Showing papers in "Foundations of Physics Letters in 2001"
TL;DR: In this paper, the authors consider entanglement for quantum states defined in vector spaces over the real numbers and give a contrasting formula for the formation of an arbitrary state of two "rebits", a rebit being a system whose Hilbert space is a 2-dimensional real vector space.
Abstract: We consider entanglement for quantum states defined in vector spaces over the real numbers. Such real entanglement is different from entanglement in standard quantum mechanics over the complex numbers. The differences provide insight into the nature of entanglement in standard quantum theory. Wootters [Phys. Rev. Lett.
80, 2245 (1998)] has given an explicit formula for the entanglement of formation of two qubits in terms of what he calls the concurrence of the joint density operator. We give a contrasting formula for the entanglement of formation of an arbitrary state of two “rebits,” a rebit being a system whose Hilbert space is a 2-dimensional real vector space.
79 citations
TL;DR: In this paper, a simple but general treatment of neutrino oscillations in the framework of quantum mechanics, using plane waves and intuitive wave packet principles when necessary, is presented.
Abstract: We present a simple but general treatment of neutrino oscillations in the framework of quantum mechanics, using plane waves and intuitive wave packet principles when necessary. We attempt to clarify some confusing statements that have recently appeared in the literature.
75 citations
TL;DR: In this article, it was shown that any interval pseudoeffect algebra maps homomorphically into an effect algebra whose states are in a one-to-one correspondence to the states of the original algebra.
Abstract: We study congruences on pseudoeffect algebras, which were recently introduced as a non-commutative generalization of effect algebras. We introduce ideals for these algebras and give a sufficient condition for an ideal to determine a congruence. Furthermore, states on pseudoeffect algebras are considered. It is shown that any interval pseudoeffect algebra maps homomorphically into an effect algebra whose states are in a one-to-one correspondence to the states of the original algebra.
49 citations
TL;DR: In this article, a Radon-like transformation was developed, in which P quasiprobability distribution for spin-1/2 states is written in terms of the tomographic probability distribution w.r.t.
Abstract: We develop a Radon-like transformation, in which P quasiprobability distribution for spin-1/2 states is written in terms of the tomographic probability distribution w.
49 citations
TL;DR: In the modern approach initiated by Gursey, these difficulties are solved by recognizing that most generalizations lead to theories describing superpositions of particles of different intrinsic spin and isospin, so that the correct interpretation emerges from the requirement of full Poincare covariance, including space and time reversal.
Abstract: Many difficulties of interpretation met by contemporary researchers attempting to recast or generalize Dirac's, Proca's, or Maxwell's theories using biquaternions or Clifford numbers have been encountered long ago by a number of physicists including Lanczos, Proca, and Einstien. In the modern approach initiated by Gursey, these difficulties are solved by recognizing that most generalizations lead to theories describing superpositions of particles of different intrinsic spin and isospin, so that the correct interpretation emerges from the requirement of full Poincare covariance, including space and time reversal, as well as reversion and gauge invariance. For instance, the doubling of the number of solutions implied by the simplest generalization of Dirac's equation (i.e., Lanczos's equation) can be interpreted as isospin. In this approach, biquaternions and Clifford numbers become powerful opportunities to formulate the Standard Model of elementary particles, as well as many of its possible generalizations, in very elegant and compact ways.
41 citations
TL;DR: An essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of ‘causal duality’ in operational quantum logic.
Abstract: A general principle: of 'causal duality' for physical systems, lying at the base: of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of quantaloids and quantaloidal morphisms appear naturally within this setting; as in the case of causal duality, they originate from primitive physical reasonings on the lattices of properties of physical systems. Furthermore, an essentially dynamical operational foundation for studying physical systems is outlined; complementary as it is to the existing static operational foundation, it leads to the natural axiomatization of 'causal duality' in operational quantum logic.
