NON-LIPSCHITZ APPROACH TO QUANTUM-MECHANICS

An attempt to reconcile quantum mechanics with Newton's laws represent ed by the non-Lipschitz formalism has been made. As a proof-of-concept , a line of equally spaced atoms was studied. It appeared that enforce ment of atom incompressibility required relaxation of the Lipschitz co ndition at the points of contact. This, in turn, led to fractional pow ers and discreteness of values of the basic parameters including energ y and action, and finally, to the uncertainty relationship between pos itions and velocities. In addition to that, the relaxation of the Lips chitz condition caused instability of velocity with respect to small c hanges of the atom position, and that introduced an element of randomn ess in the system behavior. It was shown that the only model for the p robability evolution which incorporates all the new properties of the motions is the Schrodinger equation. This means that quantum mechanics can be derived from Newton's laws if an unnecessary mathematical rest riction-the Lipschitz condition-is removed from the mathematical forma lism. Non-local properties of the model, as well as spin-effects and r elativistic corrections are discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.