Quantum, noncommutative and MOND corrections to the entropic law of gravitation. (arXiv:1709.04339v1 [physics.gen-ph])

Quantum and noncommutative corrections to the Newtonian law of inertia are
considered in the general setting of Verlinde's entropic force postulate. We
demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in
a classical setting by seeking appropriate corrections in the entropy.We
estimate the correction term by using concrete coherent states in the standard
and generalized versions of Heisenberg's uncertainty principle. Using Jackiw's
direct and analytic method we compute the explicit wavefunctions for these
states producing minimal length as well as minimal products. Subsequently we
derive a further selection criterion restricting the free parameters in the
model in providing a canonical formulation of the quantum corrected Newtonian
law by setting up the Lagrangian and Hamiltonian for the system.

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