Historical research guide · 0299 · 2010
On the Origin of Gravity and the Laws of Newton
Erik P. Verlinde
In one minute
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.
Connection
Chapter 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.
From the source
An 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
If 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
Combining 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
For 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
Repeating 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
Verlinde 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
The way in
https://arxiv.org/abs/1001.0785How to cite it
Erik P. Verlinde (2010) On the Origin of Gravity and the Laws of Newton doi:10.1007/JHEP04(2011)029