Draft:Entanglement Compression Theory

• Comment: AI generated, plus primary sourced original research. Theroadislong (talk) 12:05, 2 November 2025 (UTC)

• Comment: please remove the external links from the body of the draft, we don't use them. Theroadislong (talk) 11:58, 2 November 2025 (UTC)

---

Entanglement Compression Theory

Field	Theoretical physics

Introduction

Entanglement Compression Theory (ECT) is a framework in theoretical physics proposed by William Andrew Lawrence in 2025. It describes a deterministic link between quantum mechanics and general relativity through wavefunction compression. The framework defines a real, multiplicative compression operator, ℂ[Ψ], that acts on wave amplitude to describe local changes in density and curvature. Probability arises as a consequence of how energy divides among distinct states of the wave function. Unlike the Copenhagen interpretation or the Many-worlds interpretation, ECT describes indeterminacy as the result of incomplete observation within a deterministic system. Its core idea, stated as “Static is not a possible state. To be is to oscillate” and “The only way for anything to be is to move. And the simplest possible motion? An oscillation - a wave,” defines the causal relationship between motion and geometry. ECT and its mathematical formalism are published in open-access form on Zenodo and through the Compression Theory Institute.

Background

The search for a unified description of quantum mechanics and general relativity has led to many interpretations of quantum theory, including probabilistic models such as the Copenhagen interpretation and deterministic formulations like the Pilot-wave theory and the Many-worlds interpretation. One recurring issue among these is the statistical postulate known as the Born rule, which defines how probability is assigned to quantum states but offers no underlying causal explanation. ECT addresses this gap. Lawrence proposes that probability and curvature share a common origin within the structure of the wavefunction itself. The framework treats compression as a physical process linking energy distribution, curvature, and measurable outcomes. ECT builds on a deterministic principle stating that existence equals motion, and motion equals oscillation. Thus, spacetime geometry emerges from oscillatory compression, and quantum probability results from energy division rather than statistical assumption. The Born rule is presented as a derived outcome instead of an independent postulate.

Core concepts

Oscillation Principle

The Oscillation Principle states that existence, motion, and oscillation are equivalent. Lawrence defines oscillation as the simplest continuous motion capable of sustaining existence, treating energy as the measurable form of that motion. Physical structure is described as the stable interference of interacting waves.

Primordial Wave Equation

The Primordial Wave Equation (PWE) combines the quantum kinetic term −αₙ∇²Ψ with a real, multiplicative compression functional ℂ[Ψ]. The equation governs amplitude, density, and curvature simultaneously, maintaining deterministic evolution without statistical postulates.

Compression Operator

The compression operator ℂ[Ψ] acts on the wave amplitude to express local density variation. It is defined as a real functional of logarithmic form −c₀ ln(ρ₁ / ρ₀) + c₂ ∇² ln(ρ₁), linking matter concentration to curvature through measurable gradients. Because the operator is real, probability current is conserved and locality is preserved.

Geometric Link to Curvature

From the compression field, Lawrence derives a tensor C_{μν} = ∇_{μ}∇_{ν}(−ln ρ₁) that modifies the effective metric g^{eff}_{μν} = g_{μν} + κ̃ L_*² C^{(sym)}_{μν}. The relation provides a direct connection between wave-amplitude density and spacetime curvature, recovering general relativity as the weak-compression limit.

Born-Rule Derivation

ECT derives the Born rule from deterministic energy division. Measurable outcomes correspond to the ratio of energy in each resolvable state, pᵢ = Eᵢ / E_total = ⟨Ψ, Pᵢ Ψ⟩. Probability arises from conserved energy partition rather than intrinsic randomness, reproducing the standard quantum weights as a consequence of conservation.

Mathematical framework

Lawrence expresses Entanglement Compression Theory through the **Primordial Wave Equation (PWE)**, iħ∂ₜΨ = (−α_d∇² + V + βℂ[Ψ])Ψ, where Ψ represents the *Lawrence Universal Wave Function* (LUWF) and ℂ[Ψ] is a real, multiplicative compression operator. The equation combines the quantum kinetic term with a real functional that links amplitude, energy distribution, and curvature.

The compression operator is defined as ℂ[Ψ] = −c₀ ln(ρ₁ / ρ₀) + c₂ ∇² ln(ρ₁), with ρ₁ = |Ψ|² and constants c₀ and c₂ determined by physical scale. Because ℂ[Ψ] is real, the probability current j = (ħ / m_eff) Im(Ψ*∇Ψ) remains conserved, ensuring locality and deterministic evolution.

