Quantum particle statistics on the holographic screen leads to Modified Newtonian Dynamics (MOND)

Abstract

Employing a thermodynamic interpretation of gravity based on the holographic principle and assuming underlying particle statistics, fermionic or bosonic, for the excitations of the holographic screen leads to Modified Newtonian Dynamics (MOND). A connection between the acceleration scale $a_0$ appearing in MOND and the Fermi energy of the holographic fermionic degrees of freedom is obtained. In this formulation the physics of MOND results from the quantum-classical crossover in the fermionic specific heat. However, due to the dimensionality of the screen, the formalism is general and applies to two dimensional bosonic excitations as well. It is shown that replacing the assumption of the equipartition of energy on the holographic screen by a standard quantum-statistical-mechanics description wherein some of the degrees of freedom are frozen out at low temperatures is the physical basis for the MOND interpolating function ${\tilde \mu}$. The interpolating function ${\tilde \mu}$ is calculated within the statistical mechanical formalism and compared to the leading phenomenological interpolating functions, most commonly used. Based on the statistical mechanical view of MOND, its cosmological implications are re-interpreted: the connection between $a_0$ and the Hubble constant is described as a quantum uncertainty relation; and the relationship between $a_0$ and the cosmological constant is better understood physically.