The Entropic Universe: An Effective Field Theory for Emergent Geometry and Localized Gradient Effects [Preprint]

The Entropic Universe Theory (EUT) is a minimalist effective field theory in which a single scalar field — the entropy density S(x,t) — acts as the sole primordial dynamical entity. Spacetime curvature, time, torsion, and gravitational dynamics all emerge from the gradients of S and their interaction with temperature T, without extra dimensions or fine-tuned parameters.

Version 4 - December 21, 2025

Key update from previous versions:

• Appendix B introduces a complementary strong-gradient probe via cavitation luminescence (sonoluminescence) under variable external conditions (temperature, magnetic field, gravity), inspired by natural pistol/mantis shrimp snaps. Derived from EUT II's primordial all-to-all entropic bond ontology, this explores non-equilibrium bond reactivation and severing, with conservative toy-model projections aligning with observed trends and modest distinguishing signatures proposed for empirical scrutiny.

Version 3 - December 4, 2025

Key updates from previous versions:

• Appendix A provides the complete open-source reference design, schematic, predicted force curve, noise budget, and quantitative protocol for the decisive non-magnetic phononic test in isotopically pure sapphire or ²⁸Si.
• Explicitly predicts a detectable, reversible 10–100 fN force from purely thermal gradients (∇T ≈ 1 K mm⁻¹) at millikelvin temperatures using existing dilution-refrigerator torsion balances.
• Includes a clean null control (natural-abundance sapphire) that rules out magnetic artifacts.

A positive result in the non-magnetic phononic channel would constitute the laboratory confirmation of entropy gradients sourcing geometry. A null result at the quoted sensitivity falsifies the purely entropic origin.

No equations or core predictions from previous versions have been altered; the theory has become dramatically more robust, falsifiable, and experimentally accessible.

Author: Matthew Steiniger (ORCID 0009-0000-6069-4989), Home Laboratory, Independent Researcher

Abstract:

The Entropic Universe Theory (EUT) proposes entropy density S(x,t) as a fundamental scalar field from which spacetime geometry, gravitational effects, and temporal structure emerge. Gravity arises via the Poisson equation ∇² Φ_S = 4π ρ^{ent}, where the entropy stress-energy tensor T^{ent}_{μν} = ∂_μ S ∂ν S − (1/2) g{μν} (∂S)² (derived from variation of the kinetic term (1/2) (∂S)²) induces curvature akin to a conformal fluid. Proper time is parameterized as τ_S = ∫ (∇S / T) · dx, with temperature T = (dS/dU)^{-1} modulating gradient rigidity. Torsion emerges via a vector potential in Poincaré Gauge Theory (PGT), while the Two-State Vector Formalism enables retrocausal correlations without acausal signaling. This framework, an effective field theory inspired by entropic gravity and non-equilibrium thermodynamics, recovers general relativity in weak fields to O(h²) and predicts testable micro-scale effects in both magneto-entropic (YIG) and purely phononic systems. Version 3 introduced a decisive, magnetism-free laboratory test using only thermal gradients in isotopically enriched sapphire or ²⁸Si inside a dilution refrigerator. This non-magnetic control is predicted to produce a detectable, reversible curvature signal at the 10–100 fN level by mid-2026 with existing cryogenic technology (detailed protocol, noise budget, and predicted force curve in Appendix A). A positive result following the (∇T)² T⁴ scaling in the absence of magnetic order would constitute the first direct laboratory confirmation of entropy gradients sourcing geometry. Version 4 introduces a complementary, speculative strong-gradient probe via cavitation luminescence under variable external conditions, inspired by natural phenomena such as pistol and mantis shrimp snaps (Appendix B). Derived from EUT II's primordial bond ontology, this probe explores non-equilibrium bond reactivation and severing, offering potential distinguishing signatures for empirical scrutiny.