More Heat Than Light: Economics as Social Physics, Physics as Nature's Economics
The derivation of Jacobson does not take in to account the fact that the mass of an object and therefore its energy can change due to the displacement of matter far away from it. There is action at a distance hidden in gravity, even relativistically. The ADM and Komar definitions of mass make this non-local aspect of gravity very clear. This non-local aspect of gravity is precisely what the holographic principle is about.
Jacobson's argument is ultra local, and assumes the presence of stress energy crossing the horizon. But there is no statement about an entropic force that is influencing particles far away from the horizon. My point of view is an attempt to take a much more global view, and map out the information over a bigger part of space, even though initially I can only do that for static space times.
The statement that gravity is an entropic force is more then just saying that "it has something to do with thermodynamics". It says that motion and forces are the consequence of entropy differences. My idea is that in a theory in which space is emergent forces are based on differences in the information content, and that very general random microscopic processes cause inertia and motion. The starting point from which this all can be derived can be very, very general. In fact we don't need to know what the microscopic degrees of freedom really are. We only need a few basic properties.
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