The law of gravitation is derived from classical statistical mechanics applied to the holographic principle, that states that the description of a volume of space can be thought of as  bits of binary information, encoded on a boundary to that region, a closed surface of area . The information is evenly distributed on the surface with each bit requiring an area equal to , the so-called Planck area, from which  can thus be computed:
where  is the Planck length. The Planck length is defined as:
where  is the universal gravitational constant,  is the speed of light, and  is the reduced Planck constant. When substituted in the equation for  we find:
The statistical equipartition theorem defines the temperature  of a system with  degrees of freedom in terms of its energy  such that:
where  is the Boltzmann constant. This is the equivalent energy for a mass  according to:
The effective temperature experienced due to a uniform acceleration in a vacuum field according to the Unruh effect is:
where  is that acceleration, which for a mass  would be attributed to a force  according to Newton's second law of motion:
Taking the holographic screen to be a sphere of radius , the surface area would be given by:
From algebraic substitution of these into the above relations, one derives Newton's law of universal gravitation:
Note that this derivation assumes that the number of the binary bits of information is equal to the number of the degrees of freedom.