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Brendan Z. Foster

Publications and source records attributed to Brendan Z. Foster.

13 recordsLinked to original sources
arXiv2016

Spin on a 4D Feynman Checkerboard

We discretize the Weyl equation for a massless, spin-1/2 particle on a time-diagonal, hypercubic spacetime lattice with null faces. The amplitude for a step of right-handed chirality is proportional to the spin projection operator in the step direction, while for left-handed it is the orthogonal projector. Iteration yields a path integral for the retarded propagator, with matrix path amplitude proportional to the product of projection operators. This assigns the amplitude $i^{\pm T}\, {3}^{-B/2}\,2^{-N}$ to a path with $N$ steps, $B$ bends, and $T$ right-handed minus left-handed bends, where the sign corresponds to the chirality. Fermion doubling does not occur in this discrete scheme. A Dirac mass $m$ introduces the amplitude $iεm$ to flip chirality in any given time step $ε$, and a Majorana mass similarly introduces a charge conjugation amplitude.

quant-ph↗
arXiv2011

Phenomenology of Gravitational Aether as a solution to the Old Cosmological Constant Problem

One of the deepest and most long-standing mysteries in physics has been the huge discrepancy between the observed vacuum density and our expectations from theories of high energy physics, which has been dubbed the Old Cosmological Constant problem. One proposal to address this puzzle at the semi-classical level is to decouple quantum vacuum from space-time geometry via a modification of gravity that includes an incompressible fluid, known as Gravitational Aether. In this paper, we discuss classical predictions of this theory along with its compatibility with cosmological and experimental tests of gravity. We argue that deviations from General Relativity (GR) in this theory are sourced by pressure or vorticity. In particular, the theory predicts that the gravitational constant for radiation is 33% larger than that of non-relativistic matter, which is preferred by (most) cosmic microwave background (CMB), Lyman-Alpha forest, and Lithium-7 primordial abundance observations, while being consistent with other cosmological tests at ~2-sigma level. It is further shown that all Parametrized Post-Newtonian (PPN) parameters have the standard GR values aside from the anomalous coupling to pressure, which has not been directly measured. A more subtle prediction of this model (assuming irrotational aether) is that the (intrinsic) gravitomagnetic effect is 33% larger than GR prediction. This is consistent with current limits from LAGEOS and Gravity Probe B at ~2-sigma level.

astro-ph.CO↗
arXiv2008

Radiation Damping in Einstein-Aether Theory

This work concerns the loss of energy of a material system due to gravitational radiation in Einstein-aether theory-an alternative theory of gravity in which the metric couples to a dynamical, timelike, unit-norm vector field. Derived to lowest post-Newtonian order are waveforms for the metric and vector fields far from a nearly Newtonian system and the rate of energy radiated by the system. The expressions depend on the quadrupole moment of the source, as in standard general relativity, but also contain monopolar and dipolar terms. There exists a one-parameter family of Einstein-aether theories for which only the quadrupolar contribution is present, and for which the expression for the damping rate is identical to that of general relativity to the order worked to here. This family cannot yet be declared observationally viable, since effects due to the strong internal fields of bodies in the actual systems used to test the damping rate are not included.

gr-qc↗
arXiv2008

Strong field effects on binary systems in Einstein-aether theory

"Einstein-aether" theory is a generally covariant theory of gravity containing a dynamical preferred frame. This article continues an examination of effects on the motion of binary pulsar systems in this theory, by incorporating effects due to strong fields in the vicinity of neutron star pulsars. These effects are included through an effective approach, by treating the compact bodies as point particles with nonstandard, velocity dependent interactions parametrized by dimensionless "sensitivities". Effective post-Newtonian equations of motion for the bodies and the radiation damping rate are determined. More work is needed to calculate values of the sensitivities for a given fluid source, so precise constraints on the theory's coupling constants cannot yet be stated. It is shown, however, that strong field effects will be negligible given current observational uncertainties if the dimensionless couplings are less than roughly 0.01 and two conditions that match the PPN parameters to those of pure general relativity are imposed. In this case, weak field results suffice and imply one further condition on the couplings. Thus, there exists a one-parameter family of Einstein-aether theories with "small-enough" couplings that passes all current observational tests. No conclusion can yet be reached for large couplings.

