Showing papers in "International Journal of Theoretical Physics in 2000"
TL;DR: The generalized uncertainty principle of string theory was derived in the framework of quantum geometry by taking into account the existence of an upper limit on the acceleration of massive particles as discussed by the authors, which is the same as the upper limit of the uncertainty principle in string theory.
Abstract: The generalized uncertainty principle of string theory is derived in the frameworkof quantum geometry by taking into account the existence of an upper limit onthe acceleration of massive particles.
325 citations
TL;DR: In this paper, the fundamental relation between Lie-Backlund symmetry generators and conservation laws of an arbitrary differential equation is derived without regard to a Lagrangian formulation of the differential equation.
Abstract: The fundamental relation between Lie-Backlund symmetry generators andconservation laws of an arbitrary differential equation is derived without regardto a Lagrangian formulation of the differential equation. This relation is used inthe construction of conservation laws for partial differential equations irrespectiveof the knowledge or existence of a Lagrangian. The relation enables one toassociate symmetries to a given conservation law of a differential equation.Applications of these results are illustrated for a range of examples.
280 citations
TL;DR: In this article, the reliability of the bit erasure process is bounded by the accuracy inherent in the statistical state of the energy source(the resources) driving the process, and a general framework describing the thermodynamic worth of the resources with respect to reliable erasureor good cooling is developed.
Abstract: Landauer's principle states that the erasure of one bit of information requires thefree energy kT ln 2. We argue that the reliability of the bit erasure process isbounded by the accuracy inherent in the statistical state of the energy source(“the resources”) driving the process. We develop a general framework describingthe “thermodynamic worth” of the resources with respect to reliable bit erasureor good cooling. This worth turns out to be given by the distinguishability of theresource's state from its equilibrium state in the sense of a statistical inferenceproblem. Accordingly, Kullback—Leibler relative information is a decisivequantity for the “worth” of the resource's state. Due to the asymmetry of relativeinformation, the reliability of the erasure process is bounded rather by the relativeinformation of the equilibrium state with respect to the actual state than by therelative information of the actual state with respect to the equilibrium state (whichis the free energy up to constants).
248 citations
TL;DR: It is shown that everyD-lattice ( lattice-ordered effect algebra)P is a set-theoreticunion of maximal subsets of mutually compatible elements, called blocks, which are sub-D- lattices and sub-effect-algebras ofP which are MV-algeses closed with respect to all suprema and infima existing inP.
Abstract: We show that everyD-lattice (lattice-ordered effect algebra)P is a set-theoreticunion of maximal subsets of mutually compatible elements, called blocks.Moreover, blocks are sub-D-lattices and sub-effect-algebras ofP which areMV-algebras closed with respect to all suprema and infima existing inP.
138 citations
TL;DR: In this paper, the authors provide a self-contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation in an ordinary 4-dimensional spacetime background.
Abstract: This paper provides a self-contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation in an ordinary 4-dimensional spacetime background. This category also includes “brane world” models that treat the observed universe as a 3-brane in 5 or higher dimensional background. The first sections are concerned with purely kinematic aspects: it is shown how, to second differential order, the geometry (and in particular the inner and outer curvature) of a brane worldsheet of arbitrary dimension is describable in terms of the first, second, and third fundamental tensor. The later sections show how—to lowest order in the thin limit—the evolution of such a brane worldsheet will always be governed by a simple tensorial equation of motion whose left hand side is the contraction of the relevant surface stress tensor T¯µv with the (geometrically defined) second fundamental tensor Kμνρ, while the right hand side will simply vanish in the case of free motion and will otherwise be just the orthogonal projection of any external force density that may happen to act on the brane.
132 citations
TL;DR: In this article, the authors extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as the Kochen-Specker theorem.
Abstract: We extend the topos-theoretic treatment given in previous papers of assigningvalues to quantities in quantum theory, and of related issues such as theKochen–Specker theorem. This extension has two main parts: the use of vonNeumann algebras as a base category and the relation of our generalized valuationsto (i) the assignment to quantities of intervals of real numbers and (ii) the ideaof a subobject of the coarse-graining presheaf.
