Entropic Scalar EFT: From Entanglement Microstructure to Gravity and Cosmic Structure

Abstract

We propose that empty space is not a passive backdrop but a physical medium with a finite budget of quantum entanglement: the linking structure that allows parts of a quantum system to share state. Matter forms when some of that capacity becomes locked into stable, localized defects of the medium. A particle's mass measures how much entanglement is committed to such a defect. Gravity is the surrounding capacity-strain field: near matter, slightly less entanglement capacity is freely available, and in the weak-field limit the fractional shortfall gives the gravitational potential. The excess acceleration seen in galaxies, usually attributed to particle dark matter, is treated here as the large-scale continuation of the same capacity response rather than as a new unseen substance. The central result is that this picture is not free to be adjusted after the fact. Once one accepts the finite-capacity medium, the three founding postulates, and a specific minimal model for the smallest cell of space, the weak-field coefficients are fixed by counting the possible configurations of that cell. A single chain of calculation, with nothing left to tune galaxy by galaxy, then gives Newton's law, the acceleration scale a0 at which galaxies begin to depart from Newtonian expectations, the tight observed relation between galaxy rotation and ordinary matter, and the leading no-slip lensing structure. The electron, the lightest charged particle, plays a double role. It fixes the exchange rate between committed entanglement and mass, and it also fixes the absolute size of the smallest cell. The second step uses Many-Pasts, one of the three founding postulates: the claim that the medium's present state is supported not by a single microscopic past but by many admissible histories, weighted by how well each leads to the present. In the operational branch used here this leaves all ordinary quantum-mechanical predictions intact - Born-rule statistics and no-signaling are preserved - while making the electron's microscopic dressing memoryless, and that memorylessness fixes the substrate length. The length fixed in this way - from the electron Compton scale and the tetrahedral entropy, with no value of G entering the chain - implies a gravitational scale within about one percent of the measured Newton constant. We treat this as a calibrated coherence check, not as a clean independent prediction, because the construction's form was selected with that target partly in view. Appendix K records that provenance and the associated fork accounting. Beyond the static weak-field sector, the framework extends to time-dependent transport, clusters, cosmology, the saturated early universe, black holes, and the charged-lepton spectrum, at varying and explicitly labeled levels of closure. The completed claim of the paper is the chain from the microscopic construction to ordinary weak gravity; the later sectors are presented as conditional extensions, frontier completions, or open tests.

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