§ 4

Domains

Ten domain deep-dives — the load-bearing frameworks of current physics, audited one by one: formalism, domain of validity, known breakdowns, and the precise senses in which each framework yields. Cross-cutting structure lives in the Theory Map; the places where the frameworks clash rather than nest are catalogued in Gaps & Contradictions.

Every claim on these pages carries one of the five epistemic tags (§14.1): ESTABLISHED INFERENCE SPECULATIVE OPEN CONTESTED

1. 4.1Quantum MechanicsThe non-relativistic Hilbert-space core: stable formalism, contested interpretation.
2. 4.2Quantum Field TheoryQFT's phenomenal empirical success atop partly unproven mathematical foundations — the tension that organizes the page.
3. 4.3General RelativityGravity as Lorentzian geometry: formalism, exact solutions, singularity theorems, and the precise senses in which the theory breaks down.
4. 4.4Classical MechanicsDeterministic mechanics in its three equivalent formulations: geometry, symmetry–conservation, integrability and chaos, and where the framework yields.
5. 4.5ThermodynamicsEnergy, heat, work, and entropy, with modern extensions to fluctuation theorems, information thermodynamics, and black-hole thermodynamics.
6. 4.6Statistical MechanicsThe bridge from reversible microdynamics to irreversible thermodynamics via probability over microstates and typicality.
7. 4.7CosmologyThe ΛCDM concordance model, its thermal history, live empirical tensions (H0, S8, w(z)), and deep foundational problems.
8. 4.8Particle Physics & the Standard ModelThe Standard Model as a chiral gauge theory: the most precisely tested theory in science, and by consensus an effective one awaiting completion.
9. 4.9Information Theory & PhysicsFour strata of decreasing certainty linking information and physics: Shannon, quantum information, thermodynamics of computation, gravity.
10. 4.10Mathematics for PhysicsMathematics as the substrate of physical theory, audited layer by layer for theorem versus productive heuristic.