Showing papers in "Foundations of Physics in 2002"
TL;DR: In this article, it was shown that the observables and state space of a physical theory are quantum-mechanical, and the implications of alternative answers to a remaining open question about nonlocality and bit commitment.
Abstract: We show that three fundamental information-theoretic constraints -- the impossibility of superluminal information transfer between two physical systems by performing measurements on one of them, the impossibility of broadcasting the information contained in an unknown physical state, and the impossibility of unconditionally secure bit commitment -- suffice to entail that the observables and state space of a physical theory are quantum-mechanical. We demonstrate the converse derivation in part, and consider the implications of alternative answers to a remaining open question about nonlocality and bit commitment.
293 citations
TL;DR: In this paper, the concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics, and a formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.
Abstract: The concepts of complementarity and entanglement are considered with respect to their significance in and beyond physics. A formally generalized, weak version of quantum theory, more general than ordinary quantum theory of physical systems, is outlined and tentatively applied to two examples.
273 citations
TL;DR: In this paper, it was shown that the value of the maximal tension in General Relativity in four spacetime dimensions can be expressed as a function of a principal of maximal tension, and the relation of this principle to string theory was discussed.
Abstract: I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is \(\frac{{c^4 }}{{4G}}\). The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation between G and the classical string coupling constant α′ and the velocity of light c which does not involve Planck's constant.
86 citations
TL;DR: In this article, the polarizable vacuum (PVV) approach to general relativity (GR) has been proposed, which is derived from a model by Dicke and related to the THeμ formalism used in comparative studies of gravitational theories.
Abstract: Standard pedagogy treats topics in general relativity (GR) in terms of tensor formulations in curved space-time. An alternative approach based on treating the vacuum as a polarizable medium is presented here. The polarizable vacuum (PV) approach to GR, derived from a model by Dicke and related to the “THeμ” formalism used in comparative studies of gravitational theories, provides additional insight into what is meant by a curved metric. While reproducing the results predicted by GR for standard (weak-field) astrophysical conditions, for strong fields a divergence of predictions in the two formalisms (GR vs. PV) provides fertile ground for both laboratory and astrophysical tests to compare the two approaches.
73 citations
TL;DR: In this article, it was shown that to be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.
Abstract: The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an equivalent qubit-based quantum computer.
71 citations
TL;DR: In this article, the mathematical implementation of the Dirac formulation of quantum mechanics is presented, and a rigorous framework that unifies most of the versions of this implementation is presented for unifying them.
Abstract: We revise the mathematical implementation of the Dirac formulation of quantum mechanics, presenting a rigorous framework that unifies most of versions of this implementation.
65 citations
TL;DR: The present experimental status in the search for neutrinoless double beta decay is reviewed in this paper, with emphasis on the first indication of double-beta decay in the HEIDELBERG-MOSCOW experiment, giving first evidence for lepton number violation and a Majorana nature of the neutrinos.
Abstract: The present experimental status in the search for neutrinoless double beta decay is reviewed, with emphasis on the first indication for neutrinoless double beta decay found in the HEIDELBERG-MOSCOW experiment, giving first evidence for lepton number violation and a Majorana nature of the neutrinos Future perspectives of the field are briefly outlined
55 citations
TL;DR: In this article, the generalized second law of thermodynamics (GSL) was extended to incorporate cosmological event horizons, and it was shown that the generalized total entropy is satisfied for a wide range of models, in particular the case of an asymptotically de Sitter universe with a gas of small black holes.
Abstract: Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic worth of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.
51 citations
TL;DR: In this paper, the authors study the space geometry of a rotating disk from a theoretical and operational point of view, and give a precise definition of the space of the disk, which is not clearly defined in the literature.
Abstract: We study the space geometry of a rotating disk both from a theoretical and operational approach; in particular we give a precise definition of the space of the disk, which is not clearly defined in the literature. To this end we define an extended 3-space, which we call “relative space:” it is recognized as the only space having an actual physical meaning from an operational point of view, and it is identified as the “physical space of the rotating platform.” Then, the geometry of the space of the disk turns out to be non Euclidean, according to the early Einstein's intuition; in particular the Born metric is recovered, in a clear and self consistent context. Furthermore, the relativistic kinematics reveals to be self consistent, and able to solve the Ehrenfest's paradox without any need of dynamical considerations or ad hoc assumptions.
