On the Origin of Gravity and the Laws of Newton

TL;DR

This paper proposes that gravity and space-time are emergent from holographic information, treating gravity as an entropic force arising from entropy changes tied to matter positions. By starting from holographic screens with area-proportional degrees of freedom and applying equipartition, Verlinde derives Newton's law and, in the relativistic extension, the Einstein equations via Komar mass and Jacobson–Wald type arguments. The framework unifies inertia, gravity, and space with thermodynamic and information-theoretic notions, and connects to AdS/CFT and black hole thermodynamics, suggesting gravity is not fundamental. The approach yields a coherent, if heuristic, picture of how macroscopic gravitational dynamics emerge from microscopic information processing and holographic coarse graining, with implications for string theory and cosmology.

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.

Figures (6)

• Figure 1: A free jointed polymer is immersed in a heat bath with temperature $T$ and pulled out of its equilibrium state by an external force $F$. The entropic force points the other way.
• Figure 2: A particle with mass approaches a part of the holographic screen. The screen bounds the emerged part of space, which contains the particle, and stores data that describe the part of space that has not yet emerged, as well as some part of the emerged space.
• Figure 3: A particle with mass $m$ near a spherical holographic screen. The energy is evenly distributed over the occupied bits, and is equivalent to the mass $M$ that would emerge in the part of space surrounded by the screen.
• Figure 4: The holographic screens are located at equipotential surfaces. The information on the screens is coarse grained in the direction of decreasing values of the Newton potential $\Phi$. The maximum coarse graining happens at black hole horizons, when $\Phi/2c^2=-1$.
• Figure 5: A general mass distribution inside the not yet emerged part of space enclosed by the screen. A collection of test particles with masses $m_i$ are located at arbitrary points $\vec{r}_i$ in the already emerged space outside the screen. The forces $\vec{F}_i$ due to gravity are determined by the virtual work done after infinitesimal displacement $\delta\vec{r}_i$ of the particles.