On the Origin of Gravity and the Laws of Newton
Erik P. Verlinde
Abstract and summary · read the original at the source
In one page
Erik Verlinde asks the question most physicists had stopped asking: why is there gravity at all? His answer is that it is not a fundamental force but a statistical one — the same kind of pull that coils a stretched polymer. Nothing tugs on the polymer. It coils because far more of its microscopic arrangements are coiled than straight, and a system drifts toward the arrangements it has most of. That is an entropic force. Verlinde proposes that space works the same way. Take the holographic principle seriously — the information describing a region is stored as bits on a surface bounding it — and add two plain assumptions: the number of bits is proportional to the area, and the energy inside is shared evenly among them. Move a mass toward that surface and the stored information changes. Out falls Newton’s inverse-square law, with Newton’s constant defined by the bit count, and the law of inertia with it. The relativistic version reproduces Einstein’s equations.
Why it matters hereChapter 3 is the chapter that treats inertia and gravity as effects rather than givens, and Verlinde is the most cited modern statement of that move: a full derivation in which both come out of counting information. Chapter 13 needs it for a different reason — it is the sharpest published alternative to a medium-based account, so knowing exactly what it derives, and what it leaves open, is how the unified picture stays honest.
What it claims
01An entropic force is a macroscopic force with no microscopic force behind it: it points in the direction of increasing entropy, is proportional to temperature, and obeys the relation that force times displacement equals temperature times entropy change — the polymer in a heat bath being the standard example, where the emergent potential has no microscopic meaning.Section 2, Entropic force, Equations 2.2 to 2.4
Settled physics02If information about a particle’s position is stored in bits on a holographic screen, then the entropy on that screen changes by two pi times Boltzmann’s constant when the particle moves one Compton wavelength closer — the postulate Verlinde takes from Bekenstein’s thought experiment and applies to flat space rather than to a black hole horizon.Section 3.1, Force and inertia, Equations 3.5 and 3.6
Published and peer-reviewed03Combining that entropy postulate with the Unruh temperature associated with an accelerated frame gives Newton’s second law, force equals mass times acceleration — which Verlinde reads in reverse, as the temperature required to cause a given acceleration, making inertia itself the entropic effect.Section 3.1, Equations 3.7 to 3.9
Published and peer-reviewed04For a spherical screen, assuming only that the number of bits is proportional to the area, that the enclosed energy is divided evenly over those bits by equipartition, and that the energy equals the enclosed mass times the speed of light squared, the entropic force works out to Newton’s law of gravitation — the inverse-square law recovered from first principles, with Newton’s constant entering only as the definition of the bit density.Section 3.2, Newton’s law of gravity, Equations 3.10 to 3.13
Published and peer-reviewed05Repeating the construction on a closed surface of constant redshift, with the same bit density and equipartition rule, yields Komar’s expression for the mass contained in a volume of static curved spacetime; adapting Jacobson’s argument for null screens then leads to the full Einstein equations.Section 5.2, Derivation of the Einstein equations, Equations 5.32 to 5.35
Published and peer-reviewed06Verlinde names his own open problems: the arguments are admittedly heuristic; Planck’s constant is fixed at horizons but its role away from one is not established; the entropy implied for an equipotential screen appears to exceed the Bekenstein bound; and any observational test has to come from fluctuations in the gravitational force, which he suggests may be more pronounced for weak fields between small bodies.Section 6.4, Final comments, Equation 6.41
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Read it · abstract
Abstract
Starting from first principles and general assumptions Newton's law of gravitation is shown to arise naturally and unavoidably in a theory in which space is emergent through a holographic scenario. Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle leads us to conclude that it is actually this law of inertia whose origin is entropic.
The way in
https://arxiv.org/abs/1001.0785Submitted to arXiv on 6 January 2010 as arXiv:1001.0785 from the Institute for Theoretical Physics at the University of Amsterdam, and published as Erik P. Verlinde, ‘On the origin of gravity and the laws of Newton’, Journal of High Energy Physics 2011, article 29, doi 10.1007/JHEP04(2011)029. The arXiv posting carries the arXiv.org perpetual non-exclusive licence rather than a Creative Commons licence, so this page carries the summary, the claims and the author’s own abstract; the full preprint is free to read at the link above.
How to cite it
Erik P. Verlinde (2010) On the Origin of Gravity and the Laws of Newton. doi:10.1007/JHEP04(2011)029
Where it sits in the curriculum
Inertia and gravity from the vacuumThe unified pictureThe evidence ladder