108 citations
TL;DR: By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrodinger equation in two dimension is obtained with the potentials V(r) =ar>>\2 + br>>\4 + cr>>\6,V(r] = ar + br2 + cr¯¯−1, and V( r) = ar>>\2+ br>>\−2+ cr>>\−4 + dr>>\−6,respectively.
Abstract: By applying an ansatz to the eigenfunction, an exact closed-form solution of theSchrodinger equation in two dimension is obtained with the potentials V(r) =ar
2 + br
4 + cr
6,V(r) = ar + br2 + cr
−1,and V(r) = ar
2 + br
−2+ cr
−4 + dr
−6,respectively. The restrictions on the parameters of the given potential andthe angular momentum m are obtained.
97 citations
TL;DR: In this paper, the explicit traveling wave solutions to some well-known evolution equations, such as the MKdV-Burgers equation, the generalizedFitzhugh-Nagumo equation, and some coupledones in fluid mechanics, are given.
Abstract: By introducing a concept of “rank,” an exploratory approach is presented forfinding the explicit traveling wave solutions to some physically interestingnonlinear evolution equations in physics and other fields. To show the efficiencyof this approach, the explicit traveling wave solutions to some well-knownequations, such as the MKdV-Burgers equation, the generalizedFitzhugh-Nagumo equation, the generalized Burgers-Fisher equation, and some coupledones in fluid mechanics, are given.
82 citations
TL;DR: In this article, the authors argue that a dynamical component with negative pressure is easier to achieve than a non-vanishing cosmological constant, and they describe the quintessence scenario and its shortcomings in connection with the nagging "cosmologicalconstant problem".
Abstract: The mounting evidence that the universe is presently undergoing acceleratingexpansion has restored some credit to the scenarios with a nonvanishingcosmological constant. From the point of view of a theory of fundamentalinteractions, one may argue that a dynamical component with negative pressureis easier to achieve. As an illustration, the quintessence scenario is described andits shortcomings are discussed in connection with the nagging “cosmologicalconstant problem.”
70 citations
TL;DR: In this article, a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ∝), and OSP(8*/2N) is carried out.
Abstract: We carry out a general analysis of the representations of the superconformal algebras SU(2, 2/N), OSp(8/4, ∝), and OSp(8*/2N) and give their realization in superspace. We present a construction of their UIRs by multiplication of the different types of massless superfields (“supersingletons”). Particular attention is paid to the so-called “short multiplets.” Representations undergoing shortening have “protected dimension” and may correspond to BPS states in the dual supergravity theory in anti-de Sitter space. These results are relevant for the classification of multitrace operators in boundary conformally invariant theories as well as for the classification of AdS black holes preserving different fractions of supersymmetry.
69 citations
TL;DR: In this article, a new general-relativistic theory of cosmology is presented, which describes the universe as having a three-phase evolution with a decelerating expansion followed by a constant and an accelerating expansion, and predicts that the universe is now in the latter phase.
Abstract: A new general-relativistic theory of cosmology, the dynamical variables of whichare those of Hubble's, namely distances and redshifts, is presented. The theorydescribes the universe as having a three-phase evolution with a deceleratingexpansion followed by a constant and an accelerating expansion, and it predictsthat the universe is now in the latter phase. The theory is actually a generalizationof Hubble's law taking gravity into account by means of Einstein's theory ofgeneral relativity. The equations obtained for the universe expansion are elegantand very simple. It is shown, assuming Ω0 = 0.24, that the time at which theuniverse goes over from a decelerating to an accelerating expansion, i.e., theconstant expansion phase, occurs at 0.03 τ from the big bang, where τ is theHubble time in vacuum. Also, at that time the cosmic radiation temperature was11 K. Recent observations of distant supernovae imply, in defiance of expectations,that the universe's growth is accelerating, contrary to what has always beenassumed, that the expansion is slowing down due to gravity. Our theory confirmsthese recent experimental results by showing that the universe now is definitelyin a stage of accelerating expansion.
TL;DR: The pumping lemma in automata theory based on quantum logic is established and the equivalence between the recognizabilty by the product and union of orthomodular lattice-valued automata is shown to be equivalent to the distributivity of meet over union in the truth-value set.
Abstract: We establish the pumping lemma in automata theory based on quantum logicunder certain conditions on implication, and discuss the recognizability by theproduct and union of orthomodular lattice-valued (quantum) automata. Inparticular, we show that the equivalence between the recognizabilty by the productof automata and the conjunction of the recognizabilities by the factor automatais equivalent to the distributivity of meet over union in the truth-value set.
