SPACE–ENERGY EQUIVALENCE A Unified Physical Framework Derived from a Single Ontological Postulate

The existing foundational theories of physics — thermodynamics, general relativity, quantum mechanics, and electromagnetism — each achieve extraordinary precision within their own domains, yet they remain mutually fragmented. No single framework currently derives them from a common ontological foundation. This paper proposes that the unifying principle is concealed within the most universal phenomenon in nature: thermal expansion and contraction. A controlled bottle-and-balloon experiment establishes three inescapable facts at constant particle count: energy increases, volume increases, and the additional space is matter-free vacuum. The only logically consistent conclusion is that energy and space are interconvertible. Axiom P₀ (space is a form of energy) formalises this conclusion. From P₀ and the definition of pressure as the rate of change of space energy with volume, the master equation P = αε follows by two steps of elementary calculus, where ε is the local energy density and α ≡ Eₛpace/Eₜotal is the space-energy fraction. The canonical values of α are derived without free parameters: α₀ = 1/3 (free radiation, from three-dimensional isotropy), α = 2/3 (monatomic ideal gas, from degree-of-freedom counting), α = 2/5 (diatomic ideal gas). The complete relativistic function α (s) = (2+s²) /3 (1+s²), where s ≡ ε/ (nmc²), is derived exactly from the relativistic virial theorem with no free parameters, covering the full range from cold gas to the quark–gluon plasma (RHIC agreement 1. 2% at s ≈ 30). From this single foundation, the paper derives: all four laws of classical thermodynamics (§4) ; Newton's law of gravitation and the equivalence principle as an exact theorem (§5) ; Kepler's third law, verified against all eight planets to better than 0. 03% (§5. 5) ; post-Newtonian gravitational corrections via the Lovelock uniqueness theorem (§6†) ; gravitational wave propagation at exactly c with a distinctive scalar breathing polarisation mode absent in general relativity (§7) ; the Schrödinger equation from a variational principle (§10) ; the Bohr radius and hydrogen ground-state energy with errors of 0. 10% and 0. 07% respectively, zero free parameters (§11) ; wave–particle duality and the double-slit experiment without paradox (§11) ; the Born rule as a theorem rather than a postulate (§11) ; the boson–fermion dichotomy from the exact topological theorem π₁ (SO (3) ) = ℤ₂ (§12) ; all four Maxwell equations from a charge ontology (§14) ; and key results at the Standard Model interface including Nc = 3 from anomaly cancellation and Higgs mass naturalness (§15). Three independently falsifiable experimental predictions are stated (§18): (P1) a scalar breathing polarisation in gravitational waves, distinguishable from GR, detectable by Einstein Telescope; (P2) a T⁴-dependent enhancement of nuclear fusion cross-sections; (P3) quantum nonlinearity in extreme-density matter. All supplementary assumptions are labelled explicitly. All open problems are catalogued precisely in §19–20. The complete derivation chain from P₀ to all results, and the open-problems dependency tree, are given in §21.