worldscientific.com - 2026-10-04

Query (Google): "Why does gravity know about microscopic entropy" Verlinde -> World Scientific (accepted-article PDF and abstract page), ResearchGate, DRSTP event page (conference for 't Hooft's 80th birthday, Aug 2026, Verlinde speaking with this title), INSPIRE. Page read: https://www.worldscientific.com/doi/10.1142/S0217751X26470020 (Free Access; full text read in browser; PDF not downloaded - needs owner permission) Erik Verlinde, "Why does gravity know about microscopic entropy?", Int. J. Mod. Phys. A 41, No. 26, 2647002 (2026). Special Issue: Festschrift in Honour of Gerard 't Hooft (guest editors H. Verlinde, E. Laenen, C. P. Korthals Altes, S. De Haro, D. Dieks).

Findings (priority 1: the inventor's own later statement of the same principle) [web, URL above]

• Origin and dating: Verlinde says he first presented the idea in December 2009 at a colloquium at Utrecht University attended by 't Hooft, and that he followed arguments "similar to those of Jacobson" but added an explanation of the inertial force. Bears on claim 2 (inertia as entropic) as his stated point of difference from Jacobson 1995. Also says that, unlike 't Hooft (gravity fundamental), he concluded gravity emerges together with space and time.
• Restatement of the mechanism (sec. 1.2, 2): inertia F = ma is an "adiabatic reaction force" in which the adiabatic invariant is the entanglement entropy across Rindler horizons; Unruh temperature T = a/2pi (natural units); F = T dS/dx with dS/dx = 2 pi m "following Bekenstein" - the same postulate as the 2010 paper's eq. (3.6) in natural units.
• New framing of "entropic force": via the Born-Oppenheimer approximation and the adiabatic invariance of phase-space volume (Hertz invariant), F = T (dS/dx) at fixed E with 1/T = dS/dE. His heading-level statement: an entropic force "acts without increasing the entropy" - the entropy is an adiabatic invariant that sets magnitude and direction of the force. He also says the 2010-style naive sign argument (F = -T dS/dx) is "not correct" and that the signs work because S is invariant. Bears directly on the deep read's sign-convention notes (4.25, 5.27/5.30) and on the claim-1 wording "changes in entropy".
• Quantum coherence: in the Born-Oppenheimer regime the slow and fast wave functions factorize, so the slow system "maintain[s] all [its] quantum coherence"; decoherence only when time-scale separation breaks down. This is the inventor's answer (not citing them by name in what was read) to the Kobakhidze neutron-interferometry/GRANIT objection and to the decoherence criticism (see arxiv note: Kobakhidze 2011; Chaichian et al. 2011).
• Action/entropy correspondence (sec. 3): S = 2 pi J, T = omega/2pi, identified with Wald entropy in the Gibbons-Hawking-Wald Euclidean formalism; he states this explains "why the argumentation of Jacobson leads from thermodynamics to the gravitational equations" - "the reverse argument". Bears on claim 4 (Einstein equations) and on the circularity question in the deep read: the inventor now says the gravitational action encodes the microscopic entropy "by construction".
• Concluding remarks: "many challenging open questions" remain, "especially in the context of cosmology".