arXiv subjects

L. H. Ford

Publications and source records attributed to L. H. Ford.

At least 37 records · Page 2Linked to original sources

arXiv2018

Maximal Subvacuum Effects: A Single Mode Example

We discuss an example of a subvacuum effect, where a quantum expectation value is below the vacuum level, and is hence negative. The example is the time average of the mean squared electric field in a non-classical state where one mode is excited. We give some specific examples of such states, and discuss the lower bound on the squared field or its time average. We show when a lower bound can be obtained by diagonalization of the squared electric field operator, and calculate this bound. We also discuss the case of an instant time mean squared electric field, when the operator cannot be diagonalized. In this case, a lower bound still exists but is attained only by the limit of a sequence of quantum states. In general, the optimum lower bound on the mean squared electric field is minus one-half of the mean squared electric field in a one photon state. This provides a convenient estimate of the subvacuum effect, and may be useful for attempts to experimentally measure this effect.

quant-ph↗

arXiv2018

Spacetime geometry fluctuations and geodesic deviation

The quantum fluctuations of the geodesic deviation equation in a flat background spacetime are discussed. We calculate the resulting mean squared fluctuations in the relative velocity and separation of test particles. The effect of these quantum fluctuations of the spacetime geometry is given in terms of the Riemann tensor correlation function. Three different sources of the Riemann tensor fluctuations are considered: a thermal bath of gravitons, gravitons in a squeezed state, and the graviton vacuum state.

gr-qc↗

arXiv2017

Vacuum Quantum Stress Tensor Fluctuations: A Diagonalization Approach

Large vacuum fluctuations of a quantum stress tensor operator can be described by the asymptotic behavior of the probability distribution of the time or spacetime averaged operator. Here we focus on the case of stress tensor operators averaged with a sampling function in time. The Minkowski vacuum state is not an eigenstate of the time-averaged operator, but can be expanded in terms of its eigenstates. We calculate the probability distribution and the cumulative probability distribution for obtaining a given value in a measurement of the time-averaged operator taken in the vacuum state. In these calculations, we use the normal ordered square of the time derivative of a massless scalar field in Minkowski spacetime as an example of a stress tensor operator. We analyze the rate of decrease of the tail of the probability distribution for different temporal sampling functions, such as compactly supported functions and the Lorentzian function. We find that the tails decrease relatively slowly, as exponentials of fractional powers, in agreement with previous work using the moments of the distribution. Our results lead additional support to the conclusion that large vacuum stress tensor fluctuations are more probable than large thermal fluctuations, and may have observable effects.

hep-th↗

arXiv2017

Quantum Stress Tensor Fluctuations and Primordial Gravity Waves

We examine the effect of the stress tensor of a quantum matter field, such as the electromagnetic field, on the spectrum of primordial gravity waves expected in inflationary cosmology. We find that the net effect is a small reduction in the power spectrum, especially at higher frequencies, but which has a different form from that described by the usual spectral index. Thus this effect has a characteristic signature, and is in principle observable. The net effect is a sum of two contributions, one of which is due to quantum fluctuations of the matter field stress tensor. The other is a quantum correction to the graviton field due to coupling to the expectation value of this stress tensor. Both contributions are sensitive to initial conditions in the very early universe, so this effect has the potential to act as a probe of these initial conditions.

gr-qc↗

arXiv2016

Graviton Creation by Small Scale Factor Oscillations in an Expanding Universe

We treat quantum creation of gravitons by small scale factor oscillations around the average of an expanding universe. Such oscillations can arise in standard general relativity due to oscillations of a homogeneous, minimally coupled scalar field. They can also arise in modified gravity theories with a term proportional to the square of the Ricci scalar in the gravitational action. The graviton wave equation is different in the two cases, leading to somewhat different creation rates. Both cases are treated using a perturbative method due to Birrell and Davies, involving an expansion in a conformal coupling parameter to calculate the number density and energy density of the created gravitons. Cosmological constraints on the present graviton energy density and the dimensionless amplitude of the oscillations are discussed. We also discuss decoherence of quantum systems produced by the spacetime geometry fluctuations due to such a graviton bath.

gr-qc↗

arXiv2016

Classical enhancement of quantum vacuum fluctuations

We propose a mechanism for the enhancement of vacuum fluctuations by means of a classical field. The basic idea is that if an observable quantity depends quadratically upon a quantum field, such as the electric field, then the application of a classical field produces a cross term between the classical and quantum fields. This cross term may be significantly larger than the purely quantum part, but also undergoes fluctuations driven by the quantum field. We illustrate this effect in a model for lightcone fluctuations involving pulses in a nonlinear dielectric. Vacuum electric field fluctuations produce fluctuations in the speed of a probe pulse, and form an analog model for quantum gravity effects. If the material has a nonzero third-order susceptibility, then the fractional light speed fluctuations are proportional to the square of the fluctuating electric field. Hence the application of a classical electric field can enhance the speed fluctuations. We give an example where this enhancement can be an increase of one order of magnitude, increasing the possibility of observing the effect.

