Logical reformulation of quantum mechanics. II. Interferences and the Einstein-Podolsky-Rosen experiment

The consistent quantum interpretations of logic that were introduced in a previous paper are applied to four experiments: (1) ordinary interferences, (2) the Badurek-Rauch-Tuppinger neutron interferometry experiment, (3) the Einstein-Podolsky-Rosen experiment, and (4) the detection far away of the origin of a nonrelativistic particle initially near the origin. In the first two cases, the proposition calculus excludes the possibility of observing interferences and of asserting together through which path the particles went. It is used to provide a somewhat complete discussion of the Badurek-Rauch-Tuppinger experiment. The possibility of using logical implication allows a rather complete discussion of the EPR experiment, including the question of causality, although the lack of a relativistic version of the theory does not allow a complete discussion of causality. The last experiment leads to the following result: Detecting the position of a particle at timet sometimes allows one to determine with a finite uncertainty what its momentum was just before the position measurement, even when it is infinitely precise.     

The energy operator for infinite statistics

We construct the energy operator for particles obeying infinite statistics defined by aq-deformation of the Heisenberg algebra.The aim of this paper is to construct the energy operator for particles which obey the so-called infinite statistics defined by theq-deformation of the Heisenberg algebra. This topic was studied in the previous article [1], where a conjecture was formulated concerning the form of the energy operator. Our main result is a proof of this conjecture in a slightly modified form (cf. Remark 1).     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Massive Vector Particles Tunneling from the Neutral Rotating Anti-de Sitter Black Holes in Conformal Gravity

We investigate the massive vector particles' Hawking radiation from the neutral rotating Anti-de Sitter(AdS) black holes in conformal gravity by using the tunneling method.It is well known that the dynamics of massive vector particles are governed by the Proca field equation.Applying WKB approximation to the Proca equation,the tunneling probabilities and radiation spectrums of the emitted particles are derived.Hawking temperature of the neutral rotating AdS black holes in conformal gravity is recovered,which is consistent with the previous result in the literature.     

Mass shell technique for measuring masses of a pair of semi-invisibly decaying particles

Motivated by evidence for the existence of dark matter, many new physics models predict the pair production of new particles, followed by the decays into two invisible particles, leading to a momentum imbalance in the visible system. For the cases where all four components of the vector sum of the two "missing" momenta are measured from the momentum imbalance, we present analytic solutions of the final state system in terms of measurable momenta, with the mass shell constraints taken into account. We then introduce new variables which allow the masses involved in the new physics process, including that of the dark matter particles, to be extracted efficiently. These are compared with a selection of variables in the literature, and possible applications at lepton and hadron colliders are discussed.     

Pauli-Fierz Type Operators with Singular Electromagnetic Potentials on General Domains

We consider Dirichlet realizations of Pauli-Fierz type operators generating the dynamics of non-relativistic matter particles which are confined to an arbitrary open subset of the Euclidean position space and coupled to quantized radiation fields. We find sufficient conditions under which their domains and a natural class of operator cores are determined by the domains and operator cores of the corresponding Dirichlet-Schrödinger operators and the radiation field energy. Our results also extend previous ones dealing with the entire Euclidean space, since the involved electrostatic potentials might be unbounded at infinity with local singularities that can only be controlled in a quadratic form sense, and since locally square-integrable classical vector potentials are covered as well. We further discuss Neumann realizations of Pauli-Fierz type operators on Lipschitz domains.     

Relativistic dynamics for spin-zero and spin-half particles

The classical and quantum mechanics of a system of directly interacting relativistic particles is discussed. We first discuss the spin-zero case, where we basically follow Rohrlich in introducing a set of covariant centre of mass (CM) and relative variables. The relation of these to the classic formulation of Bakamjian and Thomas is also discussed. We also discuss the important case of relativistic potentials which may depend on total four-momentum squared. We then consider the quantum mechanical case of spin-half particles. The negative energy difficulty is solved by introducing a number of first class constraints which fix the spinor structure of physical solutions and ensure the existence of proper CM and relative variables. We derive the form of interactions consistent with Lorentz invariance, space inversion, time reversal and charge conjugation and with the above mentioned first class constraints and find that it is analogous to that for the non-relativistic case. Finally the relationship of the present work with some previous work is briefly discussed.     

