2017/12/31 by John Skilling, Kevin H. Knuth · 1 voice · 2 citations
Arts and Humanities · Mathematics · Physics and Astronomy · #Mathematical and Theoretical Analysis #Philosophy and History of Science #Quantum Mechanics and Applications #math.PR #quant-ph
paper · pdf · doi:10.1002/andp.201800057
published as J. Skilling, K. H. Knuth, 2018. The symmetrical foundation of measure, probability and quantum theories, Annalen der Physik, 1800057 · 17 pages
openalex publication_date 2018/06/13 · arxiv created 2018/08/31 · arxiv updated 2018/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantification starts with sum and product rules that express combination and partition. These rules rest on elementary symmetries that have wide applicability, which explains why arithmetical adding up and splitting into proportions are ubiquitous. Specifically, measure theory formalises addition, and probability theory formalises inference in terms of proportions. Quantum theory rests on the same simple symmetries, but is formalised in two dimensions, not just one, in order to track an object through its binary interactions with other objects. The symmetries still require sum and product rules (here known as the Feynman rules), but they apply to complex numbers instead of real scalars, with observable probabilities being modulus-squared (known as the Born rule). The standard quantum formalism follows. There is no mystery or weirdness, just ordinary probabilistic inference.