Some Thoughts on COMMUTATION RELATIONS and MEASUREMENT ACCURACY

We show that measuring the trajectories of charged particles to nite accuracy leads to the commutation relations needed for the derivation of the free space Maxwell equations using the discrete ordered calculus (DOC). We note that the nite step length derivation of the discrete di erence version of the single particle Dirac equation implies the discrete version of the p; q commutation relations for a free particle. We speculate that a careful operational analysis of the change in momenta occurring in a step-wise continuous solution of the discrete Dirac equation could supply the missing source-sink terms in the DOC derivation of the Maxwell equations, and lead to a nite and discrete (\renormalized") quantum electrodynamics (QED). Invited paper presented at the 19 annual international meeting of the ALTERNATIVE NATURAL PHILOSOPHY ASSOCIATION Wesley House, Cambridge, England, August 14-17, 1997 Work supported by Department of Energy contract DE{AC03{76SF00515.