quant-ph↗

arXiv2016

Quantum Gravitational Force Between Polarizable Objects

Since general relativity is a consistent low energy effective field theory, it is possible to compute quantum corrections to classical forces. Here we compute a quantum correction to the gravitational potential between a pair of polarizable objects. We study two distant bodies and compute a quantum force from their induced quadrupole moments due to two graviton exchange. The effect is in close analogy to the Casimir-Polder and London-van der Waals forces between a pair of atoms from their induced dipole moments due to two photon exchange. The new effect is computed from the shift in vacuum energy of metric fluctuations due to the polarizability of the objects. We compute the potential energy at arbitrary distances compared to the wavelengths in the system, including the far and near regimes. In the far distance, or retarded, regime, the potential energy takes on a particularly simple form: $V(r)=-3987\,\hbar\,c\,G^2α_{1S}\,α_{2S}/(4\,π\,r^{11})$, where $α_{1S},\,α_{2S}$ are the static gravitational quadrupole polarizabilities of each object. We provide estimates of this effect.

hep-th↗

arXiv2016

A Model for Lightcone Fluctuations due to Stress Tensor Fluctuations

We study a model for quantum lightcone fluctuations in which vacuum fluctuations of the electric field and of the squared electric field in a nonlinear dielectric material produce variations in the flight times of probe pulses. When this material has a non-zero third order polarizability, the flight time variations arise from squared electric field fluctuations, and are analogous to effects expected when the stress tensor of a quantized field drives passive spacetime geometry fluctuations. We also discuss the dependence of the squared electric field fluctuations upon the geometry of the material, which in turn determines a sampling function for averaging the squared electric field along the path of the pulse. This allows us to estimate the probability of especially large fluctuations, which is a measure of the probability distribution for quantum stress tensor fluctuations.

gr-qc↗

arXiv2015

Probability Distributions for Quantum Stress Tensors Measured in a Finite Time Interval

A meaningful probability distribution for measurements of a quantum stress tensor operator can only be obtained if the operator is averaged in time or in spacetime. This averaging can be regarded as a description of the measurement process. Realistic measurements can be expected to begin and end at finite times, which means that they are described by functions with compact support, which we will also take to be smooth. Here we study the probability distributions for stress tensor operators averaged with such functions of time, in the vacuum state of a massless free field. Our primary aim is to understand the asymptotic form of the distribution which describes the probability of large vacuum fluctuations. Our approach involves asymptotic estimates for the high moments of the distribution. These estimates in turn may be used to obtain estimates for the asymptotic form of the probability distribution. Our results show that averaging over a finite interval results in a probability distribution which falls more slowly than for the case of Lorentzian averaging, and both fall more slowly than exponentially. This indicates that vacuum fluctuations effects can dominate over thermal fluctuations in some circumstances.

hep-th↗

arXiv2015

Quantum Electric Field Fluctuations and Potential Scattering

Some physical effects of time averaged quantum electric field fluctuations are discussed. The one loop radiative correction to potential scattering are approximately derived from simple arguments which invoke vacuum electric field fluctuations. For both above barrier scattering and quantum tunneling, this effect increases the transmission probability. It is argued that the shape of the potential determines a sampling function for the time averaging of the quantum electric field operator. We also suggest that there is a nonperturbative enhancement of the transmission probability which can be inferred from the probability distribution for time averaged electric field fluctuations.

hep-th↗

arXiv2014

Decoherence induced by long wavelength gravitons

We discuss how a background bath of gravitons can induce decoherence of quantum systems. The mechanism is dephasing, the loss of phase coherence due to quantum geometry fluctuations caused by the gravitons. This effect is illustrated in a simple analog model of quantum particles in a cavity whose walls undergo position fluctuations, and create the same effect expected from spacetime geometry fluctuations. We obtain an explicit result for the decoherence rate in the limit where the graviton wavelength is large compared to the size of the quantum system, and make some estimates for this rate.

gr-qc↗

arXiv2014

An Exploration of the Limits of the Maxwell-Boltzmann Distribution

Selected aspects of the Maxwell-Boltzmann for molecular speeds are discussed, with special attention to physical effects of the low speed and high speed limits. We use simple approaches to study several topics which could be included in introductory courses, but are usually only discussed in more advanced or specialized courses.

physics.ed-ph↗

arXiv2014

Probability distributions for quantum stress tensors in two and four dimensions

The probability distributions for the smeared energy densities of quantum fields, in the two and four-dimensional Minkowski vacuum are discussed. These distributions share the property that there is a lower bound at a finite negative value, but no upper bound. Thus arbitrarily large positive energy density fluctuations are possible. In two dimensions we are able to give an exact unique analytic form for the distribution. However, in four dimensions, we are not able to give closed form expressions for the probability distribution, but rather use calculations of a finite number of moments to estimate the lower bound, and the asymptotic form of the tail of the distribution. The first 65 moments are used for these purposes. All of our four-dimensional results are subject to the caveat that these distributions are not uniquely determined by the moments. One can apply the asymptotic form of the electromagnetic energy density distribution to estimate the nucleation rates of black holes and of Boltzmann brains.

