Abstract
We clarify the problem in which occasions can gravitational force be regarded emergent from thermodynamics, by proposing an entropic mechanism that can extract the entropic gradient existing in spacetime, due to the variation of the Casini–Bekenstein bound in specific quasi-static processes with the heat flux delta Q into the whole casual wedge. We explicitly formulate the derivation of inertial force as the emergent gravitational attraction from the Entanglement First Law. We find the saturation of the bound along with the vanishing relative entropy corresponds to the variation of minimal surface. To covariant meaning, it is the Bousso bound. Besides, this understanding is connected to recent Pennington’s work on Black Hole Information Paradox, suggesting a Page-Curve function origins from removing attraction by the external heat bath. Our theory from entanglement now overcomes several criticism towards Verlinde’s original entropic force proposal, and is able to co-exist with Susskind’s Complexity Tendency. This entropic mechanism reproduces the Newton’s Second Law in Rindler space and the gravitational force (together with derivation of the Einstein equation) beyond the near-horizon region, and can be adapted into AdS/CFT and other generic situations.
Highlights
Gravitational force is special, whose origin may be approached in a totally different way from other kinds of fundamental forces, which have been quantized and unified
We show a proper adapted Emergent Gravity theory to AdS may help understanding gravitational attraction in pure AdS, and more over, possibility is there to build a connection to transform between the entropic gradient and the operator growth, once we know the generic entropic gradient in spacetime and turn it into momentum-change, through virtual processes involving intermediate states
We will show no change of local quantity H is the specific condition that leads an entropic gradient which can reproduce Newton’s 2nd Law and gravitational force in GR, as in the two cases we are familiar with definition of this bound, Rindler space and static black hole
Summary
Gravitational force is special, whose origin may be approached in a totally different way from other kinds of fundamental forces, which have been quantized and unified. The basic idea of Verlinde’s emergent gravity theory [12,13] is that the gravitational force is possibly an entropic force F = T ∇ S that usually occurs in macroscopic systems such as colloid and polymer molecules, with the entropy gradient from variation of “holographic screen” existing generally in spacetime. In this way, the theory is in an attempt to explain the falling tendency of Newton’s apples as entropy-increasing tendency of the thermodynamic second law.
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