Gravitons and Lightcone Fluctuations II: Correlation Functions

A model of a fluctuating lightcone due to a bath of gravitons is further investigated. The flight times of photons between a source and a detector may be either longer or shorter than the light propagation time in the background classical spacetime, and will form a Gaussian distribution centered around the classical flight time. However, a pair of photons emitted in rapid succession will tend to have correlated flight times. We derive and discuss a correlation function which describes this effect. This enables us to understand more fully the operational significance of a fluctuating lightcone. Our results may be combined with observational data on pulsar timing to place some constraints on the quantum state of cosmological gravitons.Comment: 16 pages and two figures, uses eps

Nonlinear transformat

A technique for designing automatic flight controllers for aircraft which utilizes the transformation theory of nonlinear systems to linear systems is presently being developed at NASA Ames Research Center. A method is considered in which a given nonlinear is transformed to a controllable linear system in Brunovsky canonical form. A linear approximation is introduced to the nonlinear system called the modified tangent model. This model is easily computed. Constructing the transformation for this model enables the designer to find an approximate transformation for the nonlinear system

The Effects of Stress Tensor Fluctuations upon Focusing

We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources. We give explicit results for the case of a scalar field on a flat background in a thermal state.Comment: 26 pages, 1 figure, new material added in Sect. III and in Appendices B and

Battery workshop

The workshop was attended by representatives from industry and government. The requirements for energy storage and the plans for battery development were reviewed. The workshop followed a debate format, with the objective of recommending improvements to the development plans presented by NASA and the Air Force. The issues addressed were: (1) significant technology deficiencies which can be identified; (2) adequacy of current and proposed programs to resolve the technology deficiencies identified; (3) additional tasks which should be undertaken, including benefits and timing; and (4) lowest priority items in the presently planned program, both in content and in timing

Restrictions on Negative Energy Density in Flat Spacetime

In a previous paper, a bound on the negative energy density seen by an arbitrary inertial observer was derived for the free massless, quantized scalar field in four-dimensional Minkowski spacetime. This constraint has the form of an uncertainty principle-type limitation on the magnitude and duration of the negative energy density. That result was obtained after a somewhat complicated analysis. The goal of the current paper is to present a much simpler method for obtaining such constraints. Similar ``quantum inequality'' bounds on negative energy density are derived for the electromagnetic field, and for the massive scalar field in both two and four-dimensional Minkowski spacetime.Comment: 17 pages, including two figures, uses epsf, minor revisions in the Introduction, conclusions unchange

Decoherence at zero temperature

Most discussions of decoherence in the literature consider the high-temperature regime but it is also known that, in the presence of dissipation, decoherence can occur even at zero temperature. Whereas most previous investigations all assumed initial decoupling of the quantum system and bath, we consider that the system and environment are entangled at all times. Here, we discuss decoherence for a free particle in an initial Schr\"{o}dinger cat state. Memory effects are incorporated by use of the single relaxation time model (since the oft-used Ohmic model does not give physically correct results)

A simple algorithm for computing canonical forms

It is well known that all linear time-invariant controllable systems can be transformed to Brunovsky canonical form by a transformation consisting only of coordinate changes and linear feedback. However, the actual procedures for doing this have tended to be overly complex. The technique introduced here is envisioned as an on-line procedure and is inspired by George Meyer's tangent model for nonlinear systems. The process utilizes Meyer's block triangular form as an intermedicate step in going to Brunovsky form. The method also involves orthogonal matrices, thus eliminating the need for the computation of matrix inverses. In addition, the Kronecker indices can be computed as a by-product of this transformation so it is necessary to know them in advance

Exact solution of the Hu-Paz-Zhang master equation

The Hu-Paz-Zhang equation is a master equation for an oscillator coupled to a linear passive bath. It is exact within the assumption that the oscillator and bath are initially uncoupled . Here an exact general solution is obtained in the form of an expression for the Wigner function at time t in terms of the initial Wigner function. The result is applied to the motion of a Gaussian wave packet and to that of a pair of such wave packets. A serious divergence arising from the assumption of an initially uncoupled state is found to be due to the zero-point oscillations of the bath and not removed in a cutoff model. As a consequence, worthwhile results for the equation can only be obtained in the high temperature limit, where zero-point oscillations are neglected. In that limit closed form expressions for wave packet spreading and attenuation of coherence are obtained. These results agree within a numerical factor with those appearing in the literature, which apply for the case of a particle at zero temperature that is suddenly coupled to a bath at high temperature. On the other hand very different results are obtained for the physically consistent case in which the initial particle temperature is arranged to coincide with that of the bath

Averaged Energy Conditions and Quantum Inequalities

Connections are uncovered between the averaged weak (AWEC) and averaged null (ANEC) energy conditions, and quantum inequality restrictions on negative energy for free massless scalar fields. In a two-dimensional compactified Minkowski universe, we derive a covariant quantum inequality-type bound on the difference of the expectation values of the energy density in an arbitrary quantum state and in the Casimir vacuum state. From this bound, it is shown that the difference of expectation values also obeys AWEC and ANEC-type integral conditions. In contrast, it is well-known that the stress tensor in the Casimir vacuum state alone satisfies neither quantum inequalities nor averaged energy conditions. Such difference inequalities represent limits on the degree of energy condition violation that is allowed over and above any violation due to negative energy densities in a background vacuum state. In our simple two-dimensional model, they provide physically interesting examples of new constraints on negative energy which hold even when the usual AWEC, ANEC, and quantum inequality restrictions fail. In the limit when the size of the space is allowed to go to infinity, we derive quantum inequalities for timelike and null geodesics which, in appropriate limits, reduce to AWEC and ANEC in ordinary two-dimensional Minkowski spacetime. We also derive a quantum inequality bound on the energy density seen by an inertial observer in four-dimensional Minkowski spacetime. The bound implies that any inertial observer in flat spacetime cannot see an arbitrarily large negative energy density which lasts for an arbitrarily long period of time.Comment: 20pp, plain LATEX, TUTP-94-1