40 citations
TL;DR: In this article, it is suggested that this problem may be resolved by considering quantum field theory rather than the quantum mechanics of particles, and the conceptual problem of non-locality is replaced with a conceptual problem, as correlated systems and observers undergo measurement-type interactions with newly-encountered objects and instruments.
Abstract: Bell's theorem depends crucially on counterfactual reasoning, and is mistakenly interpreted as ruling out a local explanation for the correlations which can be observed between the results of measurements performed on spatially-separated quantum systems. But in fact the Everett interpretation of quantum mechanics, in the Heisenberg picture, provides an alternative local explanation for such correlations. Measurement-type interactions lead, not to many worlds but, rather, to many local copies of experimental systems and the observers who measure their properties. Transformations of the Heisenberg-picture operators corresponding to the properties of these systems and observers, induced by measurement interactions, “label” each copy and provide the mechanism which, e. g., ensures that each copy of one of the observers in an EPRB or GHZM experiment will only interact with the “correct” copy of the other observer(s). The conceptual problem of nonlocality is thus replaced with a conceptual problem of proliferating labels, as correlated systems and observers undergo measurement-type interactions with newly-encountered objects and instruments; it is suggested that this problem may be resolved by considering quantum field theory rather than the quantum mechanics of particles.
38 citations
TL;DR: In this paper, it was shown that in the Rovelli relational interpretation of quantum mechanics, in which the notion of absolute or observer independent state is rejected, the conclusion of the ordinary EPR argument turns out to be frame-dependent, provided the conditions of the original argument are suitably adapted to the new interpretation.
Abstract: It is shown that in the Rovelli relational interpretation of quantum mechanics, in which the notion of absolute or observer independent state is rejected, the conclusion of the ordinary EPR argument turns out to be frame-dependent, provided the conditions of the original argument are suitably adapted to the new interpretation. The consequences of this result for the ‘peaceful coexistence’ of quantum mechanics and special relativity are briefly discussed.
34 citations
TL;DR: In this paper, a generalized Bell inequality for different times and for different quasi-spin states is developed, where the quantum quantum probabilities are modified by the decoherence approach, which enables the initial state to factorize spontaneously.
Abstract: First, a generalized Bell inequality for different times and for different quasi-spin states is developed. We focus on special quasi-spin eigenstates and times. The inequality based on a local realistic theory is violated by the CP-violating parameter [1] if the quantum theory is used to recalculate the probabilities. Next, the quantum mechanical probabilities are modified by the decoherence approach, which enables the initial state to factorize spontaneously. In this way we get a lower limit for the decoherence parameter ζ, which measures the degree of decoherence. This result is compared with the experimental value [2, 3] of the decoherence parameter ζ deduced from the data of the CPLEAR experiment [4].
25 citations
TL;DR: In this paper, an apparent violation of the uncertainty principle obtained by Kim and Shih in their realization of Popper's experiment is explained through analogy with a simple optical system, and an application of the uncertain principle to conditional measurements is investigated and found to be valid for measurements on separated sub-systems.
Abstract: Application of the uncertainty principle to conditional measurements is investigated and found to be valid for measurements on separated sub-systems. In light of this, an apparent violation of the uncertainty principle obtained by Kim and Shih in their realization of Popper's experiment [1] is explained through analogy with a simple optical system.
24 citations
TL;DR: In this article, the authors formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors.
Abstract: We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.
TL;DR: In this article, an alternative form of the CHSH inequality and extensive use of the experimentally testable property of physical locality were determined the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy's non-locality theorem can be cast.
Abstract: By using an alternative, equivalent form of the CHSH inequality and making extensive use of the experimentally testable property of physical locality we determine the 64 different Bell-type inequalities (each one involving four joint probabilities) into which Hardy's nonlocality theorem can be cast. This allows one to identify all the two-qubit correlations which can exhibit Hardy-type nonlocality.
