Schrödinger Equation for Joint Bidirectional Evolution in Time: Astrophysical Applications

A straightforward extension of quantum mechanics and quantum field theory is proposed that can describe physical systems comprising two interacting subsystems: one subsystem evolves forward in time, the other, backward. The space of quantum states is the direct sum of the states representing the respective subsystems, whereupon there are two linearly independent vacuum states, one each for the forward and the backward subspace. An indefinite metric is imposed on the space of quantum states such that purely forward (respectively, purely backward) states have positive (respectively, negative) norms. Hamiltonians are self-adjoint operators with respect to the metric, such that interactions/transitions between the subspaces can be accounted for. Given suitable definitions of input and of output states at the two ends of a time interval, input and output states separately have positive norms such that probability is conserved, and hence S-matrices are unitary. A discussion of the physics entailed in the proposed formalism is undertaken. Then as an application, a simple model of a relativistic quantum field theory is proposed. In this model, the expected vacuum energy (thought to be associated with the cosmological constant) almost vanishes uniformly for times in an interval due to cancellation of the energies of the forward and backward vacuum states; this cancellation holds whatever be the input vacuum state at the ends of the time interval. A model is advanced wherein magnetic monopoles live exclusively in backward-evolving states, and interact with forward-evolving electric charges in a certain way. Proposals for further research, particularly concerning the possible detection of advanced gravitational waves, and a conjecture on the physics of dark matter and dark energy, conclude the report.