Quantum mechanics and dynamic programming

Abstract

This brief paper continues a development in earlier publications by Rosenbrock, in which results in quantum mechanics were obtained by adding a random disturbance to Hamilton's principle. The disturbance is complex, and the resulting variational problem is solved by dynamic programming, which computes the causal relations needed to accomplish a purpose. It is shown here that this procedure leads to many results that agree with those obtained in the standard theory of quantum mechanics, but also to some that are not readily obtained in that theory. For example, certain changes at a time t_m to the end condition x_f, which will be reached at t_f>t_m, can instantaneously change some aspects of the particle's behaviour at t _m while it is still in transit. This accounts for Einstein's `spooky action at a distance'. An approach is also given to interference and entanglement, which is simpler than the standard account and may therefore be useful in quantum control and quantum computation.