The averaged null energy condition for general quantum field theories in two dimensions

It is shown that the averaged null energy condition is fulfilled for a dense, translationally invariant set of vector states in any local quantum field theory in two-dimensional Minkowski spacetime whenever the theory has a mass gap and possesses an energy-momentum tensor. The latter is assumed to be a Wightman field which is local relative to the observables, generates locally the translations, is divergence-free, and energetically bounded. Thus the averaged null energy condition can be deduced from completely generic, standard assumptions for general quantum field theory in two-dimensional flat spacetime.Comment: LateX2e, 16 pages, 1 eps figur

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Quantum interest in two dimensions

The quantum interest conjecture of Ford and Roman asserts that any negative-energy pulse must necessarily be followed by an over-compensating positive-energy one within a certain maximum time delay. Furthermore, the minimum amount of over-compensation increases with the separation between the pulses. In this paper, we first study the case of a negative-energy square pulse followed by a positive-energy one for a minimally coupled, massless scalar field in two-dimensional Minkowski space. We obtain explicit expressions for the maximum time delay and the amount of over-compensation needed, using a previously developed eigenvalue approach. These results are then used to give a proof of the quantum interest conjecture for massless scalar fields in two dimensions, valid for general energy distributions.Comment: 17 pages, 4 figures; final version to appear in PR

Design and Synthesis of a Novel Alpha-Methylene Lactone Chemotherapeutic Agent

Goniothalamin, a natural product isolated from the dried stem bark of Malaysian plants of the genus Goniothalamus, has been shown to induce apoptosis in cancer cells. The bioactivity of this molecule is though to be due to its ability to react with thiols. One mechanism involves its reaction with glutathione, a natural antioxidant found in all cells. Using a four step synthetic sequence, a novel gamma-lactone analogue of goniothalamin has been prepared that replaces the endocylic double bond in goniothalamin\u27s lactone core with an exocyclic double bond. It is anticipated that this alteration will allow the compound to react more rapidly with thiols and therefore increase its cytotoxicity towards cancer cells

Restrictions on negative energy density in a curved spacetime

Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled scalar field, in the extension of quantum inequality-type relation on flat spacetime of Ford and Roman. They found negative lower bounds for the line integrals of energy density multiplied by a sampling (weighting) function, and explicitly evaluate them for some specific spacetimes. In this paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are compact and without boundary. In the short "sampling time" limit, the bound has asymptotic expansion. Although the expansion can not be represented by locally invariant quantities in general due to the nonlocal nature of the integral, we explicitly evaluate the dominant terms in the limit in terms of the invariant quantities. We also make an estimate for the bound in the long sampling time limit.Comment: LaTex, 23 Page

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

Open and Closed Universes, Initial Singularities and Inflation

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.Comment: 27 pages, Plain TeX (figures are embedded in the file itself and they will emerge if it is processed according to the instructions at the top of the file

Nonorientable spacetime tunneling

Misner space is generalized to have the nonorientable topology of a Klein bottle, and it is shown that in a classical spacetime with multiply connected space slices having such a topology, closed timelike curves are formed. Different regions on the Klein bottle surface can be distinguished which are separated by apparent horizons fixed at particular values of the two angular variables that eneter the metric. Around the throat of this tunnel (which we denote a Klein bottlehole), the position of these horizons dictates an ordinary and exotic matter distribution such that, in addition to the known diverging lensing action of wormholes, a converging lensing action is also present at the mouths. Associated with this matter distribution, the accelerating version of this Klein bottlehole shows four distinct chronology horizons, each with its own nonchronal region. A calculation of the quantum vacuum fluctuations performed by using the regularized two-point Hadamard function shows that each chronology horizon nests a set of polarized hypersurfaces where the renormalized momentum-energy tensor diverges. This quantum instability can be prevented if we take the accelerating Klein bottlehole to be a generalization of a modified Misner space in which the period of the closed spatial direction is time-dependent. In this case, the nonchronal regions and closed timelike curves cannot exceed a minimum size of the order the Planck scale.Comment: 11 pages, RevTex, Accepted in Phys. Rev.

Averaged Energy Conditions in 4D Evaporating Black Hole Backgrounds

Using Visser's semi-analytical model for the stress-energy tensor corresponding to the conformally coupled massless scalar field in the Unruh vacuum, we examine, by explicitly evaluating the relevant integrals over half-complete geodesics, the averaged weak (AWEC) and averaged null (ANEC) energy conditions along with Ford-Roman quantum inequality-type restrictions on negative energy in the context of four dimensional evaporating black hole backgrounds. We find that in all cases where the averaged energy conditions fail, there exist quantum inequality bounds on the magnitude and duration of negative energy densities.Comment: Revtex, 13 pages, to appear in Phy. Rev.

Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such non-unitarity. The usual notion of state on a spacelike surface is lost in this generalization and familiar notions of causality are modified. There is no signaling outside the light cone, no non-conservation of energy, no ``Everett phones'', and probabilities of present events do not depend on particular alternatives of the future. However, the generalization is acausal in the sense that the existence of non-chronal regions of spacetime in the future can affect the probabilities of alternatives today. The detectability of non-unitary evolution and violations of causality in measurement situations are briefly considered. The evolution of information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0