​On the Origin of Gravity and the Laws of Newton

Erik Verlinde

Abstract

Starting from 1st 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 ma- terial 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.

Basic Idea

• Laws of Newton lead to Black Hole Thermodynamics and the holographic principle
• Holographic principle must lead to Newton's laws
• Newton's law of Gravity (and Gravity in general) is an emergent phenomena much like Hooke's law

Gravity as an entropic force

From the canonical partition function

(T,F)=\int dE dx \Omega(E,x) \exp{-\left(E+Fx)/k_BT\right)

we can derive

frac{F}{T}=\frac{\partial S}{\partial x} = -C

= -C T

Black hole entropy

Proportional to surface area of even horizon

_{BH}=\frac{kA}{4l_p^2

where

_p=\sqrt{G\hbar/c^3

(BH does not stand for 'black hole', but for Bekenstein-Hawking)

Entropy is stored on surface ' holographic principle'

Black holes also have a Hawking Temperature

_H=\frac{\hbar c^3}{8\piGMk_B

If we assume that the Bekenstein-Hawking entropy times the Hawking temperature must equal the work done by gravity, then we have

=T_H\frac{\partial S_{BH}}{\partial x

What about

• Space has one emergent holographic direction.
• There is a change of entropy in the emergent direction
• The number of degrees of freedom are proportional to the area of the screen
• The energy is evenly distributed over these degrees of freedom.