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

Khronometric theories of modified Newtonian dynamics

In 2011 Blanchet and Marsat suggested a fully relativistic version of Milgrom's modified Newtonian dynamics (MOND) in which the dynamical degrees of freedom consist of the spacetime metric and a foliation of spacetime, the khronon field. This theory is simpler than the alternative relativsitic formulations. We show that the theory has a consistent non-relativistic or slow motion limit. Blanchet and Marsat showed that in the slow motion limit the theory reproduces stationary solutions of modified Newtonian dynamics. We show that these solutions are stable to khronon perturbations in the low acceleration regime, for the cases of spherical, cylindrical and planar symmetry. For non-stationary systems in the low acceleration regime we show that the khronon field generally gives an order unity correction to the modified Newtonian dynamics.Comment: v2: Error in discussion of previous work corrected, discussion of khronon dynamics expanded, other minor corrections. v3: minor corrections and clarification