What question did this study set out to answer?

The aim is to demonstrate that the Schrödinger equation can be derived from fossil causal structure rather than being postulated.

May 24, 2026Open Access

The Schrödinger Equation as a Theorem v2

Key Points

The aim is to demonstrate that the Schrödinger equation can be derived from fossil causal structure rather than being postulated.
Derivation of the imaginary unit i from the phase boundary surface Σ.
Calculation of the reduced Planck action quantum ℏ as minimal action of closed oriented rotation on Σ.
Identification of the Hamiltonian operator Ĥ as the fossil energy density operator.
i is derived from the sign change of metric time on phase boundary surface Σ.
The action quantum ℏ is established as a minimal action associated with closed rotations.
The Hamiltonian operator Ĥ is directly identified as the operator representing fossil energy density.

Abstract

The Schrödinger equation iℏ · ∂ψ/∂τ = Ĥψ contains three elements that in standard quantum mechanics are not derived but postulated: the imaginary unit i, the reduced Planck action quantum ℏ, and the Hamiltonian operator Ĥ. This supplement shows that all three follow from the fossil causal structure. The phase boundary surface Σ =x ∈ M | tₘ (x) · tC (x) / tP² = −1 delivers i through the sign change of the metric time. The action quantum ℏ follows as the minimal action of the closed oriented rotation on Σ. The Hamiltonian Ĥ is directly the fossil energy density operator ρₕist. The Schrödinger equation is not a postulate - it is a theorem of the fossil causalstructure.

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