Schroedinger equation for joint bidirectional evolution in time:   astrophysical applications
  The theoretical framework established in arXiv:quant-ph/0404103 is extended to deal with possible astrophysical manifestations of phenomena involving reverse, as well as forward, causation in time. The basic idea is that space-time comprises the direct sum of a number of quantized fields, including a distinct physical vacuum for each space in the sum. It is presumed that these fields all contribute to, and are influenced by, gravitation, but generally do not interact electromagnetically, i.e., are mutually invisible. At least one term in the sum is proposed to consist of matter+vacuum evolving backward in time; the expectation values of energies, both of matter and vacuum, of this subspace are by construction negative, with a corresponding change of sign in classical gravitational and inertial masses. 
G. E. Hahne