From the Casimir Effect to Space-Entropy: A New Experimental Frontier for Emergent Gravity

Recent proposals of emergent gravity interpret the gravitational force as an entropiceffect, assigning to the entropy gradient in spacetime a role analogous to that ofconventional force fields. In the present work we pursue this line of research, revisitingand expanding the concepts of entropic hysteresis and the mapping t → S introducedin our previous studies [37–39]. We specifically propose an alternative description ofthe Casimir effect as a phenomenon associated with entropic variations of the microstatesconfined between conductive surfaces, rather than with vacuum quantumfluctuations alone. On the basis of this reinterpretation, we hypothesize that nanostructuredsurfaces and metamaterials can modulate the observed force—possibly eveninvert it—thus opening the way to an experimental test capable of discriminatingbetween canonical mechanisms and entropic hypotheses. Although the theoreticalframework remains speculative and requires further verification, the results presentedhere outline a pathway toward integrating quantum-vacuum physics with the thermodynamicsof information, within a paradigm in which time itself emerges as anentropic coordinate. We rigorously derive a topology–driven crossover between theCasimir quartic law F ∝ d−4 and the Newtonian inverse–square law, showing thatthe transition occurs when FC(d) = FG(d) at d ∼ 10−7 m for laboratory-scale masses.This prediction, fully developed in Secs. 3, 6 and App. H, is directly testable withforthcoming micro-torsion balances.