A New Perspective on Time Reversal Motivated by Quantum Gravity

Abstract

Time Reversal T is usually discussed in the traditional framework of quantum mechanics in which T is represented by an anti-unitary operator. But quantum gravity may well need generalization of standard quantum mechanics which may not preserve even its linear structure, let alone the unitarity of dynamics and anti-unitarity of T. Then the currently used arguments to conclude that T violation is a fundamental aspect of Nature will break down. Fortunately, it turns out that one can analyze the T-violation experiments in a much more general setting, of which classical and quantum mechanics are special cases. The setting does not require a Hilbert space, or linearity of either dynamics or symmetry operations such as T. Nonetheless, somewhat surprisingly, one would still be to use the current experiments to conclude that there is T violation at a fundamental level under rather minimal assumptions on the structure of the final quantum gravity theory.