dorsal/arxiv
View SchemaThoughts on Commutation Relations and Measurement Accuracy
| Authors | H. Pierre Noyes |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9901017 |
| URL | https://arxiv.org/abs/quant-ph/9901017 |
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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"abstract": "We show that measuring the trajectories of charged particles to finite\naccuracy leads to the commutation relations needed for the derivation of the\nfree space Maxwell equations using the {\\it discrete ordered calculus} (DOC).\nWe note that the finite step length derivation of the discrete difference\nversion of the single particle Dirac equation implies the discrete version of\nthe p,q commutation relations for a free particle. We speculate that a careful\noperational analysis of the change in momenta occurring in a step-wise\ncontinuous solution of the discrete Dirac equation could supply the missing\nsource-sink terms in the DOC derivation of the Maxwell equations, and lead to a\nfinite and discrete (``renormalized\u0027\u0027) quantum electrodynamics (QED).",
"arxiv_id": "quant-ph/9901017",
"authors": [
"H. Pierre Noyes"
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"title": "Thoughts on Commutation Relations and Measurement Accuracy",
"url": "https://arxiv.org/abs/quant-ph/9901017"
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