TL;DR: Using the symmetric energy-momentum complexes of Landau and Lifshitz, Papapetrou, and Weinberg, this paper obtained the energy of the universe in anisotropic Bianchi type I cosmological models.
Abstract: Using the symmetric energy-momentum complexes of Landau and Lifshitz,Papapetrou, and Weinberg, we obtain the energy of the universe in anisotropicBianchi type I cosmological models. The energy (due to matter plus field) isfound to be zero and this agrees with a previous result of Banerjee and Sen, whoinvestigated this problem using the Einstein energy-momentum complex. Ourresult supports the importance of the energy-momentum complexes andcontradicts the prevailing folklore that different energy-momentum complexescould give different and hence unacceptable energy distribution in a givenspace-time. The result that the total energy of the universe in these models is zerosupports the viewpoint of Tryon. Rosen computed the total energy of the closedhomogeneous isotropic universe and found it to be zero, which agrees with thestudies of Tryon.
TL;DR: An algorithm and programs for checking Greechie diagram passage byequations defining varieties of orthomodular lattices and give examples from Hilbert lattices are alsoprovide.
Abstract: We give a new algorithm for generating Greechie diagrams with arbitrary chosennumber of atoms or blocks (with 2, 3, 4, . . . atoms) and provide a computerprogram for generating the diagrams. The results show that the previous algorithmdoes not produce every diagram and that it is atleast 105 times slower. We alsoprovide an algorithm and programs for checking Greechie diagram passage byequations defining varieties of orthomodular lattices and give examples fromHilbert lattices. We also discuss some additional characteristics of Greechiediagrams.
TL;DR: In this paper, asymptotic solutions of the m-dimensional Montroll-Weiss' jump problem are obtained in terms of stable distributions, covering both the subdiffusive and the super-diffusive regime.
Abstract: Asymptotic solutions of the m-dimensional Montroll–Weiss'jump problem areobtained. They cover both the subdiffusive and the superdiffusive regime, obeyfractional differential equations, and are expressed in terms of stable distributions.Analytical investigation and numerical calculations of anomalous diffusiondistributions are performed and their properties are discussed.
TL;DR: In this paper, it was shown that a large homogeneous and isotropic universe can emerge from the quantum-gravity era with a large enough size and with sufficient homogeneity to explain its present-day large-scale structure.
Abstract: Within the context of a recently proposed family of stochastic dynamical lawsfor causal sets, one can ask whether the universe might have emerged from thequantum-gravity era with a large enough size and with sufficient homogeneityto explain its present-day large-scale structure. In general, such a scenario wouldbe expected to require the introduction of very large or very small fundamentalparameters into the theory. However, there are indications that such “fine tuning”is not necessary, and a large homogeneous and isotropic cosmos can emergenaturally thanks to the action of a kind of renormalization group associated withcosmic cycles of expansion and recollapse.
TL;DR: DecDecoherence and the approach to the classical final limit are studied in two different cases: the Mott and the cosmological problems in this paper. But the focus is on the MOTT.
Abstract: Decoherence and the approach to the classical final limit are studied in twosimilar cases: the Mott and the cosmological problems.
TL;DR: In this article, the Schild's ladder parallel transport procedure for an arbitrary connection is analyzed and it is shown that it is only capable of detecting the symmetric part of this connection.
Abstract: We analyze the Schild's ladder parallel transport procedure for an arbitraryconnection. We demonstrate that the procedure, while it can be performed forany connection, in fact is only capable of detecting the symmetric part of thisconnection. In geometries with a symmetric connection it fulfills its goal toexpress connection and parallel transport of any vector in terms of geodesics ofsuch geometries.
TL;DR: In this article, the authors studied the pulsatile flow of blood through a porous medium under the influence of body acceleration and obtained analytic expressions for axial velocity, fluid acceleration, flow rate, and shear stress.
Abstract: Pulsatile flow of blood through a porous medium has been studied studied underthe influence of body acceleration. With the help of Laplace and finite Hankeltransforms, analytic expressions for axial velocity, fluid acceleration, flow rate,and shear stress have been obtained.
