Exploring 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
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^a_b \to T^a_b + \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.
