Over the last several years the connection between thermodynamics and
Gravity has been made explicit in Black Hole physics and the Entropic Gravity
proposal. Entropic Gravity is a modern version of Sakharov's Induced Gravity
model. In Induced Gravity , spacetime is emergent and gravity is not a
fundamental force , but rather results from the collective action of
underlying micro degrees of freedom. This means that gravitons would be quasi
particles, collective excitation of micro degrees of freedom.
This was most clearly illustrated by the Velinde formalism.
dS/dE= 1/K*T
(dS/dR)*(1/F)= 1/K*T
Therefore
F= K*T*dS/dR
S= 2*pi*R*m*c/hbar
dS/dR= 2*pi*m*c/hbar
dS/dE= 2*pi*R/hbar*c= 2*pi*c/a*hbar
K*T= a*hbar/(2*pi*c) = hbar*G*M/(2*pi*c*R^2)
Which gives us
F= G*m_1*m_2/R^2
F=m*a
Therefore given that Gravity , based on this approach , is a function of
the increase of entropy , space time itself must be emergent resulting
from the increase of entropy in any given causal patch of space time. ( what
is called, when time is included, a Causal Diamond )
This is clearly illustrated in the section "Entropy and Cosmology" in Vic
Stenger's latest book, "The Fallacy of Fine Tuning" on pages 109-113.
Looking at equation (5.28) on page 113
S_max(R)- S_ave= (pi*R^2/G)*(1-R/R_H)
hbar=c=1
Where R_H is the distance to the Horizon.
For R=R_H we see that the volume of space time saturates the Bekenstein
bound while for R <<< R_H we have an entropy content far below this bound.
What is amazing about this simple relationship is that the local production
of entropy is exactly correlated with the foliation of space time. This is
a highly non local correlation, which is really not surprising, since
gravity is expected to be highly non local based on the Holographic principle.
In any case , we see that space time is emergent as a function of the
creation of entropy, that is the boundary of the causal diamond is exactly
correlated with the local production of entropy. This seems rather interesting.