
32 citations
TL;DR: The quantum theory of ur-objects proposed by C. F. von Weizsacker has to be interpreted as a quantum theory for information as discussed by the authors, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy and matter, which in ur theory appear to be directly connected with information as the fundamental substance.
Abstract: The quantum theory of ur-objects proposed by C. F. von Weizsacker has to be interpreted as a quantum theory of information. Ur-objects, or urs, are thought to be the simplest objects in quantum theory. Thus an ur is represented by a two-dimensional Hilbert space with the universal symmetry groupSU(2), and can only be characterized asone bit of potential information. In this sense it is not a spatial but aninformation atom. The physical structure of the ur theory is reviewed, and the philosophical consequences of its interpretation as an information theory are demonstrated by means of some important concepts of physics such as time, space, entropy, energy, and matter, which in ur theory appear to be directly connected with information as “the” fundamental substance. This hopefully will help to provide a new understanding of the concept of information.
TL;DR: In this article, a theory containing both electric and magnetic charges is formulated using two vectors potentials, Aμ and Cμ, which effectively hides the magnetic charge, and the symmetry associated with it, when one is at an energy scale far enough removed from the scale of the symmetry breaking.
Abstract: A theory containing both electric and magnetic charges is formulated using two vectors potentials,Aμ andCμ. This has the aesthetic advantage of treating electric and magnetic charges both as gauge symmetries, but it has the experimental disadvantage of introducing a second massless gauge boson (the “magnetic” photon) which is not observed. This problem is dealt with by using the Higgs mechanism to give a mass to one of the gauge bosons while the other remains massless. This effectively “hides” the magnetic charge, and the symmetry associated with it, when one is at an energy scale far enough removed from the scale of the symmetry breaking.
TL;DR: In this paper, it was shown that a quantum stochastic differential inclusion of hypermaximal monotone type has a unique adapted solution which is obtained as the limit of the unique adapted solutions of a one-parameter family of Lipschitzian quantum Stochastic differential equations.
Abstract: In continuation of our study of the existence of solutions of quantum stochastic differential inclusions, we first introduce and develop some aspects of the theory of maximal [resp. hypermaximal] monotone multifunctions, including the description of a number of properties of their resolvents and Yosida approximations, in the present noncommutative setting. Then, it is proved that, under a certain continuity assumption, a quantum stochastic differential inclusion of hypermaximal monotone type has a unique adapted solution which is obtained as the limit of the unique adapted solutions of a one-parameter family of Lipschitzian quantum stochastic differential equations. As examples, we show that a large class of quantum stochastic differential inclusions which satisfy the assumptions and conclusion of our main result arises as perturbations of certain quantum stochastic differential equations by some multivalued stochastic processes.
TL;DR: In this paper, the authors proposed the theory of Einstein structured spaces, which includes all types of singularities into a geometrically tractable theoretical scheme, including quasiregular and curvature singularities.
Abstract: To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces.
TL;DR: In this paper, the energy density ρ depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = (γ − 1)ρ, whereγ is a constant.
Abstract: Thermodynamics arguments have been employed to derive how the energy densityρ depends on the temperatureT for a fluid whose pressurep obeys the equation of statep = (γ −1)ρ, whereγ is a constant. Three different methods, among them the one considered by Boltzmann (Carnot cycle), lead to the expressionρ = ηTγ/(γ −1), whereη is a constant. This result also appears naturally in the framework of general relativity for spacetimes with constant spatial curvature. Some particular cases are vacuum (p = −ρ), cosmic strings (p= −1/3ρ), radiation (p = 1/3ρ), and stiff matter (p = ρ). It is also shown that such results can be adapted for blackbody radiation inN spatial dimensions.
TL;DR: In this paper, three definitions of logical independence of two von Neumann latticesPℳ1,P ℳ2 of two sub-von Neumann algebras are given and the relations of the definitions clarified.
Abstract: Three definitions of logical independence of two von Neumann latticesPℳ1,Pℳ2 of two sub-von Neumann algebras ℳ1, ℳ2 of a von Neumann algebra ℳ are given and the relations of the definitions clarified. It is shown that under weak assumptions the following notion, called “logical independence” is the strongest:A ∧ B ≠ 0 for any 0 ≠A ∈Pℳ1, 0 ≠B ∈Pℳ2. Propositions relating logical independence ofPℳ1,Pℳ2 toC*-independence,W* independence, and strict locality of ℳ1, ℳ2 are presented.
