Thoughts on Commutation Relations and Measurement Accuracy

Details Thoughts on Commutation Relations and Measurement Accuracy Thoughts on Commutation Relations and Measurement Accuracy

1999-01-08

arxiv.org/abs/quant-ph/9901017v1

Physics

Quantum Physics

LaTex, 8 pages

Scientific paper

We show that measuring the trajectories of charged particles to finite accuracy leads to the commutation relations needed for the derivation of the free space Maxwell equations using the {\it discrete ordered calculus} (DOC). We note that the finite step length derivation of the discrete difference 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 finite and discrete (``renormalized'') quantum electrodynamics (QED).

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