Supersymmetric Dirac particles in Riemann-Cartan space-time

A natural extension of the supersymmetric model of Di Vecchia and Ravndal yields a nontrivial coupling of classical spinning particles to torsion in a Riemann-Cartan geometry. The equations of motion implied by this model coincide with a consistent classical limit of the Heisenberg equations derived from the minimally coupled Dirac equation. Conversely, the latter equation is shown to arise from canonical quantization of the classical system. The Heisenberg equations are obtained exact in all powers of and thus complete the partial results of previous WKB calculations. We touch also on such matters of principle as the mathematical realization of anticommuting variables, the physical interpretation of supersymmetry transformations, and the effective variability of rest mass.     

Gyroscopic precession in non-circular orbits: a phase-locked tetrad approach

We deduce the explicit form of a phase-locked (PL) tetrad, adapted to a small spinning particle (a test gyroscope) following an arbitrary geodesic orbit in the Schwarzschild geometry of a gravitational source. We subsequently obtain the analytic expression of the gyroscopic precessional velocity Ω in a non-circular orbit, by means of the Fermi rotation coefficients related to the tetrad’s transport law. As an application, we compute the orbital shift in the spin vector, considering a spinning test particle (the gyroscope) in a slightly non-circular orbital motion in the weak gravitational field limit. We compare our results with those of other previous works.     

Tunneling Radiation of Massive Vector Bosons from Dilaton Black Holes

It is well known that Hawking radiation can be treated as a quantum tunneling process of particles from the event horizon of black hole. In this paper, we attempt to apply the massive vector bosons tunneling method to study the Hawking radiation from the non-rotating and rotating dilaton black holes. Starting with the Proca field equation that govern the dynamics of massive vector bosons, we derive the tunneling probabilities and radiation spectrums of the emitted vector bosons from the static spherical symmetric dilatonic black hole, the rotating Kaluza-Klein black hole, and the rotating Kerr-Sen black hole. Comparing the results with the blackbody spectrum, we satisfactorily reproduce the Hawking temperatures of these dilaton black holes, which are consistent with the previous results in the literature.     

Simulations of flexible membranes using a coarse-grained particle-based model with spontaneous curvature variables

We propose a simple mathematical model for lipid bilayer membranes of flexible fluid or solid state. The model consists of interacting coarse-grained particles with two extra variables. One indicates the spontaneous curvature at the particle position, and the other indicates the vector representing the direction normal to the membrane. When the spontaneous curvature variable is allowed to fluctuate significantly, the fluctuation causes a softening of the membrane and growth of large undulations as the amplitude of the fluctuation is increased. By changing the amplitude of the fluctuation in simulations, the bending rigidity of the membrane can be easily controlled. Because the proposed model includes anisotropic interactions between the particles, multilayered vesicles can be obtained through a reversible transition by weakening the strength of the anisotropic interactions.     

Covariant collapse of the state vector and realism

We point out that the assumption that a quantum-mechanical state vector collapses in a Lorentz-covariant way upon measurement is consistent, but that it implies that the state vector, and any reality which it represents, depends on position. We consider the specific example of collapse along the forward light cone of the measurement.     

Pair production and vacuum polarization of vector particles with electric dipole moments and anomalous magnetic moments

The matrix 8-component Dirac-like form of the P-odd equations for boson fields of spin 1 and 0 are obtained and the symmetry group of the equations is derived. We found exact solutions of the field equation for vector particles with arbitrary electric and magnetic moments in external constant and uniform electromagnetic fields. The differential probability of pair production of vector particles with electric dipole moments and anomalous magnetic moments by an external constant and uniform electromagnetic field has been found using exact solutions. We have calculated the imaginary and real parts of the electromagnetic field Lagrangian that takes into account the vacuum polarization of vector particles. Received: 14 April 2001 / Revised version: 13 July 2001 / Published online: 19 September 2001     

Fermion masses in a model for spontaneous parity breaking

In this paper we discuss a left–right symmetric model for elementary particles and their connection with the mass spectrum of elementary fermions. The model is based on the group . New mirror fermions and a minimal set of Higgs particles that break this symmetry down to are proposed. The model can accommodate a consistent pattern for charged and neutral fermion masses as well as neutrino oscillations. An important consequence of the model is that the connection between the left and right sectors can be implemented by the neutral vector gauge boson Z and a new heavy Z'. Received: 15 June 2000 / Revised version: 14 September 2000 / Published online: 5 February 2001     

