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Thoughts on Commutation Relations and Measurement Accuracy

H. Pierre Noyes
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Abstract

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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H. Pierre Noyes. 1999-01-08. Thoughts on Commutation Relations and Measurement Accuracy. https://arxiv.org/abs/quant-ph/9901017

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