50 citations
TL;DR: In this article, a frequency analysis of the EPR-Bell argumentation is performed and it is shown that the existence of probability distributions of the Kolmogorov type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes.
Abstract: We perform a frequency analysis of the EPR-Bell argumentation. One of the main consequences of our investigation is that the existence of probability distributions of the Kolmogorov-type which was supposed by some authors is a mathematical assumption which may not be supported by actual physical quantum processes. In fact, frequencies for hidden variables for quantum particles and measurement devices may fluctuate from run to run of an experiment. These fluctuations of frequencies for micro-parameters need not contradict to the stabilization of frequencies for physical observables. If, nevertheless, micro-parameters are also statistically stable, then violations of Bell's inequality and its generalizations may be a consequence of dependence of collectives corresponding to two different measurement devices. Such a dependence implies the violation of the factorization rule for the simultaneous probability distribution. Formally this rule coincides with the well known BCHS locality condition (or outcome independence condition). However, the frequency approach implies totally different interpretation of dependence. It is not dependence of events, but it is dependence of collectives. Such a dependence may be induced by the same preparation procedure.
49 citations
TL;DR: In this paper, the impossibility of formulating a modal interpretation of the type proposed by Bub that exhibits serious Lorentz invariance at the fundamental level is proved. But this is not the case for modal interpretations of the types proposed by the authors of this paper.
Abstract: A proof is given, at a greater level of generality than previous “no-go” theorems, of the impossibility of formulating a modal interpretation that exhibits “serious” Lorentz invariance at the fundamental level. Particular attention is given to modal interpretations of the type proposed by Bub.
TL;DR: In this article, the classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric or magnetic dipoles or a solenoid is placed between the electron beams forming the interference pattern.
Abstract: Classical electromagnetic forces can account for the experimentally observed phase shifts seen in an electron interference pattern when a line of electric dipoles or a line of magnetic dipoles (a solenoid) is placed between the electron beams forming the interference pattern.
TL;DR: In this article, the spectrum of horizon area of quantized black holes is quantized by imposing suitable boundary conditions on the reduced phase space of the theory to incorporate the thermodynamic properties of these black holes and then performing a simplifying canonical transformation.
Abstract: Bekenstein proposed that the spectrum of horizon area of quantized black holes must be discrete and uniformly spaced. We examine this proposal in the context of spherically symmetric charged black holes in a general class of gravity theories. By imposing suitable boundary conditions on the reduced phase space of the theory to incorporate the thermodynamic properties of these black holes and then performing a simplifying canonical transformation, we are able to quantize the system exactly. The resulting spectra of horizon area, as well as that of charge are indeed discrete. Within this quantization scheme, near-extremal black holes (of any mass) turn out to be highly quantum objects, whereas extremal black holes do not appear in the spectrum, a result that is consistent with the postulated third law of black hole thermodynamics.
TL;DR: In this paper, a framework for developing a coherent theory of mathematics and physics together is described, and the main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength.
Abstract: As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Godel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language must have representations as states of physical systems already in the domain of a coherent theory.
TL;DR: In this article, an objective (noncontextual and local) interpretation of quantum mechanics can be constructed, which contradicts some well-established beliefs following from the standard interpretation of the theory and from known no-go theorems.
Abstract: An SR model is presented that shows how an objective (noncontextual and local) interpretation of quantum mechanics can be constructed, which contradicts some well-established beliefs following from the standard interpretation of the theory and from known no-go theorems. The SR model is not a hidden variables theory in the standard sense, but it can be considered a hidden parameters theory which satisfies constraints that are weaker than those usually imposed on standard hidden variables theories. The SR model is also extended in a natural way that shows how a broader theory embodying quantum mechanics can be envisaged which is realistic in a semantic sense, hence compatible with various “realistic” perspectives.
