The Oscillation Principle

Entanglement Compression Theory (ECT) derives probability, deterministic quantum dynamics, and spacetime curvature from a single structural requirement: existence must persist as motion, and the simplest persistent motion is oscillation. From this requirement, probability, geometry, and general relativity arise as deterministic consequences rather than independent postulates.

This paper introduces the Oscillation Principle: static states are physically untenable, and oscillation is the only realizable form of existence. Energy, motion, and wave behavior are not distinct categories but different descriptions of a single oscillatory act, expressed concisely as waves = motion = energy. From this premise, entanglement, compression, and probabilistic structure follow as necessary consequences.

Planck units, historically treated as dimensional cutoffs, are reinterpreted as descriptors of the minimal oscillatory event: ℓₚ as spatial span, tₚ as temporal recurrence, and Eₚ as causal amplitude. These quantities describe the first physically meaningful wavelength, period, and amplitude from which dimensional extension emerges. Curvature appears when compression reaches its entropy boundary, linking oscillatory structure to geometric response.

Within ECT, the local speed of light arises from compression through c(x)² = T(x)/C(x), where T(x) denotes tension and C(x) compression. Probability emerges through deterministic energy partition, and curvature arises from compression gradients. The Oscillation Principle unifies these relations and provides a geometric interpretation of ℓₚ, tₚ, and Eₚ as properties of a primordial oscillatory event.

This paper serves as the conceptual foundation of Entanglement Compression Theory. Readers seeking formal derivations, operator structure, and falsifiability protocols should consult Theory of Derived Probability and Entanglement Compression (DOI: 10.5281/zenodo.15786696) and its Mathematical Foundations companion.

For a visual demonstration of deterministic structure emergence under the Primordial Wave Equation (PWE) and its prediction of dark-matter-like halos, see:
https://compressiontheoryinstitute.org

Version 5 (February 2026).
Refined conceptual language to align fully with the Oscillation Principle, clarifying the non-static ontology and the interpretation of Planck units as descriptors of minimal oscillatory structure. No formal equations, claims, or empirical predictions were altered.

Version 4 (February 9, 2026).
Replaced incorrect DOI in header.

Version 3 (January 2026).
Introduced a constraint-based structural justification of the Oscillation Principle, clarifying why persistent motion necessarily takes oscillatory form. No physical claims, formal results, or conclusions were altered.

Version 2 (January 2026).
Minor editorial alignment to clarify axiomatic classification, canonical ordering within Entanglement Compression Theory, and language consistency with later foundational papers. No substantive claims, derivations, or conclusions were altered from the original 2025 release.