A Finite-Register Framework for Mathematical Physics (The Geometrical Universe Series)
English | October 17, 2026 | ASIN: B0HN94TT7Z | 320 pages | Epub | 5.79 MB
What does it take to turn a finite mathematical structure into a testable physical theory?In A Finite-Register Framework for Mathematical Physics, Gerald W. Scanlon investigates this question through finite collections of states and modes, their symmetries, and the maps that connect registers of different sizes.Beginning with finite counts, centered geometry, and operator algebras, the book develops a framework for examining which structures can be preserved across registers-and which require additional assumptions. Across twenty-five chapters, it explores applications to quantum dynamics, measurement, entanglement, topology, field theory, gravity, and cosmology.Topics include:* Finite-register constructions, symmetry, and cross-register compatibility* Quantum measurement, decoherence, locality, and information geometry* Coarse graining, tensor networks, and quantum error correction* Scalar fields, fermions, gauge structure, and Standard Model consistency* Causal reconstruction, relational time, black holes, and cosmological models* Parameter selection, physical calibration, and falsifiable predictionThroughout, the book makes the assumptions behind each construction explicit. Exact results are distinguished from conditional extensions, and numerical correspondences are assessed separately from independent predictions. Boundary and no-go results identify what the finite framework leaves undetermined and help define the requirements for further progress.The final chapters examine how mathematical models acquire empirical meaning: through specified observables, shared parameters, quantified uncertainty, and tests capable of rejecting a proposed physical connection. The framework's unresolved physical questions form an explicit research agenda.Written for researchers and advanced graduate students in mathematical physics, quantum foundations, quantum information, and related fields, this standalone monograph assumes familiarity with linear algebra and quantum mechanics. No knowledge of the author's previous books is required.For readers investigating finite approaches to fundamental physics, it offers a structured way to examine what a model establishes, what it assumes, and what would make it testable.
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