Foundations
Established Physics That PM Builds Upon
This page showcases the well-established equations, constants, and experimental measurements from the scientific literature that Principia Metaphysica builds upon. These are NOT predictions or new formulas—they are the proven foundation of modern physics.
... Foundational Equations
... Physics Domains
Foundational Equations — Standard Notation
Foundational Equations — EML Mirror Phase Operator Form
Einstein Field Equations
$$G_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$
The Einstein field equations relate the curvature of spacetime (encoded in the Einstein tensor
Gμν) to the energy-momentum content (Tμν). The cosmological constant Λ
drives the accelerated expansion measured by DESI 2025, consistent with the PM prediction
w₀ = −23/24 ≈ −0.9583.
G_uv = ops.sub(ops.ricci_tensor(g_uv), ops.mul(ops.div(1,2), ops.mul(ops.ricci_scalar(g_uv), g_uv)))
EFE = ops.add(G_uv, ops.mul(Lambda, g_uv)) == ops.mul(ops.div(ops.mul(8, pi_val), ops.pow(c, 4)), T_uv)
EML Mirror Phase form:
Curvature ops (ops.ricci_tensor, ops.ricci_scalar) act on the metric tensor g_uv.
The cosmological constant term ops.mul(Lambda, g_uv) enters as an additive operator.
In PM: Λ is not a free parameter — it is constrained by the b₃=24 topology via
Lambda = ops.inv(ops.mul(b3, Vol_V7)) (vacuum residue after G₂ compactification).
Mirror Phase Mathematics form — same numerical result as standard notation.
Dirac Equation
$$(i \gamma^\mu \partial_\mu - m)\psi = 0$$
The Dirac equation describes relativistic spin-½ fermions. In the PM framework, the
4096-component Primordial Spinor Field ΨP arises from the Clifford algebra
Cl(26,1) of the M27(24,1,2) bulk. The three fermion generations
(ngen = χeff/(4·b₃) = 144/48 = 3) are spectral residues of the
Dirac operator on the G₂ holonomy manifold V₇.
dirac_op = ops.sub(ops.mul(ops.mul(i_unit, gamma_mu), partial_mu), m_fermion)
dirac_eq = ops.apply(dirac_op, psi) == eml_scalar(0)
EML Mirror Phase form:
The Dirac operator is built from ops.mul of the imaginary unit, gamma matrices, and
the partial derivative operator, minus the mass term. In PM:
n_gen = ops.div(chi_eff, ops.mul(eml_scalar(4), b3))
= ops.div(eml_scalar(144), eml_scalar(48)) = eml_scalar(3) — three generations
from G₂ topology, not a free parameter.
Mirror Phase Mathematics form — same numerical result as standard notation.
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