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Thanks for your question. For some reason I wasn’t able to submit a reply to your previous comment, but I’m in now.
The general rule for understanding the behaviour and propagation of the final wavefunction in my theory is to think about what happens with the usual, initial wavefunction and then do the same thing but in the opposite time direction. If you’re puzzled about something with the final psi, ask yourself if you would still be puzzled if you were just talking about the initial psi instead. For example, aspects of the usual Bohm Theory of Measurement are maintained in my model. In the standard theory, the measurement interaction (e.g., an externally applied potential) causes the initial wavefunction to spread so that the relevant eigenstates become spatially separate like the fingers of a hand. In spacetime, the fingers point in the forwards time direction. The same thing is assumed to happen with the final wavefunction as it goes through the interaction region coming from the future, except the fingers now point in the backwards time direction. So the final boundary condition is fixed in an analogous way to the state preparation of an initial psi. More details on this are in the measurement section of my 2008 paper.
Unlike classical physics, there is no doubt that two boundary conditions are needed in this picture, since otherwise Bell’s nonlocality could not be explained in a Lorentz invariant fashion via a spacetime zigzag. The reason for two wavefunctions is then simply to move the mathematical information about the two boundary conditions from both the earlier time ti and the later time tf to the present time t so we can calculate the effect on the present state (e.g., the particle’s velocity). Also, without both initial and final conditions, it is not possible to reduce the configuration space description usually required for the many-particle case back to a description in real space, as explained in my present paper.
I hope I’ve understood your questions correctly.