A Variance Inequality for Meromorphic Measurement Functions under Exterior Probability

Swagatam Sen

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arXiv · 2007.05131

A Variance Inequality for Meromorphic Measurement Functions under Exterior Probability

Swagatam Sen

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Abstract

The problem of measuring an unbounded system attribute near a singularity has been discussed. Lenses have been introduced as formal objects to study increasingly precise measurements around the singularity and a specific family of lenses called Exterior probabilities have been investigated. It has been shown that under such probabilities, measurement variance of a measurable function around a 1st order pole on a complex manifold, consists of two separable parts - one that decreases with diminishing scale of the lenses, and the other that increases. It has been discussed how this framework can lend mathematical support to ideas of non-deterministic uncertainty prevalent at a quantum scale. In fact, the aforementioned variance decomposition allows for a minimum possible variance for such a system irrespective of how close the measurements are. This inequality is structurally similar to Heisenberg uncertainty relationship if one considers energy/momentum to be a meromorphic function of a complex spacetime.

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Swagatam Sen. 2020-07-10. A Variance Inequality for Meromorphic Measurement Functions under Exterior Probability. https://arxiv.org/abs/2007.05131

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