Aether

Abstract: We study a generally covariant model in which local Lorentz invariance is broken by a dynamical unit timelike vector field ${u}^{a}$---the ``aether.'' Such a model makes it possible to study the gravitational and cosmological consequences of preferred frame effects, such as ``variable speed of light'' or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effective theory of the aether which involves only the antisymmetrized derivative ${\ensuremath{ abla}}_{[a}{u}_{b]}.$ Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transverse excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether generally develops gradient singularities which signal a breakdown of this effective theory. Including the symmetrized derivative in the action for the aether field may cure this problem.

Abstract: Market: Physicists, interested lay readers, and historians of science. This survey of the history of electrodynamics provides insight into the revolutionary advances made in physics during 19th and the first quarter of the 20th centuries. The first volume covers the theories of classical physics from the time of Plato to the end of the 19th century. The second volume examines the origins of the discoveries that paved the way for modern physics with the emphasis on special relativity, quantum theories, general relativity, matrix mechanics, and wave mechanics.

Abstract: Market: Physicists, interested lay readers, and historians of science. This survey of the history of electrodynamics provides insight into the revolutionary advances made in physics during 19th and the first quarter of the 20th centuries. The first volume covers the theories of classical physics from the time of Plato to the end of the 19th century. The second volume examines the origins of the discoveries that paved the way for modern physics with the emphasis on special relativity, quantum theories, general relativity, matrix mechanics, and wave mechanics.

Abstract: Local Lorentz invariance violation can be realized by introducing extra tensor fields in the action that couple to matter. If the Lorentz violation is rotationally invariant in some frame, then it is characterized by an ``aether,'' i.e., a unit timelike vector field. General covariance requires that the aether field be dynamical. In this paper we study the linearized theory of such an aether coupled to gravity and find the speeds and polarizations of all the wave modes in terms of the four constants appearing in the most general action at second order in derivatives. We find that in addition to the usual two transverse traceless metric modes, there are three coupled aether-metric modes.