A new uncertainty principle

TL;DR

This paper rigorously demonstrates that for scattered particles, the true distribution function cannot be determined, but the average over finite velocity solid-angle elements can be calculated, highlighting a fundamental uncertainty principle.

Contribution

It introduces a new uncertainty principle showing the indeterminacy of the true distribution function for scattered particles.

Findings

True distribution function is fundamentally indeterminate.

Average distribution over finite velocity solid-angle can be computed.

Mathematically rigorous proof of the uncertainty principle.

Abstract

By examining two counterexamples to the existing theory, it is shown, with mathematical rigor, that as far as scattered particles are concerned the true distribution function is in principle not determinable (indeterminacy principle or uncertainty principle) while the average distribution function over each predetermined finite velocity solid-angle element can be calculated.