What question did this study set out to answer?

The aim is to derive quantum dynamics and Lorentz invariance from the Coverage Principle.

April 25, 2026Open Access

Deterministic Growth Dynamics of Causal Graphs IV: Derivation of Quantum Mechanics

Key Points

The aim is to derive quantum dynamics and Lorentz invariance from the Coverage Principle.
Developing a deterministic mechanism for quantum uncertainty based on operational ambiguity.
Deriving fundamental principles like the uncertainty relation and the Born rule from a variational principle.
Exploring the compatibility of various mathematical structures with quantum mechanics.
The uncertainty relation and the Born rule are derived without assuming stochasticity.
Unitary evolution and the Schrödinger equation are rigorously formulated.
Lorentzian signature (− + ++) and the group SO(3, 1) are established as compatible structures.

Abstract

The present paper continues the DGDCG I–III programme by deriving quantum dynamics and Lorentz invariance from a single axiom — the Coverage Principle. A deterministic mechanism for the emergence of quantum uncertainty is proposed for the first time: it is interpreted as the operational ambiguity of coarse-graining at finite structural resolution r∗, rather than as fundamental stochasticity. On this basis, the uncertainty relation, the Born rule, unitary evolution, and the Schrödinger equation are rigorously derived. The Lorentzian signature (− + ++) and the group SO(3, 1) emerge as the unique structure compatible with the complex phase of the geometric action and the irreversibility of Frontier growth. All results follow from a variational principle without additional physical postulates.

Deterministic Growth Dynamics of Causal Graphs IV: Derivation of Quantum Mechanics

Key Points

Abstract

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