The Schrödinger equation is normally introduced as a foundational postulate of quantum mechanics. In this article, we show that Schrödinger evolution arises naturally from the informational throughput framework defined by three relations connecting energy density to a bounded update capacity χ. Without assuming Hilbert space axioms, wavefunction ontology, or spacetime geometry, conservation of informational throughput forces norm-preserving evolution, which uniquely leads to complex phase rotation and the Schrödinger equation. The result suggests that quantum dynamics may emerge from finite informational processing capacity of physical reality.
The Schrödinger equation is normally introduced as a foundational postulate of quantum mechanics. In this article, we show that Schrödinger evolution arises naturally from the informational throughput framework defined by three relations connecting energy density to a bounded update capacity χ. Without assuming Hilbert space axioms, wavefunction ontology, or spacetime geometry, conservation of informational throughput forces norm-preserving evolution, which uniquely leads to complex phase rotation and the Schrödinger equation. The result suggests that quantum dynamics may emerge from finite informational processing capacity of physical reality.
Standard quantum mechanics introduces Hilbert space, unitary evolution, the Born rule, and tensor-product composition as foundational elements of its formalism. General relativity introduces curved spacetime geometry and Einstein field equations. This work develops a conserved informational-throughput framework in which normalized quantum-state structure and Newtonian-limit gravitational time dilation arise from a common set of relations connecting local energy density to finite informational capacity. Starting from the informational demand relation κ = ρ_E V A₀/(ħc), the throughput field χ(r) = √(1 − 2κ/r), and the derived Capacity-Conservation Law (CCL), χ² + L = 1, we develop a unified informational route to a normalized Hilbert-compatible state structure, Schrödinger-type evolution, Born-style probability weighting, Tsirelson-limited shared-capacity correlations, and gravitational time dilation via χ(r) ≡ proper time rate k(r). In this framework, quantum coherence, superposition, entanglement, and probability are interpreted as consequences of conserved informational throughput rather than as independent postulates. The same scalar χ links quantum-state normalization with gravitational clock suppression.
This work presents a reconstruction of quantum mechanics in which Schrödinger-type dynamics emerges from reversible probabilistic evolution rather than being postulated. Starting from a normalized probability density, we impose reversible probability dynamics, Fisher information geometry, and classical correspondence. These compatibility conditions yield coupled real equations equivalent to the continuity equation and the Hamilton–Jacobi equation with an additional information curvature (quantum potential) term. By combining density and phase into a complex amplitude, the Schrödinger equation appears as a compact encoding of reversible statistical flow. The result is mathematically equivalent to the Madelung hydrodynamic formulation and structurally connected to Bohmian mechanics, but derived without assuming Hilbert space, operator axioms, or measurement postulates. The work can therefore be viewed as an information-geometric derivation of quantum dynamics: quantum theory arises as the unique consistent representation of reversible probability flow. Keywords: quantum foundations, quantum reconstruction, emergent quantum mechanics, derivation of the Schrödinger equation, information geometry, Fisher information, Hamilton–Jacobi theory, Madelung formulation, Bohmian mechanics, reversible probability dynamics
Standard quantum mechanics introduces Hilbert space, unitary evolution, the Born rule, and tensor-product composition as foundational elements of its formalism. General relativity introduces curved spacetime geometry and Einstein field equations. This work develops a conserved informational-throughput framework in which normalized quantum-state structure and Newtonian-limit gravitational time dilation arise from a common set of relations connecting local energy density to finite informational capacity. Starting from the informational demand relation κ = ρ_E V A₀/(ħc), the throughput field χ(r) = √(1 − 2κ/r), and the derived Capacity-Conservation Law (CCL), χ² + L = 1, we develop a unified informational route to a normalized Hilbert-compatible state structure, Schrödinger-type evolution, Born-style probability weighting, Tsirelson-limited shared-capacity correlations, and gravitational time dilation via χ(r) ≡ proper time rate k(r). In this framework, quantum coherence, superposition, entanglement, and probability are interpreted as consequences of conserved informational throughput rather than as independent postulates. The same scalar χ links quantum-state normalization with gravitational clock suppression.
This article is the second part of a three-paper sequence developing Ontological Field Theory (OFT) as a unified framework grounding quantum mechanics in foundational ontological principles. The trilogy is structured as follows: Part I — Conceptual Necessity:Why Quantum Mechanics Is Inevitable: Ontological Continuity and the Necessity of Quantum Dynamics establishes that quantum mechanics follows necessarily from minimal requirements on coherent being, independently of specific physical postulates. Part II — Technical Realization:Derivation of the Schrödinger Equation from Ontological Field Theory provides the explicit field-theoretic derivation showing how the Schrödinger equation emerges as the non-relativistic limit of a covariant ontological field. Part III — Critical Context:Why Classical Physics Is an Approximation: Decoherence, Coarse-Graining, and the Limits of Determinism explains why classical determinism and trajectories arise only as emergent, approximate descriptions of fundamentally quantum and relational dynamics. Each article is logically self-contained, but the full argument is distributed across the three contributions. The conceptual analysis motivates the mathematics; the mathematics grounds the physics; and the critical examination situates classical intuition as a limiting case rather than a foundation. The papers are intended to be read as a coherent whole. We argue that quantum mechanics is not an arbitrary empirical framework but an inevitable consequence of minimal ontological requirements. Assuming only that being must exist necessarily, remain consistent, be relational, and admit self-reference, we show that classical deterministic physics is structurally insufficient. Quantum dynamics emerges as the unique low-energy realization of coherent ontological continuity. This work complements explicit field-theoretic derivations by clarifying why quantum mechanics could not have been otherwise.
This paper derives Schrödinger evolution as a structural consequence of coherent persistence rather than as a postulate of quantum mechanics. Starting from minimal requirements for viable propagation—linearity, norm preservation, and continuity—we show that admissible evolution must be unitary and generated by a self-adjoint operator. The resulting Schrödinger equation describes reversible propagation within the space of viable states, while irreversible selection arises separately from the return operation. This separation clarifies the relation between unitary dynamics and measurement without introducing collapse mechanisms or stochastic dynamics. Schrödinger evolution thus emerges as the unique form of continuous, coherence-preserving propagation compatible with structural closure and return, completing the dynamical layer of the Structural Coherence framework.
This work explores a simple question: why does nature end up using equations that look quantum? Instead of starting from the usual quantum axioms (wavefunctions, operators, measurement rules), we begin with three much weaker and more intuitive requirements: • physical evolution should be reversible • distinguishability between states should have a consistent geometry • classical mechanics must appear as a limiting case From only these conditions, probability flow is forced to acquire a phase degree of freedom, and an information–geometric curvature term inevitably appears. When the two are combined, the resulting dynamics takes the form of the Schrödinger equation. The point of the paper is not to claim that quantum mechanics is fully derived, nor that measurement theory is explained. Rather, it shows that once reversible probabilistic dynamics is required to be geometrically consistent, quantum-type evolution becomes extremely hard to avoid. In this sense, the wavefunction can be interpreted not as a mysterious physical object, but as a natural coordinate system describing consistent probability flow.