DNA and the double helix: statistical equilibrium and Neumann's principle

TL;DR

This paper provides a rigorous proof of Neumann's principle in crystallography using group theory and quantum statistical mechanics, reinforcing the fundamental understanding of crystal symmetry in x-ray diffraction.

Contribution

It offers the first plausible proof of Neumann's principle, clarifying its validity through mathematical and physical analysis.

Findings

Neumann's principle is valid under certain conditions.

A correction to previous assumptions is proposed.

The proof links symmetry with quantum statistical mechanics.

Abstract

Neumann's principle (that the symmetry of a crystal measurement cannot be lower than that of its point-group) is a corner- stone of crystallography: were it false, then the technique of x-ray diffraction (double-helix, DNA) might well not exist. The literature variously regards its truth as obvious, intuitive, axiomatic or even impossible [10], without further analysis or proof. After identifying and correcting a false lead/start, we give a plausible proof of Neumann's principle, using group theory and quantum statistical mechanics.