Statistical Mechanics of Classical Systems with Distinguishable Particles

The properties of classical models of distinguishable particles are shown to be identical to those of a corresponding system of indistinguishable particles without the need for ad hoc corrections. An alternative to the usual definition of the entropy is proposed. The new definition in terms of the logarithm of the probability distribution of the thermodynamic variables is shown to be consistent with all desired properties of the entropy and the physical properties of thermodynamic systems. The factor of 1/N! in the entropy connected with Gibbs' Paradox is shown to arise naturally for both distinguishable and indistinguishable particles. These results have direct application to computer simulations of classical systems, which always use distinguishable particles. Such simulations should be compared directly to experiment (in the classical regime) without correcting them to account for indistinguishability.     

Self-gravitating darkon fluid with anisotropic scaling

The fluid model for the dark sector of the universe (darkon fluid), introduced previously in Phys. Rev. D 80, 083513, 2009, is reformulated as a modified model involving only variables from the physical phase space. The Lagrangian of the model does not possess a free particle limit and hence the particles it describes, darkons, exist only as a self-gravitating fluid. This darkon fluid presents a dynamical realization of the zero-mass Galilean algebra extended by anisotropic dilational symmetry with dynamical exponent z=\frac53z=\frac{5}{3}. The model possesses cosmologically relevant solutions which are identical to those in the previous paper. We derive also the equations for the cosmological perturbations at early times and determine their solutions. In addition, we discuss also some implications of adding higher spatial-derivative terms.     

Concept of Photorefractive Connection Module by Photorefractive Four-Wave Mixing with Extraordinary Writing Beams and an Ordinary Reading Beam

We propose a new optical network device photorefractive connection module (PRCM) which operates as optical switch, amplifier and signal distributor controlled by parallel optical signals. Simple optical control bus systems can be realized by cascade connection of PRCMs. PRCM branches off a desired channel from the spatial multiplexed optical bus line by appropriate setting of the control beam pattern. PRCM uses cross polarized four wave mixing (CPFWM) with extraordinary polarized writing beams and an ordinary polarized reading beam to achieve a high connection gain to the next PRCM stage. We analyze the phase matching angle of CPFWM in which the optical paths of two pump beams are slightly different. The phase conjugate reflectivity indicating a branching ratio of optical signal is derived and calculated in consideration of the phase mismatching Δk. The optimum pump ratio and the grating vector orientation for the largest phase conjugate reflectivity and signal amplification factor are discussed for optical design of PRCM. Since the measured signal beam power after passing through the BaTiO₃ crystal is three or four times higher than its incident power, PRCM has a sufficient connection gain for optical bus and interconnection systems.     

Testing local position invariance with four cesium-fountain primary frequency standards and four NIST hydrogen masers

We report the most sensitive tests to date of the assumption of local position invariance (LPI) underlying general relativity, based on a 7 yr comparison of cesium and hydrogen atomic clocks (frequency standards). The latest results place an upper limit that is over 20 times smaller than the previous most sensitive tests; this is consistent with the null shift predicted by LPI. The result is based on precise comparisons of frequencies of four hydrogen masers maintained by NIST, with four independent Cs fountain clocks--one at NIST and three in Europe--as the Sun's gravitational potential at Earth's surface varies due to Earth's orbital eccentricity.     

Relativistic quantum mechanics of spin-zero and spin-half particles

We consider the quantum mechanics of directly interacting relativistic particles of spin-zero and spin-half. We introduce a scalar product in the vector space of physical states which is finite, positive definite and relativistically invariant and keeps orthogonal eigenstates of total four momentum belonging to different eigenvalues. This allows us to show that the vector space of physical states is, in fact, a Hilbert space. The case of two particles is explicitly considered and the Cauchy problem of physical wave function illustrated. The problem of a spin-1/2 particle interacting with a spin-zero particle is considered and a new equation is proposed for two spin-1/2 particles interacting via the most general form of interaction possible. The restrictions due to Hermiticity, space inversion and time reversal invariance are also considered.