Gravity and Relativity from Boundary-Equivalent Lightcones in Information–Pressure Theory

Description Gravity and Relativity from Boundary-Equivalent Lightcones in Information-Pressure Theory This paper derives classical gravitational phenomena and special relativity from two principles: the Information-Pressure Theory (IPT) axioms (entropy–area capacity bounds on null surfaces) and the Boundary-Equivalence Lightcone Axiom (BELA), which defines physical equivalence as identity of null-boundary records. Key results: Gravity as boundary normalization: The gravitational field emerges as a lapse function N(x) relating local clocks to reference time. Gravitational acceleration is g = −c²∇ln N. Light bending and Shapiro delay: Derived as Fermat-principle optics in a graded refractive index n(x) = A(x)/N(x), yielding the standard deflection angle α = 4GM/(c²b). Einstein equation from Clausius balance: Local horizon thermodynamics with entropy capacity S/A = k_B/(4Λ²) yields the null-projected Einstein equation, fixing G = c³Λ²/ℏ. Quantum-gravity bridge: Relative entropy monotonicity under boundary coarse-graining implies a quantum focusing inequality (QFC-shaped); its semiclassical limit recovers Raychaudhuri focusing. Special relativity: Lorentz transformations emerge as the automorphisms preserving null-boundary structure (null-cone preservation implies L^T η L = η). Mass–energy equivalence: E = mc² follows from Unruh temperature and modular Hamiltonian structure on local Rindler horizons. The IPT axioms are derived from first principles (information-theoretic reasoning without presupposing general relativity); a separate semiclassical derivation provides a modern-physics consistency check. The gravitational coupling G is not an independent input but emerges from the entropy–area resolution scale Λ. Keywords Information-Pressure Theory, IPT, BELA, Boundary-Equivalence Lightcone Axiom, emergent gravity, holographic principle, entropy bounds, null surfaces, horizon thermodynamics, Jacobson thermodynamics, Einstein equation, Raychaudhuri equation, quantum focusing, special relativity, Lorentz invariance, mass-energy equivalence, Planck scale, gravitational coupling, causal diamonds, null congruences, generalized entropy