TL;DR: In this paper, an elastic interpretation of the electrodynamic forces is presented, which is based on the theory of elasticity, and it is shown that the elastic interpretation is compatible with Einstein's special relativity.
Abstract: In his famous treatise, Maxwell presumed explicitly, without developing it, an elastic interpretation of his electrodynamics; the relevant quotation is given in the introduction. It is in that spirit that we have developed the theory of the elastic interpretation here presented. We show that the Maxwell equations and the electrodynamic forces can formally be obtained from the theory of elasticity. An electromagnetic field can be considered as a deformation of a certain elastic medium Œ. This deformation is created by volumetric densities of “deforming couples” and of “irrotational deforming forces” that act on Œ. A distribution of electric charges is proportional to the divergence of the deforming couples. The electrodynamic forces are due to the interactions between such deformations. Even though the consistency of the elastic interpretation of electrodynamics is demonstrated by the fact that it gives back Maxwell's equations, and the electrodynamic forces, we show that the elastic interpretation is compatible with Einstein's special relativity. Then we demonstrate that an adequate density of irrotational deforming forces can produce the same effects on light propagation as those of a Schwarzschild metric background. This fact suggests a possible extension to take into account many of the effects attributed to the geometrical structure of the general relativity. Thus, we have given an elastic interpretation to the action at distance, and contributed to eliminate the inconsistency mentioned by Einstein, implying in his view, an incompleteness of the Maxwell theory. In future works, we hope to give an elastic interpretation for additional aspects of the particle waves and of general relativity and for the electroweak and strong fields.
TL;DR: In this paper, a unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space.
Abstract: A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing value of the conjugate momentum in the real wave function case are surmounted. In one dimension, a new form of the general solution of the quantum Hamilton-Jacobi equation leading straightforwardly to the general form of the Schrodinger wave function is proposed. For unbound states, it is shown that the invariance of the reduced action under a dilatation plus a rotation of the wave function in the complex space implies that microstates do not appear. For bound states, it is shown that some freedom subsists and gives rise to the manifestation of microstates not detected by the Schrodinger wave function.
Journal Article•
TL;DR: In this article, the fundamental operational principle of the MEG is explained using a version of higher symmetry electrodynamics known as O(3) electrodynamic, which is based on the empirical existence of two circular polarization states of electromagnetic radiation.
Abstract: Recently, Bearden el al. developed a device which is known as a motionless electromagnetic generator (MEG) and which produces a coefficient of performance (COP) far in excess of unity. The device has been independently replicated by Naudin. In this communication, the fundamental operational principle of the MEG is explained using a version of higher symmetry electrodynamics known as O(3) electrodynamics, which is based on the empirical existence of two circular polarization states of electromagnetic radiation, and which has been developed extensively in the literature. The theoretical explanation of the MEG with O(3) electrodynamics is straightforward: Magnetic energy is taken directly ex vacua and used to replenish the permanent magnets of the MEG device, which therefore produces a source of energy that, in theory, can be replenished indefinitely from the vacuum. Such a result is incomprehensible in U(1) Maxwell-Heaviside electrodynamics.
TL;DR: In this paper, it was shown that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension.
Abstract: We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges, and calculate Planck's constant from quantities defined in the underlying classical gauge theory.
TL;DR: In this paper, momentum transfer effects are taken into account in the analysis of Welcher-Weg measurements, and it is shown how a measurement in one location (the WW apparatus) influences the wave function at another location (beam-splitter or 2-slit wall) and fixes momentum at that second place, exactly as that of the EPR effect.
Abstract: In the present analysis of Welcher–Weg (WW) measurements, momentum transfer effects are taken into account. Although the WW apparatus that “determines” which-way might not include any momentum transfer, there is a momentum transfer to the macroscopic entangled parts of the system (beam-splitter and mirrors in Mach–Zehnder interferometer or macroscopic double-slit wall in 2-slit experiments). We show how a measurement in one location (the WW apparatus) influences the wavefunction at another location (the beam-splitter or 2-slit wall) and fixes momentum at that second place, exactly as that of the EPR effect.
