Title : From quantum structure to chemical and biochemical laws: A unified projection geometry framework for thermodynamics, kinetics, reactions, transport, and magnetism
Abstract:
Contemporary chemistry, biochemistry, and physics are built upon a collection of highly successful yet conceptually fragmented models. Electrons are alternately described as particles, waves, charge densities, quasiparticles, or transient carriers depending on experimental and computational context. Thermodynamics, kinetics, transport, and magnetic response emerge phenomenologically from microscopic theory, while biochemical processes—such as metabolism, enzymatic catalysis, protein folding, and membrane transport—are typically treated as domain-specific extensions rather than as structurally grounded consequences of quantum theory. Although these descriptions yield accurate predictions, they lack a unified structural explanation for why such diverse representations coexist and remain simultaneously valid.
This work presents a unified projection-geometry framework (B–Chem) and related/restricted biological framework that reorganizes chemical, biochemical, and physical phenomena without modifying established quantum mechanics, thermodynamics, or the Standard Model. The central premise is that physical and biochemical entities are not primitive particles or fixed objects, but stratified algebraic fiber objects defined over a contextual manifold. Observable quantities arise exclusively through admissible projections, which select context-compatible components of the underlying structure. Projection, rather than force or dynamics, is treated as the primary organizing operation.
Within this framework, the chemically relevant electron is not assumed to be a permanently existing particle. Instead, it is interpreted as a context-dependent projection event of an underlying field–geometry state. Charge density, phase coherence, spin, transient structure, and relativistic compatibility occupy distinct algebraic strata, with familiar electron models—point particles, Schrödinger waves, densities, spinors, quasiparticles, and effective Kohn–Sham electrons—emerging as stable operational projections selected by experimental or environmental conditions. Constants such as Avogadro’s number and the Faraday constant retain their full quantitative role but are reinterpreted as projection-scaling relations, rather than as evidence of fixed microscopic particle inventories.
Thermodynamics, chemical kinetics, reaction mechanisms, transport, and magnetic response emerge naturally as geometric consequences of projection admissibility and projection curvature. Entropy, free energy, irreversibility, and rate laws are shown to arise from structural restriction of admissible projections rather than from additional microscopic assumptions. Transport and diffusion appear as projection-mediated redistribution of admissible states, while magnetic and spin-dependent phenomena arise from quaternionic and split-algebraic orientation residues that remain compatible with chemical observability.
The framework extends consistently to biochemistry by restricting admissible projections to biologically meaningful regimes. Metabolic pathways, including glycolysis, carbohydrate chemistry, lipid organization, membrane structure, and protein behavior are interpreted as chemically admissible projections under biological constraints. Protein folding and conformational dynamics are reformulated as admissible projection collapse and structured motion on low-dimensional manifolds, resolving classical paradoxes without altering thermodynamic descriptions. Enzymatic catalysis, regulation, and transport arise from controlled modulation of projection constraints rather than from ad hoc mechanistic assumptions.
Across all scales—from subatomic structure to biochemical organization—the framework preserves standard equations and experimentally validated predictions while providing a single structural ontology. The result is a conservative yet unifying reinterpretation that explains why existing models work, how they are related, and where their domains of validity arise, without introducing new forces, particles, or modified dynamics.
