anywhere in space. In all these cases the emergence of the holographic direction is accompanied by redshifts, and related to some coarse graining procedure. If all these combined ideas are correct there should exist a general framework that describes how space emerges together with gravity.
Usually holography is studied in relativistic contexts. However, the gravitational force is also present in our daily non-relativistic world. The origin of gravity, whatever it is, should therefore also naturally explain why this force appears the way it does, and obeys Newton law of gravitation. In fact, when space is emergent, also the other laws of Newton have to be re-derived, because standard concepts like position, velocity, acceleration, mass and force are far from obvious. Hence, in such a setting the laws of mechanics have to appear alongside with space itself. Even a basic concept like inertia is not given, and needs to be explained again.
In this paper we present a holographic scenario for the emergence of space and address the origins of gravity and inertia, which are connected by the equivalence principle. Starting from first principles, using only space independent concepts like energy, entropy and temperature, it is shown that Newton’s laws appear naturally and practically unavoidably. Gravity is explained as an entropic force caused by a change in the amount of information associated with the positions of bodies of matter.
A crucial ingredient is that only a finite number of degrees of freedom are associated with a given spatial volume, as dictated by the holographic principle. The energy, that is equivalent to the matter, is distributed evenly over the degrees of freedom, and thus leads to a temperature. The product of the temperature and the change in entropy due to the displacement of matter is shown to be equal to the work done by the gravitational force. In this way Newton’s law of gravity emerges in a surprisingly simple fashion.
The holographic principle has not been easy to extract from the laws of Newton and Einstein, and is deeply hidden within them. Conversely, starting from holography, we find that these well known laws come out directly and unavoidably. By reversing the logic that lead people from the laws of gravity to holography, we will obtain a much sharper and even simpler picture of what gravity is. For instance, it clarifies why gravity allows an action at a distance even when there in no mediating force field.
The presented ideas are consistent with our knowledge of string theory, but if correct they should have important implications for this theory as well. In particular, the description of gravity as being due to the exchange of closed strings can no longer be valid. In fact, it appears that strings have to be emergent too.
We start in section 2 with an exposition of the concept of entropic force. Section 3 illustrates the main heuristic argument in a simple non relativistic setting. Its gen- eralization to arbitrary matter distributions is explained in section 4. In section 5 we extend these results to the relativistic case, and derive the Einstein equations. The conclusions are presented in section 7.