(adsbygoogle = window.adsbygoogle || []).push({}); T. Padmanabhan said:In fact, considerable amount of evidence has accumulated over the years suggesting such a connection between horizon thermodynamics and microstruc- ture of spacetime and indicating that gravity is better described as an emergent phenomenon like elasticity or fluid mechanics [13, 14]. In particular, it has been shown that: (a) The field equations of gravity reduce to a thermodynamic identity on the horizons in a wide variety of models much more general than just Einstein’s gravity [15]. (b) It is possible to obtain [16] the field equations of gravity — again for a wide class of theories — from purely thermodynamic considerations by extremising a suitable entropy density for spacetime.

In this paradigm, one considers spacetime (described by the metric, curva-

ture etc.) as a physical system analogous to a gas or a fluid (described by density, velocity etc.). The fact that either physical system (spacetime or gas) exhibits thermal phenomena shows that there must exist microstructure in either sys- tem. Therefore one does not try to quantize gravity but instead attempts to provide a quantum description of spacetime. This is identical in spirit to the fact that one does not quantize, say, the variables in the Navier-Stokes equation (which is analogous to the gravitational field equation) to obtain a quantum theory of matter but instead identifies the appropriate microscopic degrees of freedom (molecules, atoms, ....) and develops a quantum theory of these de- grees of freedom. We do not yet know what are the correct microscopic degrees of freedom of the spacetime; but the horizon thermodynamics provides a clue along the following lines.

This connection between macroscopic thermodynamics and the existence of

microscopic degrees of freedom comes out clearly — for both gas and space- time — in the equipartition law ∆E = (1/2)(∆n)kB T connecting the number of degrees of freedom ∆n required to store and energy ∆E at the temperature T . In the case of a gas, ∆n scales as the volume of the substance and essen- tially counts the number of molecules.

page 4

"therefore one does not try to quantize gravity but instead attempts to provide a quantum description of spacetime." In other words, canonical quantum gravity is wrong.

What quantum description of spacetime lends itself most readily to this entropic-emergent understanding of gravity? Do either leading approach work in this context? In string theory, space is infinitely continuous (result of lorentz invariance), do spin networks carry the right kind of microscopic degree of freedom for this idea to work?

http://arxiv.org/abs/1007.5066

Finite entanglement entropy from the zero-point-area of spacetime

Authors: T. Padmanabhan

(Submitted on 28 Jul 2010)

Abstract: The calculation of entanglement entropy S of quantum fields in spacetimes with horizon shows that, quite generically, S (a) is proportional to the area A of the horizon and (b) is divergent. I argue that this divergence, which arises even in the case of Rindler horizon in flat spacetime, is yet another indication of a deep connection between horizon thermodynamics and gravitational dynamics. In an emergent perspective of gravity, which accommodates this connection, the fluctuations around the equipartition value in the area elements will lead to a minimal quantum of area, of the order of L_P^2, which will act as a regulator for this divergence. In a particular prescription for incorporating L_P^2 as zero-point-area of spacetime, this does happen and the divergence in entanglement entropy is regularized, leading to S proportional to (A/L_P^2) in Einstein gravity. In more general models of gravity, the surface density of microscopic degrees of freedom is different which leads to a modified regularisation procedure and the possibility that the entanglement entropy - when appropriately regularised - matches the Wald entropy.

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# Finite entanglement entropy from the zero-point-area of spacetime

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