TL;DR: In this article, the precession of an orbiting gyroscope in a general weak-gravitational field described by a Newtonian potential (the gravitoelectric field) and a vector potential was analyzed.
Abstract: We review the derivation of the metric for a spinning body of any shape andcomposition using linearized general relativity theory (LGRT), and also obtainthe same metric using a transformation argument The latter derivation makes itclear that the linearized metric contains only the Eddington α and γ parameters,so no new parameter is involved in frame-dragging or Lense—Thirring effectsWe then calculate the precession of an orbiting gyroscope in a general weakgravitational field described by a Newtonian potential (the gravitoelectric field)and a vector potential (the gravitomagnetic field) Next we make a multipoleanalysis of the potentials and the precession equations, giving all of these interms of the spherical harmonics moments of the density distribution The analysisis not limited to an axially symmetric source, although the Earth, which is themain application, is very nearly axisymmetric Finally, we analyze the precessionin regard to the Gravity Probe B (GP-B) experiment, and find that the effect ofthe Earth's quadrupole moment (J2) on the geodetic precession is large enoughto be measured by GP-B (a previously known result), but the effect on theLense—Thirring precession is somewhat beyond the expected GP-B accuracy
TL;DR: In this paper, a scheme for an algebraic quantization of the causal sets of Sorkin et al. is presented, along the lines of a similar algebraization and quantum interpretation of finitary topological spaces due to Zapatrin and thisauthor.
Abstract: A scheme for an algebraic quantization of the causal sets of Sorkin et al. ispresented. The suggested scenario is along the lines of a similar algebraizationand quantum interpretation of finitary topological spaces due to Zapatrin and thisauthor. To be able to apply the latter procedure to causal sets Sorkin's 'semanticswitch' from 'partially ordered sets as finitary topological spaces' to 'partiallyordered sets as locally finite causal sets' is employed. The result is the definition of'quantum causal sets'. Such a procedure and its resulting definition are physicallyjustified by a property of quantum causal sets that meets Finkelstein's requirementfor 'quantum causality' to be an immediate, as well as an algebraically represented,relation between events for discrete locality's sake. The quantum causal setsintroduced here are shown to have this property by direct use of a result fromthe algebraization of finitary topological spaces due to Breslav, Parfionov, andZapatrin.
TL;DR: In this paper, an algebraic quantization procedure for discretized spacetime models is suggested based on the duality between finitary substitutes and their incidence algebras, and the provided limiting procedure that yields conventional manifold characteristicsof spacetime structures is interpreted in quantum algebraic framework as acorrespondence principle.
Abstract: An algebraic quantization procedure for discretized spacetime models is suggestedbased on the duality between finitary substitutes and their incidence algebras.The provided limiting procedure that yields conventional manifold characteristicsof spacetime structures is interpreted in the quantum algebraic framework as acorrespondence principle.
TL;DR: In this paper, a plane transitivity property is proposed to characterize classical Hilbert spaces among infinite-dimensional orthomodular spaces as apossible partial substitute for the 'defective' axioms.
Abstract: Three of the traditional quantum axioms (orthocomplementation, orthomodularity,and the covering law) show incompatibilities with two products introduced byAerts for the description of joint entities. Inspired by Soler's theorem and Holland'sAUG axiom, we propose a property of 'plane transitivity,' which also characterizesclassical Hilbert spaces among infinite-dimensional orthomodular spaces, as apossible partial substitute for the 'defective' axioms.
TL;DR: In this article, the authors formulate a paradox in relation to the description of a joint entity consisting of two subentities by standard quantum mechanics, and propose a solution to the paradox by the interpretation of density states as pure states.
Abstract: We formulate a paradox in relation to the description of a joint entity consistingof two subentities by standard quantum mechanics. We put forward a proposalfor a possible solution, entailing the interpretation of 'density states' as 'purestates.' We explain where the inspiration for this proposal comes from and howits validity can be tested experimentally. We discuss the consequences of theproposal for quantum axiomatics.
TL;DR: In this article, a generalization of the Calogero-Vasiliev algebra, where Cλ is the cyclic group of order λ, is studied both from mathematical and applied viewpoints.
