Paul J. Werbos
Published 2003-09-02, updated 2003-09-04Version 2
Quantum Field Theory (QFT) makes predictions by combining assumptions about (1) quantum dynamics, typically a Schrodinger or Liouville equation; (2) quantum measurement, usually via a collapse formalism. Here I define a "classical density matrix" rho to describe ensembles of states of ordinary second-order classical systems (ODE or PDE). I prove that the dynamics of the field observables, phi and pi, defined as operators over rho, obey precisely the usual Louiville equation for the same field operators in QFT, following Weinberg's treatment. I discuss implications in detail - particularly the implication that the difference between quantum computing and quantum mechanics versus classical systems lies mainly on the measurement side, not the dynamic side. But what if measurement itself were to be derived from dynamics and boundary conditions? An heretical realistic approach to building finite field theory is proposed, linked to the backwards time interpretation of quantum mechanics.
Comments: 19 pages. The pdf text contains the title and long abstract as published in IJBC, 10/2002. The IJBC original was next to a paper by Chua&Roska arguing that Cellular Neural Networks attain the limits of PDE computing. The revision on 9/4/3 fixes small typos in equations 73&92 of the original
Journal: P.Werbos, Classical ODE and PDE Which Obey Quantum Dynamics, International Journal of Bifurcation and Chaos, Vol. 12, No. 10 (2002) 2031-2049
Reconstruction Approach to Quantum Dynamics of Bosonic Systems
Lecture Notes in Quantum Mechanics
Quantum Dynamics as a Stochastic Process
