Seeing how the entropic theory of gravity by Verlinde is popping up all over the place, I thought I’d write up a summary of what it is so that I don’t forget. Fortunately, I remembered an excellent explanation has already been written elsewhere! So another job well done that I don’t have to do well. Here’s an example from a toy model:

Our toy universe consists of six ‘ray paths’ that form the edges of a tetrahedron. Each ray path can be in two distinct states: occupied or empty. This accounts for a total of 26 = 64 states. Three ray paths meet at each vertex. If all three are empty, the vertex represents ‘a hole’ that gets filled with at least one particle. If any of the three ray paths is occupied, the vertex is ‘full’ and can not contain any particle.

Throw the die, note down the number of spots, and check the corresponding ray path in the tetrahedron:

A) If the ray path is occupied, make it empty, unless doing so would create more than two vertices containing particles.

B) If the ray path is empty, occupy it, unless this would result in zero particle vertices.

Again throw the die and repeat ad infinitum. This simple process creates a sequence of configurations, each of which contains two particles occupying either two different vertices (two particles in two distinct holes), or the same vertex (two particles in the same hole).

In this model there is no explicit force acting between the two particles. So one might naively postulate that both particles will jump randomly from vertex to vertex, and will be as often at the same vertex as at different vertices. This is not the case. The reason is simply that there are 16 states with one hole, against only 6 states with two holes (by allowing only for one and two-hole configurations, 42 of the 64 total number of microstates are forbidden).

Another way of looking at this is that for a given vertex to contain a particle, the three ray paths meeting at that vertex need to be empty. This reduces the entropy (the number of bits needed to describe the tetrahedron universe) by three. For two given vertices to contain a particle, both vertices need to have three empty ray paths. One would therefore expect an entropy reduction of 3 + 3 = 6 bits. However, both vertices necessarily have one ray path in common, and an entropy reduction of 6 – 1 = 5 bits results. However, if both particles are accomodated at the same vertex, both particles dictate the same three ray paths to be empty. In other words: there is 3 common ray paths and an entropy reduction of 6 – 3 = 3 bits results. So, the two particles being together at the same vertex creates a smaller entropy reduction compared to the case of the two particles being seperate. In other words, two particles together at one vertex corresponds to significantly more states than two particles at separate vertices. This is all that is needed for a tendency for both particles to stick together.

That gives the gist of this whole entropic universe idea, and it’s pretty clever. Read the whole post for a more detailed explanation beyond the toy model, along with some excellent explanatory animations.