TL;DR: In this paper, a new electromagnetic test of breakdown of local Lorentz invariance is proposed based on the detection of a non-zero force between a circular steady current and a charge, both at rest in the Earth frame.
Abstract: We propose a new electromagnetic test of breakdown of local Lorentz invariance. It is based essentially on the detection of a non-zero force between a circular steady current and a charge, both at rest in the Earth frame. A preliminary experimental run gave a positive evidence for such an effect, which appears strongly dependent on the orientation of the circuit. Possible theoretical interpretations are briefly discussed.
TL;DR: In this article, the authors use Padoa's principle of independence of primitive symbols in axiomatic systems in order to discuss the mathematical role of time and space-time in some classical physical theories.
Abstract: We use Padoa’s principle of independence of primitive symbols in axiomatic systems in order to discuss the mathematical role of time and space-time in some classical physical theories. We show that time is eliminable in Newtonian mechanics and that space-time is also dispensable in Hamiltonian mechanics, Maxwell’s electromagnetic theory, the Dirac electron, classical gauge fields, and general relativity.
TL;DR: In this article, the authors review Misra's representation of quantum states by probability measures on the projective Hilbert space and investigate some properties of that correspondence in detail, and the fundamental probabilistic aspect of these results is discussed.
Abstract: We review Misra's representation of quantum states by probability measures on the projective Hilbert space and investigate some properties of that correspondence in detail. Furthermore, the fundamental probabilistic aspect of these results is discussed.
TL;DR: In this article, the physical semantics of quantum event structures are analyzed from the perspective of the categorical scheme of Part I and an interpretation of the quantum event structure is proposed. But this interpretation is restricted to quantum events.
Abstract: In this paper we analyze the physical semantics and propose an interpretation of quantum event structures from the perspective offered by the categorical scheme of Part I.
TL;DR: In this paper, a mathematical scheme for the analysis of quantum event structures is proposed based on category theoretical methods and it is shown that there exists an adjunctive correspondence between Boolean presheaves of event algebras and quantum event algesbras.
Abstract: In this paper a mathematical scheme for the analysis of quantum event structures is being proposed based on category theoretical methods. It is shown that there exists an adjunctive correspondence between Boolean presheaves of event algebras and quantum event algebras. The adjunction permits a characterization of quantum event structures as Boolean manifolds of event structures.
TL;DR: In this paper, the authors combine recent results of Clifton and Halvorson [1] with structural results of the author [2, 3] concerning the local observables in thermofield theory.
Abstract: We combine recent results of Clifton and Halvorson [1] with structural results of the author [2–5] concerning the local observables in thermofield theory. A number of interesting consequences are discussed.
TL;DR: In this article, the authors construct a Bell's inequality for a pair of synchronously coupled variable-order Generalized Rossler Systems, with arbitrarily binarized final states, motivated by a parallel between quantum cryptography and chaos synchronization cryptography.
Abstract: Motivated by a parallel between quantum cryptography and chaos synchronization cryptography, we construct a Bell's inequality for a pair of synchronously coupled variable-order Generalized Rossler Systems, with arbitrarily binarized final states. In the infinite-order limit, although dynamical parameters cannot be extracted from the coupling signal in finite time, the inequality is violated, as with entangled quantum states. The violations are weaker than in quantum theory, vanishing as the differences between corresponding parameters of the coupled systems become small. The fact that Bell's inequality can be violated for a pair of classical systems that are not discernibly connected supports the possibility of a realist interpretation of quantum mechanics.
TL;DR: In this article, the authors present a review of various approaches in the literature towards the derivation of so-called thermodynamic uncertainty relations in statistical thermodynamics, and show that some of these approaches are sound, whereas others were found to be incoherent and could not withstand the scrutiny of logical analysis.
