  The fact that the equations of motion for matter remain invariant when a
constant is added to the Lagrangian suggests postulating that the field
equations of gravity should also respect this symmetry. This principle implies
that: (1) the metric cannot be varied in any extremum principle to obtain the
field equations; and (2) the stress-tensor of matter should appear in the
variational principle through the combination $T_{ab}n^an^b$ where $n_a$ is an
auxiliary null vector field, which could be varied to get the field equations.
This procedure selects naturally the Lanczos-Lovelock models of gravity in
$D$-dimensions and Einstein's theory in $D=4$. Identifying $n_a$ with the
normals to the null surfaces in the spacetime leads to a thermodynamic
interpretation for gravity, in the macroscopic limit. Several geometrical
variables and the equation describing the spacetime evolution acquire a
thermodynamic interpretation.
  Extending these ideas one level deeper, we can obtain this variational
principle from a distribution function for the ``atoms of spacetime'', which
counts the number of microscopic degrees of freedom of the geometry. This is
based on the curious fact that the renormalized spacetime endows each event
with zero volume, but finite area!