TL;DR: In this paper, an experimental realization of the Popper's experiment is presented, where a narrow slit is placed in the path of photon 1 which provides precise knowledge about its position along the y-axis and because of the quantum entanglement this in turn provides precise information of the position y of its twin, photon 2.
Abstract: An entangled pair of photon 1 and 2 are emitted in opposite directions along the positive and negative x-axis. A narrow slit is placed in the path of photon 1 which provides precise knowledge about its position along the y-axis and because of the quantum entanglement this in turn provides precise knowledge of the position y of its twin, photon 2. Does photon 2 experience a greater uncertainty in its momentum, i.e., a greater Δp y , due to the precise knowledge of its position y? This is the historical thought experiment of Sir Karl Popper which was aimed to undermine the Copenhagen interpretation in favor of a realistic viewpoint of quantum mechanics. Thispaper reports an experimental realization of the Popper’s experiment. One may not agree with Popper’s position on quantum mechanics; however, it calls for a correct understanding and interpretation of the experimental results.
TL;DR: The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems, and provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information while obeying some simple rules.
Abstract: We formulate an elementary statistical game which captures the essence of some fundamental quantum experiments such as photon polarization and spin measurement. We explore and compare the significance of the principle of maximum Shannon entropy and the principle of minimum Fisher information in solving such a game. The solution based on the principle of minimum Fisher information coincides with the solution based on an invariance principle, and provides an informational explanation of Malus' law for photon polarization. There is no solution based on the principle of maximum Shannon entropy. The result demonstrates the merits of Fisher information, and the demerits of Shannon entropy, in treating some fundamental quantum problems. It also provides a quantitative example in support of a general philosophy: Nature intends to hide Fisher information, while obeying some simple rules.
TL;DR: In this paper, the authors used Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics.
Abstract: We use Padoa's principle of independence of primitive symbols in axiomatic systems in order to show that time is dispensable in continuum thermodynamics, according to the axiomatic formulation of Gurtin and Williams We also show how to define time by means of the remaining primitive concepts of Gurtin and Williams system Finally, we introduce thermodynamics without time as a primitive concept
TL;DR: In this article, it was shown that the existence of stable, spatially extended material objects, if not the very existence of the physical world, may require the validity of both the standard model of elementary particle physics and general relativity.
Abstract: Does a world that contains chemistry entail the validity of both the standard model of elementary particle physics and general relativity, at least as effective theories? This article shows that the answer may very well be affirmative. It further suggests that the very existence of stable, spatially extended material objects, if not the very existence of the physical world, may require the validity of these theories.
TL;DR: In this article, it was shown that the existence of real superluminal propagation and communication of particles and fields, free of causality problems, implies that real physical faster-than-light propagation into gravitation, electrodynamics and quantum theory is possible.
Abstract: General relativity has a geometric and a field interpretation. If angular momentum conservation is invoked in the geometric interpretation to explain experiments, the causality principle is violated. The field interpretation avoids this problem by allowing faster-than-light propagation of gravity in forward time. All existing experiments are in agreement with that interpretation. This implies the existence of real superluminal propagation and communication of particles and fields, free of causality problems. The introduction of real physical faster-than-light propagation into gravitation, electrodynamics and quantum theory has important consequences for physics.
TL;DR: In this article, the Bloch vector is treated as a hyperbolic vector, called a gyrovector, and the set of all these density matrices is brought under the umbrella of gyro vector spaces.
Abstract: Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects that form the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented.
TL;DR: In this article, an explicit transformation is given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest.
Abstract: Recently it has been shown that transformations of Heisenberg-picture operators are the causal mechanism which allows Bell-theorem-violating correlations at a distance to coexist with locality in the Everett interpretation of quantum mechanics. A calculation to first order in perturbation theory of the generation of EPRB entanglement in nonrelativistic fermionic field theory in the Heisenberg picture illustrates that the same mechanism leads to correlations without nonlocality in quantum field theory as well. An explicit transformation is given to a representation in which initial-condition information is transferred from the state vector to the field operators, making the locality of the theory manifest.