Abstract: In a previous paper (Found. Phys.29, 655 (1999)), we have presented a review of various approaches in the literature towards the derivation of so-called thermodynamic uncertainty relations in statistical thermodynamics. This review has been critical. We have argued that some of these approaches are sound, i.e., they reach a valid conclusion, albeit under restricted conditions, whereas others were found to be incoherent and could not withstand the scrutiny of logical analysis. In the latter category we have included work of Lavenda on this topic. However, in a comment (Found. Phys. Lett.13, 487 (2000)), Lavenda claims to have uncovered “fundamental errors” in our paper. In this reply we show that these claims are mistaken.
TL;DR: The Ithaca interpretation of quantum mechanics, proposed in 1996 by David Mermin, seeks to reduce the interpretive puzzles of Quantum mechanics to the single puzzle of interpreting objective quantum probabilities as mentioned in this paper.
Abstract: The Ithaca interpretation of quantum mechanics, proposed in 1996 by David Mermin, seeks to reduce the interpretive puzzles of quantum mechanics to the single puzzle of interpreting objective quantum probabilities. Some suggestions are made as to how the numerical values of quantum probabilities could be ontologically based in a world containing all the possible outcomes of all probabilistic processes. It is then shown that Hardy's paradox, discussed by Mermin, can be resolved when probabilities are interpreted in this way.
TL;DR: In this article, it was shown that the principles of general relativity can be used to explain the principle of the motionless electromagnetic generator (MEG), which takes electromagnetic energy from Riemannian curved space-time and in consequence outputs about twenty times more energy than inputted.
Abstract: It is shown that the principles of general relativity as developed by Sachs [1] can be used to explain the principles of the motionless electromagnetic generator (MEG), which takes electromagnetic energy from Riemannian curved space-time and in consequence outputs about twenty times more energy than inputted [2]. Therefore, it is shown in the most general manner that electromagnetic energy can be extracted from vacuum and used to power working devices such as the MEG, devices which are reproducible and repeatable [2].
TL;DR: It is claimed that ‘pain’ consciousness might be correlated in a certain way with the relative binding of opiates to receptors in a subject's brain.
Abstract: There is a tradition in science that regards consciousness as merely epiphenornenal. Accordingly, physical systems can create and influence consciousness, but consciousness can have no influence on physical systems. Indeed, the current understanding of quantum mechanics provides no way for consciousness to alter the wave function of a quantum mechanical state. Furthermore, there is nothing in molecular biology that would suggest that the human body is anything more that an automaton that operates on the basis of purely physical and chemical interactive forces. However, I believe that the epiphenomenal view is fundamentally flawed, and I suggest the following experiments as a way of demonstrating the existence of an influence of consciousness on material systems. The first uses Positron Emission Tomography (PET) with a human subject, and the second used autoradiography with rats. Detailed arguments for my position can be found in three papers that have been published in recent years. A brief summery of the arguments is initially given below, where it is claimed that ‘pain’ consciousness might be correlated in a certain way with the relative binding of opiates to receptors in a subject's brain.
TL;DR: In this article, the authors formulated the Lorentz covariant statistical physics and thermodynamics within the preferred frame approach, and derived the transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lipschitz invariant measure on the phase space.
Abstract: The Lorentz covariant statistical physics and thermodynamics is formulated within the preferred frame approach. The transformation laws for geometrical and mechanical quantities such as volume and pressure as well as the Lorentz-invariant measure on the phase space are found using Lorentz transformations in absolute synchronization. Next, the probability density and partition function are investigated using the preferred frame approach, and the transformation laws for internal energy, entropy, temperature and other thermodynamical potentials are established. The Lorentz covariance of basic thermodynamical relations, including Clapeyron's equation and Maxwell's relations is shown. Finally, the relation of presented approach to the previous approaches to relativistic thermodynamics is briefly discussed.