Schr�dinger equation as an operator acting on test functions describing observing systems and the EPR correlation

Abstract

A reformulation of quantum mechanics is introduced by regarding the Schrodinger equationE(f+) = 0 for the retarded particle wavef+ as an operator (functional) acting on the test functionf− satisfying the boundary conditions of the observing system: 〈E(f+),f−〉 = 0. The variational expression for the transition amplitude of a particle between the particle source and the detector naturally arises in the dual space of the particle field and the test function. In the two-slit electron interference experiment, the test function plays the role of the “quantum potential” which carries the information of the detector and the slit locations backwards in time, while in the Einstein-Podolsky-Rosen process the test function describes the time reversed process of a pair of spatially separated fermions with arbitrarily chosen spin orientations progressing backwards in time to form a spherically symmetric compound state. The separation of the kinematics (spin correlation and the dynamics (spacetime aspect) of the EPR process is pointed out.