The Necessity of Natural Physics, Volume I asks a simple but demanding question: when separate physical systems are combined, which features of their joint description are truly unavoidable, and which belong only to familiar convention? Rather than assuming standard quantum mechanics from the outset, the book reconstructs the common structural ground of composite systems and then follows every serious surviving alternative—including classical, complex, real, quaternionic, Jordan-algebraic, generalized probabilistic, and non-tensor forms—until each is either excluded, identified with another, or left open for further physical testing. Existing physics therefore remains fully admissible, but it is no longer granted priority without proof. The aim is not to replace successful theory by speculation, but to determine whether nature could have been otherwise—and, if not, why not.
The Necessity of Natural Physics, Volume I asks a simple but demanding question: when separate physical systems are combined, which features of their joint description are truly unavoidable, and which belong only to familiar convention? Rather than assuming standard quantum mechanics from the outset, the book reconstructs the common structural ground of composite systems and then follows every serious surviving alternative—including classical, complex, real, quaternionic, Jordan-algebraic, generalized probabilistic, and non-tensor forms—until each is either excluded, identified with another, or left open for further physical testing. Existing physics therefore remains fully admissible, but it is no longer granted priority without proof. The aim is not to replace successful theory by speculation, but to determine whether nature could have been otherwise—and, if not, why not.
This book is the third stage of a continuous research programme and is not intended to be read in isolation. To understand its premises and dependency structure, readers should first read The Necessity of Structure, followed by The Necessity of Quantum Structure. Across eight interdependent volumes spanning more than 1,800 pages, The Admissibility of Natural Physics asks how far modern physics can be reconstructed without simply assuming its familiar ingredients from the outset. Taking the previously established single-system quantum framework as its starting point, it develops a step-by-step account of composite systems, interaction, identical particles, locality, quantum fields, gauge structure, particle sectors, physical parameters, gravity, and cosmology. At every stage, the work distinguishes what is genuinely derived from what is measured, assumed, conditional, representational, or still unresolved. It culminates in a unified master constraint and a frozen prospective empirical testing protocol, while insisting that unsupported conclusions must remain open rather than being forced into an artificially complete theory.
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
The Necessity of Natural Physics, Volume II reconstructs physical process structure without assuming primitive particles, fields, spacetime, Hamiltonians, environments or quantum formalism. Beginning from the survivor family established in Volume I, it derives and classifies processes, interaction, reversibility, generators, ancillary stability, instruments, dilation, reduced dynamics, memory, resources, carrier identity, exchange, statistics and occupation across classical, quantum and generalized structural branches. A complete tribunal then excludes inconsistent constructions, merges predictively equivalent representations and carries the remaining process-world families forward to the reconstruction of regional physics.
This paper fails to derive quantum mechanics from a few simple postulates. However, it gets very close, and does so without much exertion. More precisely, I obtain a representation of finite-dimensional probabilistic systems in terms of Euclidean Jordan algebras, in a strikingly easy way, from simple assumptions. This provides a framework within which real, complex and quaternionic QM can play happily together and allows some (but not too much) room for more exotic alternatives. (This is a leisurely summary, based on recent lectures, of material from the papers arXiv:1206:2897 and arXiv:1507.06278, the latter joint work with Howard Barnum and Matthew Graydon. Some further ideas are also explored, developing the connection between conjugate systems and the possibility of forming stable measurement records and making connections between this approach and the categorical approach to quantum theory.).
This paper extends the results of Hyperbolic Degree Bounds Signaling Dimension in Generalized Probabilistic Theories (Zenodo DOI: 10.5281/zenodo.22946778), which established that the signaling dimension of every canonical finite-dimensional Euclidean Jordan algebra (EJA) equals its Jordan rank. We investigate the consequences of this single-system identity under recursive composition. Combining the injectivity of local effect-space tensor products in standard non-signaling composites with the no-hypersignaling (NH) principle, we prove that the normalized linear-dimension ratio η_lin(S) = dim(S)/sign.dim(S)² is supermultiplicative. Consequently, any local excess above unity is amplified under repeated composition. For canonical EJA composites satisfying the structural axioms of Barnum, Graydon, and Wilce, product Jordan frames and NH enforce multiplicativity of composite rank. Together with established EJA classification results, this yields the conditional recursive constraint dim(J) ≤ rank(J)². Within this framework, quaternionic matrix Jordan systems and spin factors V_n with n ≥ 4 are excluded, while real matrix systems remain subcritical and complex matrix systems exactly saturate the bound. We also obtain finite-copy exclusion criteria and identify exact NH violations in specified EJA composition rules, including doubled complex and quaternionic composites. The analysis does not assume local tomography. Its conclusions are conditional on NH and the stated composition axioms; they do not establish unique selection of complex quantum theory. This work provides a compositional continuation of the preceding hyperbolic-signaling result, connecting classical simulation requirements to structural constraints on Jordan probabilistic theories.