arXiv:2609.24269

On the Born rule in a new quantum approach

Inge S. Helland

quant-phSubmitted Sep 21, 2026• Announced Sep 22, 2026• 0 citations• Revised Oct 5, 2026 (v4)

Abstract

IIn the context of a new approach towards quantum foundation, the Born rule is proved under weak conditions through several steps. One step gives a generalized likelihood principle, a result of independent interest. The main condition behind the Born rule is a consequence of the likelihood principle of statistics. This principle is discussed from several points of view. The whole approach leads to a simpler state concept than the traditional one in finite-dimensional quantum mechanics. It also provides links to statistical theory and to Andrei Khrennikov's macroscopical quantum-like models.

Comments: 17 pages

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