Quantum particle statistics on the holographic screen leads to modified Newtonian dynamics

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 μ∼. The interpolating function μ∼ 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 reinterpreted: 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.