A Critical Treatise on the Load-Bearing Assumptions of Quantum Mechanics, Thermodynamics, and Computation

Abstract

The electron is the most precisely measured particle in physics and the workhorse of modern computation, yet the theoretical structure in which it lives rests on a series of assumptions that are load-bearing but rarely interrogated: the complex Hilbert-space postulate, the spin-statistics theorem's dependence on $3+1$ dimensions and Poincaré invariance, the Archimedean real-number valuation of every measured quantity, the thermodynamic foundations of irreversible computation, and the identification of the electron itself as a fixed, elementary object rather than a vacuum- and environment-dependent excitation. This treatise does not reject any of these assumptions; it maps them. Each assumption is stated explicitly, the edifices built on it are identified, its confirmed predictions are separated from its postulates, alternative formulations are catalogued, and falsifiability conditions are defined. Why a reader should care: every one of the assumptions examined here bears directly on a live technological or experimental frontier — energy-efficient computation, topological quantum computing, high-temperature superconductivity, precision metrology, and quantum gravity — and several of them (the reality of quasiparticles with fractional charge and statistics, the failure of the spin-statistics theorem in $2+1$ dimensions, the emergence of particles from different vacua) are already known to be false as universal statements. Premise-depth disclosure: the claims of this treatise are analytical and taxonomic rather than axiomatic-deductive; it introduces no new physical postulate, and its conclusions are as deep as the published physics it cites — its own unanalyzable primitives are ordinary set theory, the standard model of measurement practice, and the requirement of empirical adequacy, all named here rather than hidden. The treatise concludes with a consolidated falsifiability map and a registry of open questions, so that the assumptions themselves can be promoted from articles of faith to objects of experiment. Keywords: quantum foundations, spin-statistics theorem, quasiparticles, Landauer's principle, Ostrowski's theorem, Hilbert space, anyons, thermodynamics of computation, premise depth, falsifiability ---