TL;DR: In this paper, the authors argue that purely local experiments can distinguish a stationary charged particle in a static gravitational field from an accelerated particle in (gravity-free) Minkowski space.
Abstract: We argue that purely local experiments can distinguish a stationary charged particle in a static gravitational field from an accelerated particle in (gravity-free) Minkowski space. Some common arguments to the contrary are analyzed and found to rest on a misidentification of “energy.”
TL;DR: In this paper, the Cartan equations defining simple spinors are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two.
Abstract: The Cartan equations defining simple spinors (renamed “pure” by C. Chevalley) are interpreted as equations of motion in compact momentum spaces, in a constructive approach in which at each step the dimensions of spinor space are doubled while those of momentum space increased by two. The construction is possible only in the frame of the geometry of simple or pure spinors, which imposes contraint equations on spinors with more than four components, and then momentum spaces result compact, isomorphic to invariant-mass-spheres imbedded in each other, since the signatures result steadily Lorentzian; starting from dimension four (Minkowski) up to dimension ten with Clifford algebra ℂl(1, 9), where the construction naturally ends. The equations of motion met in the construction are most of those traditionally postulated ad hoc: from Weyl equations for neutrinos (and Maxwell's) to Majorana ones, to those for the electroweak model and for the nucleons interacting with the pseudoscalar pion, up to those for the 3 baryon-lepton families, steadily progressing from the description of lower energy phenomena to that of higher ones. The 3 division algebras: complex numbers, quaternions and octonions appear to be strictly correlated with Clifford algebras and then with this spinor-geometrical approach, from which they appear to gradually emerge in the construction, where they play a basic role for the physical interpretation: at the third step complex numbers generate U(1), possible origin of the electric charge and of the existence of charged—neutral fermion pairs, explaining also easily the opposite charges of proton-electron. Another U(1) appears to generate the strong charge at the fourth step. Quaternions generate the signature of space-time at the first step, the SU(2) internal symmetry of isospin and, in the gauge term, the SU(2)L one, of the electroweak model at the third step; they are also at the origin of 3 families; in number equal to that of quaternion imaginary units. At the fifth and last step octonions generate the SU(3) internal symmetry of flavour, with SU(2) isospin subgroup and, in the gauge term, the one of color, correlated with SU(2)L of the electroweak model. These 3 division algebras seem then to be at the origin of charges, families and of the groups of the Standard model. In this approach there seems to be no need of higher dimensional (>4) space-time, here generated by the four Poincare translations, and dimensional reduction from ℂl(1,9) to ℂl(1,3) is equivalent to decoupling of the equations of motion. This spinor-geometrical approach is compatible with that based on strings, since these may be expressed bilinearly (as integrals) in terms of Majorana–Weyl simple or pure spinors which are admitted by ℂl(1, 9) = R(32).
TL;DR: In this paper, it was shown that no interpretation of the quantum theory can avoid a measurement problem involving the observer, assuming that no observable physical phenomena exist beyond those predicted by the theory.
Abstract: A goal of most interpretations of quantum mechanics is to avoid the apparent intrusion of the observer into the measurement process. Such intrusion is usually seen to arise because observation somehow selects a single actuality from among the many possibilities represented by the wavefunction. The issue is typically treated in terms of the mathematical formulation of the quantum theory. We attempt to address a different manifestation of the quantum measurement problem in a theory-neutral manner. With a version of the two-slit experiment, we demonstrate that an enigma arises directly from the results of experiments. Assuming that no observable physical phenomena exist beyond those predicted by the theory, we argue that no interpretation of the quantum theory can avoid a measurement problem involving the observer.
TL;DR: In this paper, a relativistic analysis connecting hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov-Bohm phase shift is suggested.
