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Results for “distinction” 5 papers
Adelic. Adeles, restricted products and adelic constructions Tagged papers: 45.
Quantum Statistics from the Adelic Product Formula: The Squarefree Origin of the Fermi-Dirac/Bose-Einstein Distinction
Why are there two quantum statistics, and only two, in three spatial dimensions? This paper reads the Bose–Einstein and Fermi–Dirac occupation distributions as the maximum-entropy solutions of one lattice with two multiplicity rules. On the unrestricted integer lattice the Euler factor at each prime…
The Self-Referential Scalar Family: e, the Half-Turn, and the Unification of Information Theory, Statistics, Thermodynamics, and QND Measurement in the Adelic Picture
Standard information theory measures uncertainty at the archimedean place; the adelic program extends it to all completions of the rationals, carrying a p-adic valuation entropy alongside Shannon entropy. This paper shows that the two most familiar distributions of statistical mechanics are already…
The Adelic Distinction: Physics as Automorphic Representation Theory on the Idele Class Group
Ostrowski's theorem (1916) establishes that every completion of the rational numbers $\mathbb{Q}$ is either the real Archimedean place $\mathbb{R}$ or a $p$-adic non-Archimedean place $\mathbb{Q}_p$. Physics has, for a century, restricted itself to the Archimedean completion alone — using real…
Invariant Patterns and the Adelic Refactoring of Fundamental Physics
This paper proposes a systematic refactoring of fundamental physics around a single organizing principle: physics is the study of invariant patterns under specified classes of transformations. Stripping away anthropocentric conventions --- measurement units and the privileged status of Archimedean…
The Adelic Physics Program: Epistemological Foundations and Communications Framework
The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is ℚ (the rational numbers), not ℝ (the real numbers). Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of ℚ be physically meaningful, transforming the…
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