TL;DR: In this paper, a new approach to quantize gravity based on the notion of differential algebra is suggested, and it is shown that the differential geometry of this object cannot be described in terms of points.
Abstract: A new approach to quantize gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object cannot be described in terms of points. A spatialization procedure giving rise to points by losing part of the entire structure is discussed. The counterparts of the traditional objects of differential geometry are studied.
TL;DR: The orthoalgebras, introduced by Foulis and Randall and studied by various authors, have recently become a significant mathematical structure of the logico-algebraic foundation of quantum theories.
Abstract: The orthoalgebras, introduced by Foulis and Randall and studied by various authors, have recently become a significant mathematical structure of the logicoalgebraic foundation of quantum theories. In this paper we give a coherent account of states (=finitely additive measures) on orthoalgebras. In the first section we review basic properties of (and constructions with) orthoalgebras and develop a useful “pasting technique” (Theorem 1.12 and Proposition 1.16) applied later in this paper (and possibly elsewhere, too). We also exhibit orthoalgebras with rather interesting and “exotic” state spaces (Example 1.20 and Proposition 1.21). In the second section we construct orthoalgebras with preassigned state space properties. We prove a state representation theorem (Theorem 2.1) and obtain an orthoalgebraic version of Shultz's theorem (Theorem 2.7). In the third section we make a thorough analysis of the extension problem for states on orthoalgebras. We first study the orthoalgebras whose state spaces are finite dimensional. For these orthoalgebras we find a necessary and sufficient condition to allow extensions of states over larger orthoalgebras (Theorem 3.4). Then we prove that all Hilbertian orthoalgebras as well as all Boolean orthoalgebras allow extensions of states over larger orthoalgebras (Theorems 3.10 and 3.12).
TL;DR: In this paper, the path integral quantization for higher derivative Chern-Simons theories in (2+1) dimensions coupled to fermions is treated, and the diagrammatic and the Feynman rules are constructed and the regularization and renormalization of this higher derivative model are analyzed in the framework of perturbation theory.
Abstract: The path integral quantization for higher derivative Chern-Simons theories in (2+1) dimensions coupled to fermions is treated. The diagrammatic and the Feynman rules are constructed and the regularization and renormalization of this higher derivative model are analyzed in the framework of the perturbation theory. Finally, the unitarity problem related to the possible appearance of ghost states with negative norm is also discussed.
TL;DR: In this article, higher-order Lagrangian mechanics on the k-velocity manifold were studied, and the invariants to the infinitesimal symmetries were explicitly written.
Abstract: We study higher-order Lagrangian mechanics on thek-velocity manifold. The variational problem gives rise to new concepts, such as main invariants, Zermelo conditions, higher-order energies, and new conservation laws. A theorem of Noether type is proved for higher-order Lagrangians. The invariants to the infinitesimal symmetries are explicitly written. All this construction is a natural extension of classical Lagrangian mechanics.
TL;DR: In this paper, a potential model for an unsharp histories approach to quantum theory based on difference posets as abstract models for the set of effects is considered, and it is shown that the sets of all histories in this approach have an algebraic structure of a difference poset.
Abstract: Direct limits and tensor products of difference posets are studied. In the spirit of a recent paper by Isham, a potential model for an “unsharp histories” approach to quantum theory based on difference posets as abstract models for the set of effects is considered. It is shown that the set of all histories in this approach has an algebraic structure of a difference poset.
TL;DR: A tensor product of difference posets and/or, equivalently, of effect algebras is defined in this paper, and an equivalent condition is presented, using the notion of D-test spaces generalizing test spaces of Randall and Foulis.
Abstract: A tensor product of difference posets and/or, equivalently, of effect algebras, which generalize orthoalgebras and orthomodular posets, is defined, and an equivalent condition is presented. The proof uses the notion of D-test spaces generalizing test spaces of Randall and Foulis. In particular, we show that a tensor product for difference posets with a nonempty system of probability measures exists.
TL;DR: In this article, the concept of pseudo-partial Painleve property is introduced for the first time which could assist in finding solutions to equations that do not possess the painleve properties.