gr-qc↗

arXiv2014

Vacuum Lightcone Fluctuations in a Dielectric

A model for observable effects of electromagnetic vacuum fluctuations is presented. The model involves a probe pulse which traverses a slab of nonlinear optical material with a nonzero second order polarizability. We argue that the pulse interacts with the ambient vacuum fluctuations of other modes of the quantized electric field, and these vacuum fluctuations cause variations in the flight time of the pulse through the material. The geometry of the slab of material defines a sampling function for the quantized electric field, which in turn determines that vacuum modes whose wavelengths are of the order of the thickness of the slab give the dominant contribution. Some numerical estimates are made, which indicate that fractional fluctuations in flight time of the order of $10^{-9}$ are possible in realistic situations. The model presented here is both an illustration of a physical effect of vacuum fluctuations, and an analog model for the lightcone fluctuations predicted by quantum gravity.

hep-th↗

arXiv2014

An Analog Model for Light Propagation in Semiclassical Gravity

We treat a model based upon nonlinear optics for the semiclassical gravitational effects of quantum fields upon light propagation. Our model uses a nonlinear material with a nonzero third order polarizability. Here a probe light pulse satisfies a wave equation containing the expectation value of the squared electric field. This expectation value depends upon the presence of lower frequency quanta, the background field, and modifies the effective index of refraction, and hence the speed of the probe pulse. If the mean squared electric field is positive, then the pulse is slowed, which is analogous to the gravitational effects of ordinary matter. Such matter satisfies the null energy condition and produce gravitational lensing and time delay. If the mean squared field is negative, then the pulse has a higher speed than in the absence of the background field. This is analogous to the gravitational effects of exotic matter, such as stress tensor expectation values with locally negative energy densities, which lead to repulsive gravitational effects, such as defocussing and time advance. We give some estimates of the magnitude of the effects in our model, and find that they may be large enough to be observable. We also briefly discuss the possibility that the mean squared electric field could be produced by the Casimir vacuum near a reflecting boundary.

gr-qc↗

arXiv2013

Non-Cancellation of Quantum Geometry Fluctuations

Quantum vacuum fluctuations tend to be strongly anti-correlated, which reduces their observable effects. However, time dependence can upset the cancellation of these anti-correlated fluctuations and greatly enhance their effects. This form of non-cancellation is investigated for spacetime geometry fluctuations driven by the vacuum stress tensor fluctuations of the electromagnetic field. The time dependence can take the form of sinusoidal conformal metric perturbations or of time variation of the gravitational constant, both of which can arise from modifications of the gravitational action. We examine two observable quantities, luminosity fluctuations and redshift fluctuations, both of which can arise from stress tensor fluctuations. We find that both quantities can grow with increasing distance between a source and an observer. This secular growth raises the possibility of observing spacetime geometry fluctuation effects at length scales far longer than the Planck scale.

gr-qc↗

arXiv2013

Negative Energy Seen By Accelerated Observers

The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The quantum inequalities severely limit the utilization of negative energy to produce gross macroscopic effects, such as violations of the second law of thermodynamics. The restrictions on the sampled energy density along the worldlines of accelerated observers are much weaker than for inertial observers. Here we will illustrate this with several explicit examples. We consider the worldline of a particle undergoing sinusoidal motion in space in the presence of a single mode squeezed vacuum state of the electromagnetic field. We show that it is possible for the integrated energy density along such a worldline to become arbitrarily negative at a constant average rate. Thus the averaged weak energy condition is violated in these examples.This can be the case even when the particle moves at non-relativistic speeds. We use the Raychaudhuri equation to show that there can be net defocussing of a congruence of these accelerated worldlines. This defocussing is an operational signature of the negative integrated energy density. These results in no way invalidate nor undermine either the validity or utility of the quantum inequalities for inertial observers. In particular, they do not change previous constraints on the production of macroscopic effects with negative energy, e.g., the maintenance of traversable wormholes.

gr-qc↗

arXiv2012

Decoherence induced by fluctuating boundaries

The effects of fluctuating boundaries on a superposition state of a quantum particle in a box is studied. We consider a model in one space dimension in which the initial state is a coherent superposition of two energy eigenstates. The locations of the walls of the box are assumed to undergo small fluctuation with a Gaussian probability distribution. The spatial probability density of the particle contains an interference term, which is found to decay in time due to the boundary fluctuations. At late times, this term vanishes and the quantum coherence is lost. The system is now described by a density matrix rather than a pure quantum state.This model gives a simple illustration of how environment-induced decoherence can take place in quantum systems. It can also serve as an analog model for the effects of spacetime geometry fluctuations on quantum systems.

quant-ph↗