Entropic Scalar EFT: Entanglement-Entropy Origins of Gravity, Mass, Time, and Cosmic Structure

Abstract

We develop a self-contained theoretical framework in which quantum entanglement entropy underlies the emergence of spacetime geometry, gravity, inertial mass, and cosmic evolution. The central claim is that “dark matter” and “dark energy” are not mysterious substances but rather manifestations of how quantum information—specifically entanglement—shapes spacetime. In this entanglement-based scalar effective field theory (EFT), gradients and deficits of entanglement entropy serve as sources of spacetime curvature. By augmenting Einstein’s field equations with an extra stress-energy component from the entanglement field, the framework provides a unified explanation for phenomena traditionally ascribed to dark matter and dark energy. Galactic rotation curves that remain flat at large radii are explained by entanglementinduced curvature instead of unseen mass. Likewise, the excess gravitational lensing observed in galaxy clusters arises here with no gravitational “slip” between metric potentials ( = at leading order), so light deflection is correctly predicted by the same entropic curvature that governs galaxy dynamics. Cosmic acceleration and the late-time expansion rate are addressed through a homogeneous background mode of the entanglement field, which modifies the early-universe expansion history. Treated as an additional scalar component in the Friedmann equations, this mode provides an early energy injection near matter–radiation equality that reduces the sound horizon at recombination. Under the requirement that the CMB acoustic angle remains fixed, this mechanism shifts the CMB-inferred Hubble constant H_0 from roughly 67 to 69 km s^1 Mpc^1, alleviating the Hubble tension by about half. The remaining discrepancy with local distance-ladder measurements may reflect residual systematics in late-time calibration. In addition, the theory predicts a weak entropic time dilation effect—clock rates depend slightly on local entanglement entropy density—though this variation is constrained to be extremely small in weak-field environments (typically at or below the 10−8 fractional level, with much smaller differential laboratory signatures). Furthermore, the rest mass of particles is proposed to be proportional to the quantum information (entanglement entropy) they carry, via a universal constant _m. This mass–entropy equivalence ties the origin of inertia directly to entanglement content. We also elevate a “Many-Pasts Hypothesis” – the notion that past histories are not unique and fixed, but are instead weighted probabilistically by their consistency with the present entangled state – to a central principle of the framework. This yields a dynamic, probabilistic formulation of history that maintains quantum coherence on cosmic scales while ensuring no violations of causality or signaling. All key equations are derived from a covariant action or from first principles, with careful attention to units and consistency. The result is a falsifiable alternative to CDM: invisible dark components are replaced by measurable informational properties of spacetime. We discuss how black holes fit into this picture as maximal-entropy configurations whose Bekenstein–Hawking area law emerges from entanglement microstructure. Finally, we outline experimental and observational tests—from precision galactic rotation curves and gravitational lensing in cosmic voids to laboratory-scale entanglement experiments—that can validate or refute the theory. In summary, this work provides a unified, entanglement-centric account of space, time, gravity, and cosmology, highlighting concrete physical meanings and predictive power for each new quantity introduced.

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