The concept of Existence and the derivation of a Quantum Force

Abstract

We define a new dynamical variable, the relative existence e, in terms of space and time. Taking it as a generalized positional coordinate, we show that for conservative systems the canonically conjugated momentum is identified as the classical force. Applying Wilson-Sommerfeld-Bohr's quantum conditions for a conditionally periodic motion, we derive an expression for the quantum force, F = hbar k f_e, where k is the wave number and f_e is the characteristic frequency of the system. Applying Dirac's method to the Poisson Brackets involving existence and force, we obtain the uncertainty relation Delta e Delta F >= hbar/2. The force quantization may have already been observed in stimulated bichromatic optical force experiments, used to deflect, decelerate and manipulate laser-cooled atomic beams.