The LUWF serves as a global solution describing all entangled configurations. Each observable state corresponds to a projection of Ψ onto a measurable subspace, and the energy division among those projections yields the Born-rule probabilities derived in ECT. In the weak-compression limit, where curvature effects vanish, the formulation reduces to the standard Schrödinger equation.

Earlier theoretical studies on varying constants, Lorentz symmetry, and quantum probability include works by Magueijo (2003), Barrow and Magueijo (2005), Kostelecký and Russell (2011), Uzan (2011), Deutsch (1999), and Zurek (2005).

Relation to other interpretations

Entanglement Compression Theory differs from earlier interpretations of quantum mechanics in its treatment of probability, determinism, and geometry. Where most interpretations treat the Born rule as a statistical axiom, ECT derives it from conservation of energy within a deterministic wave equation.

Interpretation	Determinism	Treatment of Probability	View of Reality	Relation to Geometry
Copenhagen interpretation	Indeterministic	Fundamental postulate (Born rule)	Observation defines state	Geometry independent of measurement
Pilot-wave theory (de Broglie–Bohm)	Deterministic with hidden variables	Derived from particle trajectories	Wave guides particle motion	Geometry treated as external
Many-worlds interpretation	Deterministic branching	Probability from branch weighting	All outcomes realized	Geometry implicit in universal wavefunction
String theory	Deterministic field dynamics in higher dimensions	Probability from quantum field amplitudes	Reality built from vibrating one-dimensional objects	Geometry fundamental to physical law, typically fixed background
Entanglement Compression Theory (Lawrence, 2025)	Deterministic, no hidden variables	Derived from energy division pᵢ = Eᵢ / E_total	Reality defined by oscillatory persistence	Curvature and probability share a common origin through compression

ECT departs from the Copenhagen interpretation by eliminating intrinsic randomness, from the Pilot-wave model by removing hidden variables, and from the Many-Worlds interpretation by replacing branching with deterministic energy partition. It also differs from String theory by treating geometry as an emergent property of amplitude compression rather than as a pre-existing background. Its mathematical structure treats curvature and probability as expressions of the same compression dynamics that sustain the wavefunction.

Reception and coverage

Search overviews from Google, Perplexity, and Bing describe *Entanglement Compression Theory* as a deterministic framework linking quantum mechanics, relativity, and cosmology through wavefunction compression. A Google Search overview from October 2025 characterizes the theory as “a new theoretical framework proposing that spacetime, matter, and physical phenomena emerge from a universal entangled wavefunction that undergoes deterministic compression,” noting its distinction from information-theory models and its geometric component connecting curvature and compression. A corresponding summary preserved through Perplexity describes it as “an emerging framework in theoretical physics proposing that spacetime, gravity, and quantum phenomena arise from the compression dynamics of entangled quantum states,” referencing the Lawrence Universal Wave Function (LUWF) as the unifying field construct. An archived Bing search record lists independent entries for the theory and its author across Zenodo, Academia.edu, ORCID, Wikidata, Amazon, and the Compression Theory Institute website, documenting its indexing across both academic and public databases.

These search-result summaries and documentation snapshots are preserved through Zenodo for verifiability and historical record. Primary publications are indexed through Zenodo, OSF, Academia.edu, ResearchGate, and Google Scholar under institutional attribution to the Compression Theory Institute, providing open-access distribution of the theory’s source material.

Development and dissemination

The framework is published through the open-access Compression Theory Institute (CTI) on Zenodo. Principal works include the theoretical foundation, the mathematical and gravitational formalism, the oscillation-based derivation, and the tensor-compression formulation. A supplementary dataset records independent search-engine indexing and archived automated summaries across Google, Bing, and Perplexity, providing open documentation of dissemination and external verification.

Publications

The principal works establishing *Entanglement Compression Theory* are published through the Compression Theory Institute on Zenodo and indexed in public research archives:

• Lawrence, W.A. (2025). Theory of Derived Probability and Entanglement Compression. Zenodo. doi:10.5281/zenodo.15786696
• Lawrence, W.A. (2025). Mathematical Foundations of Derived Probability and ECT: Well-Posedness and Gravitational Tests. Zenodo. doi:10.5281/zenodo.17071135
• Lawrence, W.A. (2025). The Oscillation Principle. Zenodo. doi:10.5281/zenodo.17058692
• Lawrence, W.A. (2025). Unified Derivation of Probability, Curvature, and Compression Geometry in Entangled Systems. Zenodo. doi:10.5281/zenodo.17349900

See also

• Wave function
• Quantum gravity
• General relativity
• Quantum cosmology
• Interpretations of quantum mechanics

External links

• Compression Theory Institute