gr-qc↗
arXiv2008

Constraints and gauge transformations: Dirac's theorem is not always valid

A standard tenet of canonical quantum gravity is that evolution generated by a Hamiltonian constraint is just a gauge transformation on the phase space and therefore does not change the physical state. The basis for this belief is a theorem of Dirac that identifies primary first-class constraints as generators of physically irrelevant motions. We point out that certain assumptions on which Dirac based his argument do not hold for reparametrization invariant systems, and show that the primary Hamiltonian constraint of these systems does generate physical motion. We show explicitly how the argument fails for systems described by Jacobi's principle, which has a structure closely resembling that of general relativity. We defer discussion of general relativity and the implications for quantum gravity to a later paper.

gr-qc↗
arXiv2007

Lorentz violation and perpetual motion

We show that any Lorentz violating theory with two or more propagation speeds is in conflict with the generalized second law of black hole thermodynamics. We do this by identifying a classical energy-extraction method, analogous to the Penrose process, which would decrease the black hole entropy. Although the usual definitions of black hole entropy are ambiguous in this context, we require only very mild assumptions about its dependence on the mass. This extends the result found by Dubovsky and Sibiryakov, which uses the Hawking effect and applies only if the fields with different propagation speeds interact just through gravity. We also point out instabilities that could interfere with their black hole {\it perpetuum mobile}, but argue that these can be neglected if the black hole mass is sufficiently large.

hep-th↗
arXiv2006

Post-Newtonian parameters and constraints on Einstein-aether theory

We analyze the observational and theoretical constraints on ``Einstein-aether theory", a generally covariant theory of gravity coupled to a dynamical, unit, timelike vector field that breaks local Lorentz symmetry. The results of a computation of the remaining post-Newtonian parameters are reported. These are combined with other results to determine the joint post-Newtonian, vacuum-Cerenkov, nucleosynthesis, stability, and positive-energy constraints. All of these constraints are satisfied by parameters in a large two-dimensional region in the four-dimensional parameter space defining the theory.

gr-qc↗
arXiv2005

Noether charges and black hole mechanics in Einstein-aether theory

The Noether charge method for defining the Hamiltonian of a diffeomorphism-invariant field theory is applied to "Einstein-aether" theory, in which gravity couples to a dynamical, timelike, unit-norm vector field. Using the method, expressions are obtained for the total energy, momentum, and angular momentum of an Einstein-aether space-time. The method is also used to discuss the mechanics of Einstein-aether black holes. The derivation of Wald, and Iyer and Wald, of the first law of black hole thermodynamics fails for this theory, because the unit vector is necessarily singular at the bifurcation surface of the Killing horizon. A general identity relating variations of energy and angular momentum to a surface integral at the horizon is obtained, but a thermodynamic interpretation, including a definitive expression for the black hole entropy, is not found.

gr-qc↗
arXiv2005

The physical gravitational degrees of freedom

When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing two general principles: 1) time is derived from change; 2) motion and size are relative. We write down an explicit action based on them. We obtain not only GR in the CMC gauge, in its Hamiltonian 3 + 1 reformulation but also all the equations used in York's conformal technique for solving the initial-value problem. This shows that the independent gravitational degrees of freedom obtained by York do not arise from a gauge fixing but from hitherto unrecognized fundamental symmetry principles. They can therefore be identified as the long-sought Hamiltonian physical gravitational degrees of freedom.

gr-qc↗
arXiv2005

Metric Redefinitions in Einstein-Aether Theory

`Einstein-Aether' theory, in which gravity couples to a dynamical, time-like, unit-norm vector field, provides a means for studying Lorentz violation in a generally covariant setting. Demonstrated here is the effect of a redefinition of the metric and vector field in terms of the original fields and two free parameters. The net effect is a change of the coupling constants appearing in the action. Using such a redefinition, one of the coupling constants can be set to zero, simplifying studies of solutions of the theory.

gr-qc↗
arXiv2004

Quantum field theory on a growing lattice

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.

hep-th↗
arXiv2004

A first-principles derivation of York scaling and the Lichnerowicz-York equation

The only efficient and robust method of generating consistent initial data in general relativity is the conformal technique initiated by Lichnerowicz and perfected by York. In the spatially compact case, the complete scheme consists of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition, and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the Lichnerowicz-York equation for the conformal factor (psi) of the physical metric (psi)^4(g_{ij}) given an initial unphysical 3-metric (g_{ij}). The CMC condition and LFE introduce a distinguished foliation (definition of simultaneity) on spacetime, and separate scaling laws for the canonical momenta and their trace are used. In this article, we derive all these features in a single package by seeking a gauge theory of geometrodynamics (evolving 3-geometries) invariant under both three-dimensional diffeomorphisms and volume-preserving conformal transformations.

gr-qc↗