Exploring the Nature of Gravity

Understand

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.