Abstract: Cλ-extended oscillator algebras generalizing the Calogero—Vasiliev algebra,where Cλ is the cyclic group of order λ, are studied both from mathematical andapplied viewpoints. Casimir operators of the algebras are obtained and used toprovide a complete classification of their unitary irreducible representations underthe assumption that the number operator spectrum is nondegenerate. Deformedalgebras admitting Casimir operators analogous to those of their undeformedcounterparts are looked for, yielding three new algebraic structures. One of themincludes the Brzezi´nski et al. deformation of the Calogero—Vasiliev algebra as aspecial case. In its bosonic Fock-space representation, the realization ofCλ-extended oscillator algebras as generalized deformed oscillator ones is shown toprovide a bosonization of several variants of supersymmetric quantum mechanics:parasupersymmetric quantum mechanics of order p = λ − 1 for any λ, as wellas pseudosupersymmetric and orthosupersymmetric quantum mechanics of ordertwo for λ = 3.
TL;DR: In this paper, the entropy of the Dirac field was shown to be proportional to the sum of the areas of the two event horizons in Schwarzschild-de Sitter space-time, a blackhole horizon and a cosmological horizon.
Abstract: There are two event horizons in Schwarzschild–de Sitter space-time, a blackhole horizon and a cosmological horizon. They have different temperatures. Theradiation between them is of course not in thermal equilibrium. According to themembrane model suggested by us, the two horizons can be thought of as twoindependent thermodynamic systems in equilibrium. Their Dirac field entropiesare calculated via a membrane model. The result shows that the entropy of theDirac field is proportional to the sum of the areas of the two event horizons. Ifwe choose the same cutoff as that of Klein–Gordon field, the entropy of theDirac field is \(3\tfrac{1}{2}\) times that of Klein–Gordon field. This agrees with previousresults.
TL;DR: In this paper, it was shown that, contrary to prior claims, the ratio of variance to its mean squared being of the order unity does not imply a failure of semiclassical gravity, which is more a consequence of the quantum nature of the state of the matter field than any inadequacy of the theory of spacetime withquantum matter as source.
Abstract: From calculations of the variance, or the fluctuations, and the mean energy densityof a massless scalar field in the Minkowski vacuum as a function of an intrinsicscale defined by the world function between two nearby points (as used in pointseparation regularization), we show that, contrary to prior claims, the ratio ofvariance to its mean squared being of the order unity does not imply a failureof semiclassical gravity. It is more a consequence of the quantum nature of thestate of the matter field than any inadequacy of the theory of spacetime withquantum matter as source.
TL;DR: This work focuses on environment induced decoherence and its degree of usefulness for the interpretation of quantum theory, and discusses the emergence of a classical world.
Abstract: We give a short, critical review of the issue of decoherence. We establish the most general framework in which decoherence can be discussed, how it can be quantified, and how it can be measured. We focus on environment induced decoherence and its degree of usefulness for the interpretation of quantum theory. We finally discuss the emergence of a classical world. An overall emphasis is given in pointing at common fallacies and misconceptions.
TL;DR: The notion of finitary spacetime sheaves was introduced in this paper based on locally finite approximations of the continuous topology of a bounded region of a spacetimemanifold.
Abstract: The notion of finitary spacetime sheaves is introduced based on locally finiteapproximations of the continuous topology of a bounded region of a spacetimemanifold. Finitary spacetime sheaves are seen to be sound mathematical modelsof approximations of continuous spacetime observables.
TL;DR: In this paper, the EPR-Bell paradox is analyzed and it is shown that in the realm of quantum physics there exists action at a distance, or at least superluminal causal propagation is possible; that is, either relativity theory or Reichenbach's common cause principle fails.
Abstract: Reichenbach's common cause principle claims that if there is correlation betweentwo events and none of them is directly causally influenced by the other, thenthere must exist a third event that can, as a common cause, account for thecorrelation. The EPR-Bell paradox consists in the problem that we observecorrelations between spatially separated events in the EPR experiments whichdo not admit common-cause-type explanation, and it must therefore be concludedthat, contrary to relativity theory, in the realm of quantum physics there existsaction at a distance, or at least superluminal causal propagation is possible; thatis, either relativity theory or Reichenbach's common cause principle fails.By means of closer analyses of the concept of common cause and a more precisereformulation of the EPR experimental scenario, I sharpen the conclusion wecan draw from the violation of Bell's inequalities.