Abstract: A fundamentally new understanding of the classical electromagnetic interaction of a point charge and a magnetic dipole moment through order v 2 /c 2 is suggested. This relativistic analysis connects together hidden momentum in magnets, Solem's strange polarization of the classical hydrogen atom, and the Aharonov–Bohm phase shift. First we review the predictions following from the traditional particle-on-a-frictionless-rigid-ring model for a magnetic moment. This model, which is not relativistic to order v 2 /c 2 , does reveal a connection between the electric field of the point charge and hidden momentum in the magnetic moment; however, the electric field back at the point charge due to the Faraday-induced changing magnetic moment is of order 1/c 4 and hence is negligible in a 1/c 2 analysis. Next we use a relativistic magnetic moment model consisting of many superimposed classical hydrogen atoms (and anti-atoms) interacting through the Darwin Lagrangian with an external charge but not with each other. The analysis of Solem regarding the strange polarization of the classical hydrogen atom is seen to give a fundamentally different mechanism for the electric field of the passing charge to change the magnetic moment. The changing magnetic moment leads to an electric force back at the point charge which (i) is of order 1/c 2 , (ii) depends upon the magnetic dipole moment, changing sign with the dipole moment, (iii) is odd in the charge q of the passing charge, and (iv) reverses sign for charges passing on opposite sides of the magnetic moment. Using the insight gained from this relativistic model and the analogy of a point charge outside a conductor, we suggest that a realistic multi-particle magnetic moment involves a changing magnetic moment which keeps the electromagnetic field momentum constant. This means also that the magnetic moment does not allow a significant shift in its internal center of energy. This criterion also implies that the Lorentz forces on the charged particle and on the point charge are equal and opposite and that the center of energy of each moves according to Newton's second law F=Ma where F is exactly the Lorentz force. Finally, we note that the results and suggestion given here are precisely what are needed to explain both the Aharonov–Bohm phase shift and the Aharonov–Casher phase shift as arising from classical electromagnetic forces. Such an explanation reinstates the traditional semiclassical connection between classical and quantum phenomena for magnetic moment systems.
TL;DR: In this paper, ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime, at least in the non-quantum case, and all the possible models of spacetime are obtained.
Abstract: Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime, at least in the non-quantum case. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.
TL;DR: In this paper, a solid-state Maxwell demon is proposed that utilizes the electric field energy of an open-gap p-n junction for laboratory testable, solid state Maxwell demon.
Abstract: A laboratory-testable, solid-state Maxwell demon is proposed that utilizes the electric field energy of an open-gap p-n junction. Numerical results from a commercial semiconductor device simulator (Silvaco International–Atlas) verify primary results from a 1-D analytic model. Present day fabrication techniques appear adequate for laboratory tests of principle.
TL;DR: Several errors in Stapp's interpretation of quantum mechanics and its application to mental causation are pointed out in this article, and an interpretation of (standard) quantum mechanics that avoids these errors is presented.
Abstract: Several errors in Stapp's interpretation of quantum mechanics and its application to mental causation (Henry P. Stapp, “Quantum theory and the role of mind in nature,” Foundations of Physics
31, 1465–1499 (2001)) are pointed out. An interpretation of (standard) quantum mechanics that avoids these errors is presented.
TL;DR: In this paper, an alternative way of making sense of a world of uncaused clicks is presented, which does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.
Abstract: In a recent article, O. Ulfbeck and A. Bohr [Found. Phys.
31, 757 (2001)] have stressed the genuine fortuitousness of detector clicks, which has also been pointed out, in different terms, by the present author [Am. J. Phys.
68, 728 (2000)]. In spite of this basic agreement, the present article raises objections to the presuppositions and conclusions of Ulfbeck and Bohr, in particular their rejection of the terminology of indefinite variables, their identification of reality with “the world of experience,” their identification of experience with what takes place “on the spacetime scene,” and the claim that their interpretation of quantum mechanics is “entirely liberated” from classical notions. An alternative way of making sense of a world of uncaused clicks is presented. This does not invoke experience but deals with a free-standing reality, is not fettered by classical conceptions of space and time but introduces adequate ways of thinking about the spatiotemporal aspects of the quantum world, and does not reject indefinite variables but clarifies the implications of their existence.