Abstract: In 1987 C. C. Dyer, G. C. McVittie, and L. M. Oattes derived the (two) field equations for shear-free, spherically symmetric perfect fluid spacetimes which admit a conformai symmetry. We use the techniques of the Lie and Painleve analyses of differential equations to find solutions of these equations. The concept of a pseudo-partial Painleve property is introduced for the first time which could assist in finding solutions to equations that do not possess the Painleve property. The pseudo-partial Painleve property throws light on the distinction between the classes of solutions found independently by P. Havas and M. Wyman. We find a solution for all values of a particular parameter for the first field equation and link it to the solution of the second equation. We indicate why we believe that the first field equation cannot be solved in general. Both techniques produce similar results and demonstrate the close relationship between the Lie and Painleve analyses. We also show that both of the field equations of Dyeret al. may be reduced to the same Emden-Fowler equation of index two.
TL;DR: In this paper, the conformal symmetry vector in static, spherically symmetric spacetimes is obtained in terms of functions subject to a number of integrability conditions that also place restrictions on the metric.
Abstract: We obtain the conformal symmetry vector in static, spherically symmetric spacetimes, in terms of functions subject to a number of integrability conditions that also place restrictions on the metric. Some conformal symmetries found previously are regained as special cases.
TL;DR: In this paper, the authors investigate quasilinear and weakly linear QMV algebras as a generalization of the algebraic structure of all effects of a Hilbert space and study the varieties generated by these classes.
Abstract: We investigate quasilinear and weakly linear QMV algebras as a generalization of the algebraic structure of all effects of a Hilbert space and we study the varieties generated by these classes. Finally, we prove some results concerning locally finite and Archimedean QMV algebras.
TL;DR: In this article, a detailed review of the Dubois-Violette approach to non-commutative differential calculus is presented, and some perspectives and open questions are discussed, as well as new models of Yang-Mills-Higgs theories.
Abstract: We present a detailed review of the Dubois-Violette approach to noncommutative differential calculus. The noncommutative differential geometry of matrix algebras and the noncommutative Poisson structures are treated in some detail. We also present the analog of Maxwell's theory and new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions.
TL;DR: In this article, the authors studied Bell-type inequalities of ordern with emphasis on the casen = 2 in the framework of the structure of an orthomodular lattice, which is a logicoalgebraic model of quantum mechanics.
Abstract: We study Bell-type inequalities of ordern with emphasis on the casen = 2 in the framework of the structure of an orthomodular lattice, which is a logicoalgebraic model of quantum mechanics. We give necessary and sufficient conditions for the validity of Bell-type inequalities of order 2. In particular, we study Bell-type inequalities in various structures connected with a Hilert space, and we give a characterization of Boolean algebras via the validity of certain Bell-type inequalities.
TL;DR: In this paper, the covariant description of the Hamiltonian formalism for constrained field systems is considered and applications to gauge theories are given, where the equivalence of solutions is shown for affine and quadratic Lagrangians.
Abstract: We are concerned with the covariant description of the Hamiltonian formalism for constrained field systems. The relation with the Lagrangian formalism is considered and applications to gauge theories are given. Both formalisms are developed on the same space, namely the momentum space. The equivalence of solutions is shown to hold for affine and quadratic Lagrangians. The Yang-Mills equations are put into a Hamiltonian form by means of acomplete family of Hamiltonians. This completeness property appears in a nice way as agauge-type condition connected with the Hamilton equations and generalizing the notion of gauge condition usually dealt with in gauge theory.
TL;DR: The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroupL and a distinguished subsetM such that perspectivity with respect to M is a congruence on L.
Abstract: Orthomodular lattices and posets, orthoalgebras, and D-posets are all examples of partial Abelian semigroups. So, too, are the event structures of test spaces. The passage from an algebraic test space to its logic (an orthoalgebra) is an instance of a general construction involving a partial Abelian semigroupL and a distinguished subsetM\( \subseteq \)L such that perspectivity with respect toM is a congruence onL. The quotient ofL by such a congruence is always a cancellative, unital PAS, and every such PAS arises canonically as such a quotient.
TL;DR: In this paper, the authors propose a representation of quantum mechanics where all pure and mixed states of a n-dimensional quantum entity are represented as points of a subset of an 2-dimensional real space.
Abstract: We propose a representation of quantum mechanics where all pure and mixed states of a n-dimensional quantum entity are represented as points of a subset of an
2-dimensional real space. We introduce the general measurements of quantum mechanics on this entity, determined by sets of mutual orthogonal points of the representation space. Within this framework we construct a hidden measurement model for an arbitrary finite dimensional quantum entity.