Foundational Physics

Principia Metaphysica builds upon well-established physics. This section provides detailed explanations of the foundational equations from which the framework derives. Each formula can be traced back to experimentally verified physics.

Established Physics Derived in PM PM-Specific

General Relativity & Gravity

Established

Einstein Field Equations

G_μν + Λg_μν = 8πG T_μν

Established

Einstein-Hilbert Action

S = ∫ d⁴x √|g| R

Established

Ricci Tensor & Scalar

R_μν, R = g^μνR_μν

Quantum Field Theory

Established

Dirac Equation

(iγ^μ∂_μ - m)ψ = 0

Established

Dirac Lagrangian

ℒ = ψ(iγ^μ∂_μ - m)ψ

Established

Clifford Algebra

{γ^μ, γ^ν} = 2g^μν

Established

Yang-Mills Theory

ℒ = -¼F_μν^aF^aμν

Extra Dimensions & Unification

Established

Kaluza-Klein Theory

Dimensional reduction: 13D → 6D → 4D

Established

G₂ Manifolds

7D holonomy manifolds for M-theory

PM Internal Geometry Established

Calabi-Yau Manifolds

Ricci-flat Kähler manifolds (comparison)

Established

SO(10) Grand Unification

16-dimensional spinor representation

Thermodynamics & Statistical Mechanics

Established

Boltzmann Entropy

S = k_B ln Ω

Established

KMS Condition

Thermal equilibrium states

Established

Tomita-Takesaki Theory

Modular automorphisms

PM-Derived Formulas

These formulas are derived within Principia Metaphysica from the foundational physics above.

PM-Specific

Pneuma Lagrangian

Ψ_P(iΓ∇ - m)Ψ_P

Derived

13D Einstein-Hilbert

M_*¹¹R

Derived

Generation Formula

n_gen = χ/24

PM-Specific

Thermal Time Relation

t = α_T ⋅ S