On January 6th 2010, Erik Verlinde (a string theorist well known for his Matrix theory work) submitted a paper (arXiv:1001.0785) to arXiv entitled "On the Origin of Gravity and the Laws of Newton", in which he derives Newton's law of gravitation by assuming the microscopic structure of space-time is holographic. This led to a flurry of follow up papers, including notable notes by Lee Smolin (arXiv:1001.3668) and Jerzy Kowalski-Glikman (arXiv:1002.1035). In all papers, there are two basic assumptions made, from which the derivations follow. The first is a postulated microscopic holographic screen, or boundary Hilbert space, which is spherical, with surface area A=4*pi*r^2. The second is the expression for the change in entropy, which in the Jerzy Kowalki-Glikman paper arises from the entropy of a Misner string in Taub-NUT space. Any serious microscopic candidate theory for entropic gravity should be able to shed light on these two basic assumptions.
As of now, a precise microscopic theory for entropic gravity is not available, with LQG and SO(4,1) BF theory being considered as possible candidates. Ironically, the new found connection to Misner strings in Taub-NUT space makes it also probable that M-theory (suitably compactified) is the proper microscopic theory behind entropic gravity. Stay tuned.
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