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.
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