arXiv subjects

W. C. Schieve

Publications and source records attributed to W. C. Schieve.

13 recordsLinked to original sources

arXiv2008

Monte Carlo Generation of Bohmian Trajectories

We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=nδt (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\infty and δt -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.

quant-ph↗

arXiv2007

Slightly Bimetric Gravitation

The inclusion of a flat metric tensor in gravitation permits the formulation of a gravitational stress-energy tensor and the formal derivation of general relativity from a linear theory in flat spacetime. Building on the works of Kraichnan and Deser, we present such a derivation using universal coupling and gauge invariance. Next we slightly weaken the assumptions of universal coupling and gauge invariance, obtaining a larger ``slightly bimetric'' class of theories, in which the Euler-Lagrange equations depend only on a curved metric, matter fields, and the determinant of the flat metric. The theories are equivalent to generally covariant theories with an arbitrary cosmological constant and an arbitrarily coupled scalar field, which can serve as an inflaton or dark matter. The question of the consistency of the null cone structures of the two metrics is addressed. A difficulty for Logunov's massive gravitation on this front is noted.

gr-qc↗

arXiv2007

Universally Coupled Massive Gravity

We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.

gr-qc↗

arXiv2004

Nonsingularity of Flat Robertson-Walker Models in the Special Relativistic Approach to Einstein's Equations

Recently the neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity has been substantially resolved. Consistency requires that the flat metric's null cone be respected by the null cone of the effective curved metric. While consistency is not automatic, thoughtful use of the naive gauge freedom resolves the problem. After briefly recapitulating how consistent causality is achieved, we consider the flat Robertson-Walker Big Bang model. The Big Bang singularity in the spatially flat Robertson-Walker cosmological model is banished to past infinity in Minkowski spacetime. A modified notion of singularity is proposed to fit the special relativistic approach, so that the Big Bang becomes nonsingular.

gr-qc↗

arXiv2004

Null Cones and Einstein's Equations in Minkowski Spacetime

If Einstein's equations are to describe a field theory of gravity in Minkowski spacetime, then causality requires that the effective curved metric must respect the flat background metric's null cone. The kinematical problem is solved using a generalized eigenvector formalism based on the Segré classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Securing the correct relationship between the two null cones dynamically plausibly is achieved using the naive gauge freedom. New variables tied to the generalized eigenvector formalism reduce the configuration space to the causality-respecting part. In this smaller space, gauge transformations do not form a group, but only a groupoid. The flat metric removes the difficulty of defining equal-time commutation relations in quantum gravity and guarantees global hyperbolicity.

gr-qc↗

arXiv2002

Null Cones in Lorentz-Covariant General Relativity

The oft-neglected issue of the causal structure in the flat spacetime approach to Einstein's theory of gravity is considered. Consistency requires that the flat metric's null cone be respected, but this does not happen automatically. After reviewing the history of this problem, we introduce a generalized eigenvector formalism to give a kinematic description of the relation between the two null cones, based on the Segre' classification of symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a method to enforce special relativistic causality by using the naive gauge freedom to restrict the configuration space suitably. A set of new variables just covers this smaller configuration space and respects the flat metric's null cone automatically. In this smaller space, gauge transformations do not form a group, but only a groupoid. Respecting the flat metric's null cone ensures that the spacetime is globally hyperbolic, indicating that the Hawking black hole information loss paradox does not arise.

gr-qc↗

arXiv2001

Flat Spacetime Gravitation with a Preferred Foliation

Paralleling the formal derivation of general relativity as a flat spacetime theory, we introduce in addition a preferred temporal foliation. The physical interpretation of the formalism is considered in the context of 5-dimensional ``parametrized'' and 4-dimensional preferred frame contexts. In the former case, we suggest that our earlier proposal of unconcatenated parametrized physics requires that the dependence on $τ$ be rather slow. In the 4-dimensional case, we consider and tentatively reject several areas of physics that might require a preferred foliation, but find a need for one in the process (``flowing'') theory of time. We then suggest why such a foliation might reasonably be unobservable.

gr-qc↗

arXiv2001

Light Cone Consistency in Bimetric General Relativity

General relativity can be formally derived as a flat spacetime theory, but the consistency of the resulting curved metric's light cone with the flat metric's null cone has not been adequately considered. If the two are inconsistent, then gravity is not just another field in flat spacetime after all. Here we discuss recent progress in describing the conditions for consistency and prospects for satisfying those conditions.

gr-qc↗

arXiv1998

Perihelion Precession in the Special Relativistic Two-Body Problem

The classical two-body system with Lorentz-invariant Coulomb interaction V=-k/rho is solved in 3+1 dimensions using the manifestly covariant Hamiltonian mechanics of Stueckelberg. Particular solutions for the reduced motion are obtained which correspond to bound attractive, unbound attractive, and repulsive scattering motion. A lack of perihelion precession is found in the bound attractive orbit, and the semi-classical hydrogen spectrum subsequently contains no fine structure corrections. It is argued that this prediction is indicative of the correct classical special relativistic two-body theory for the limit of no magnetic interaction.

physics.class-ph↗

arXiv1996

Hadronic Resonance Spectrum May Help in Resolution of Meson Nonet Enigmas

The identification of problematic meson states as the members of the quark model $q\bar{q}$ nonets by using a hadronic resonance spectrum is discussed. The results favor the currently adopted $q\bar{q}$ assignments for the axial-vector, tensor, and 1 $^3F_4$ $J^{PC}=4^{++}$ meson nonets, and suggest a new $q\bar{q}$ assignment for the scalar meson nonet which favors the interpretation of the $f_0(980)$ and $f_0(1710)$ mesons as non-$q\bar{q}$ objects. We also suggest that the 2 $^3S_1$ $\frac{1}{2}(1^{-})$ state should be identified with the $K^\ast (1680)$ rather than $K^\ast (1410)$ meson.

hep-ph↗

arXiv1996

A New Relativistic High Temperature Bose-Einstein Condensation

We discuss the properties of an ideal relativistic gas of events possessing Bose-Einstein statistics. We find that the mass spectrum of such a system is bounded by $μ\leq m\leq 2M/μ_K,$ where $μ$ is the usual chemical potential, $M$ is an intrinsic dimensional scale parameter for the motion of an event in space-time, and $μ_K$ is an additional mass potential of the ensemble. For the system including both particles and antiparticles, with nonzero chemical potential $μ,$ the mass spectrum is shown to be bounded by $|μ|\leq m\leq 2M/μ_K,$ and a special type of high-temperature Bose-Einstein condensation can occur. We study this Bose-Einstein condensation, and show that it corresponds to a phase transition from the sector of continuous relativistic mass distributions to a sector in which the boson mass distribution becomes sharp at a definite mass $M/μ_K.$ This phenomenon provides a mechanism for the mass distribution of the particles to be sharp at some definite value.

hep-th↗

arXiv1995

On Relativistic Bose-Einstein Condensation

hep-th↗

arXiv1995

Towards a Realistic Equation of State of Strongly Interacting Matter

We consider a relativistic strongly interacting Bose gas. The interaction is manifested in the off-shellness of the equilibrium distribution. The equation of state that we obtain for such a gas has the properties of a realistic equation of state of strongly interacting matter, i.e., at low temperature it agrees with the one suggested by Shuryak for hadronic matter, while at high temperature it represents the equation of state of an ideal ultrarelativistic Stefan-Boltzmann gas, implying a phase transition to an effectively weakly interacting phase.

hep-th↗