Is gravity an intrinsically quantum phenomenon? Dynamics of gravity from the entropy of space-time and the principle of equivalence

The two surprising features of gravity are (a) the principle of equivalence and (b) the connection between gravity and thermodynamics. Using principle of equivalence and special relativity in the local inertial frame, one could obtain the insight that gravity must possess a geometrical description. We show that, using the same principle of equivalence, special relativity and quantum theory in the local Rindler frame one can obtain the Einstein-Hilbert action functional for gravity and thus the dynamics of the space-time. This approach, which essentially involves postulating that the horizon area must be proportional to the entropy, uses the local Rindler frame as a natural extension of the local inertial frame and leads to the interpretation that the gravitational action represents the free energy of the space-time geometry. As an aside, one also obtains a natural explanation as to: (i) why the covariant action for gravity contains second derivatives of the metric tensor and (ii) why the gravitational coupling constant is positive. The analysis suggests that gravity is intrinsically holographic and even intrinsically quantum mechanical.