Quantum inequalities in two dimensional Minkowski spacetime

We generalize some results of Ford and Roman constraining the possible behaviors of renormalized expected stress-energy tensors of a free massless scalar field in two dimensional Minkowski spacetime. Ford and Roman showed that the energy density measured by an inertial observer, when averaged with respect to that observers proper time by integrating against some weighting function, is bounded below by a negative lower bound proportional to the reciprocal of the square of the averaging timescale. However, the proof required a particular choice for the weighting function. We extend the Ford-Roman result in two ways: (i) We calculate the optimum (maximum possible) lower bound and characterize the state which achieves this lower bound; the optimum lower bound differs by a factor of three from the bound derived by Ford and Roman for their choice of smearing function. (ii) We calculate the lower bound for arbitrary, smooth positive weighting functions. We also derive similar lower bounds on the spatial average of energy density at a fixed moment of time.Comment: 6 pages, no figures, uses revtex 3.1 macros, to appear in Phys Rev D. Minor revisions and generalizations added 7/16/9

The basics of gravitational wave theory

Einstein's special theory of relativity revolutionized physics by teaching us that space and time are not separate entities, but join as ``spacetime''. His general theory of relativity further taught us that spacetime is not just a stage on which dynamics takes place, but is a participant: The field equation of general relativity connects matter dynamics to the curvature of spacetime. Curvature is responsible for gravity, carrying us beyond the Newtonian conception of gravity that had been in place for the previous two and a half centuries. Much research in gravitation since then has explored and clarified the consequences of this revolution; the notion of dynamical spacetime is now firmly established in the toolkit of modern physics. Indeed, this notion is so well established that we may now contemplate using spacetime as a tool for other science. One aspect of dynamical spacetime -- its radiative character, ``gravitational radiation'' -- will inaugurate entirely new techniques for observing violent astrophysical processes. Over the next one hundred years, much of this subject's excitement will come from learning how to exploit spacetime as a tool for astronomy. This article is intended as a tutorial in the basics of gravitational radiation physics.Comment: 49 pages, 3 figures. For special issue of New Journal of Physics, "Spacetime 100 Years Later", edited by Richard Price and Jorge Pullin. This version corrects an important error in Eq. (4.23); an erratum is in pres