Chapter 03 · The Nature of Space and Time/Emergent Spacetime & Gravity

Verlinde Entropic Gravity

2010 / 2016 · Erik Verlinde

Gravity is an entropic force from information on holographic screens. The 2016 dark-matter extension has been substantially constrained by weak-lensing tests.

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In one sentence

Verlinde proposed that gravity is not a fundamental force but an entropic effect arising from changes in information on holographic screens. The 2016 extension to dark matter has been substantially constrained by 2017-2019 weak-lensing and radial-acceleration-relation tests.

The claim

Verlinde's 2010 framework. Verlinde proposed that gravity emerges as an entropic force when matter moves relative to holographic screens that encode information about distant spacetime. As matter shifts position, the entropy of information on these screens changes; this entropy gradient produces a force, identified as gravity. The 2010 paper derived Newton's law of gravitation, and sketched a relativistic generalization, from this thermodynamic-holographic picture. The framework remains conceptually interesting independent of any specific dark-matter claim.

The 2016 dark-matter extension. In Emergent Gravity and the Dark Universe (2017, SciPost), Verlinde extended the framework to claim that what we attribute to dark matter is also emergent, arising from the entanglement structure of microscopic degrees of freedom in a de Sitter spacetime. This produces a specific scale-dependent extra gravitational potential that should reproduce MOND-like rotation curves and lensing profiles without invoking a particle.

Observational tests have substantially constrained the 2016 extension. Brouwer et al. 2017 ran the first weak-lensing test against KiDS data and found the prediction consistent with observations at galaxy scales but unable to distinguish from standard particle dark matter with comparable parameters. Lelli et al. 2017 tested the prediction against the radial acceleration relation and found inconsistencies with the predicted scaling. Tamosiunas et al. 2019 tested at galaxy-cluster scales and found significant tension with observed cluster density profiles. The 2016 dark-matter extension is not refuted but is substantially constrained; the 2010 entropic-gravity framework remains live as a separate conceptual program.

The family stance

Spacetime is not fundamental. It emerges from a deeper structure: entanglement patterns, thermodynamic relations on horizons, or discrete causal ordering. None of these has been confirmed; each makes some testable predictions but most operate at conceptual or structural levels.

Predictions

2010 framework: Newton's law of gravity recovered as an entropic force on holographic screens; relativistic generalization should match GR at leading order
2016 dark-matter extension: a specific scale-dependent extra gravitational potential producing MOND-like behavior in galaxies, without dark-matter particles
Specific baryonic Tully-Fisher-like relations between baryonic mass and apparent dark mass; deviations from the predicted scaling falsify the dark-matter extension

Evidence

Brouwer et al. 2017 weak-lensing test: prediction is consistent with KiDS-450 data at galaxy scales, though it doesn't clearly distinguish from particle dark matter with matched parameters
The 2010 entropic derivation recovers Newton's law and is conceptually independent of the 2016 dark-matter claim

Counterpoints

Lelli, McGaugh & Schombert (2017) tested the 2016 prediction against the radial acceleration relation across ~150 SPARC-database galaxies and found inconsistencies with the predicted scaling at low accelerations
Tamosiunas et al. (2019) tested the prediction at galaxy-cluster scales and found significant tension with observed lensing profiles
The original 2010 entropic derivation has been criticized for assuming too much input (Bekenstein-Hawking entropy-area law, Unruh temperature) to legitimately derive Newton's gravity from first principles
The microscopic model of underlying degrees of freedom remains vague; critics see the framework as under-specified compared to explicit dark-matter models
No fully relativistic, calculable version of the 2016 dark-matter scheme exists; observational analyses use phenomenological approximations

Variants in this family

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Verlinde 2010 derivation: posit a holographic screen at some surface; matter on one side. The entropy of information on the screen changes as matter moves toward or away. By the first law dE = T dS with Unruh temperature T = a / (2π), an entropic force F = T (dS / dx) emerges. Identifying this with gravitational attraction recovers F = G m M / r².

Verlinde 2016 dark-matter scheme: in a de Sitter spacetime there is additional entropic information from the cosmological horizon. This produces an extra contribution to the gravitational potential that grows logarithmically with mass and falls off slowly with distance, mimicking MOND-like behavior at galaxy scales. The functional form has V_extra(r) ~ sqrt(M / r) at large r.

Observational tests, technical details: Brouwer 2017 stacked galaxy-galaxy weak lensing in KiDS-450 + GAMA and found the predicted excess gravity at the right magnitude, but the test doesn't distinguish from standard NFW dark-matter profiles. Lelli 2017 compared the prediction to the SPARC galaxy database and found it fails to reproduce the observed radial-acceleration-relation scaling at low accelerations. Tamosiunas 2019 found galaxy-cluster predictions miss observed lensing profiles at >= 3σ tension.