Atoms of Spacetime and the Nature of Gravity

I clarify the differences between various approaches in the literature which attempt to link gravity and thermodynamics. I then describe a new perspective(1) based on the following features: (1) As in the case of any other matter field, the gravitational field equations should also remain unchanged if a constant is added to the Lagrangian; in other words, the field equations of gravity should remain invariant under the transformation T-b(a) -> T-b(a) + delta(a)(b) (constant). (2) Each event of spacetime has a certain number (f) of microscopic degrees of freedom ('atoms of spacetime'). This quantity f is proportional to the area measure of an equi-geodesic surface, centered at that event, when the geodesic distance tends to zero. The spacetime should have a zero-point length in order for f to remain finite. (3) The dynamics is determined by extremizing the heat density at all events of the spacetime. The heat density is the sum of a part contributed by matter and a part contributed by the atoms of spacetime, with the latter being L-P(-4) f. The implications of this approach are discussed.