On the Holographic Bound in Newtonian Cosmology.

The holographic principle sets an upper bound on the total (Boltzmann) entropy content of the Universe at around 10 123 k B ( k B being Boltzmann's constant). In this work we point out the existence of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian approximation.