Matt Ford は物理学者ではないようだが Verlindeの論文にはついていけるだろう。
A mind-bending proposal
Dr. Verlinde's proposition is not entirely unique. Others have argued that gravity, instead of being a fundamental force of the Universe, is instead an emergent phenomenon. A good deal of this thinking comes from the fact that the equations that describe gravity (in the Newtonian limit, at least) are mathematically similar to those that describe other emergent phenomena, such as fluid mechanics or thermodynamics. Where Dr. Verlinde goes the next step forward is by arguing for a definite mechanism behind gravity: differences in entropy.
In his freely available manuscript, entitled "On the Origin of Gravity and the Laws of Newton,"—the title seemingly paying homage to Einstein's famous paper whereby special relativity was laid out—Verlinde sets out his case for why gravity is, as he terms it, an "entropic force." The manuscript uses a combination of the holographic principle and black hole thermodynamics to (re)derive the basic equations of motion that Newton presented over 300 years prior.
Verlinde makes extensive use of the holographic principle in his derivations. He works with a thought experiment that assumes one has a holographic screen—one where all the information about what is contained inside of it is encoded as bits on its surface—and asks how it would interact with matter or energy that is being held just outside of it.
To show how Newton's equations of universal gravitation are derived, Verlinde begins with the difference in entropy between a mass M and a spherical holographic screen with entropy S—the information encoded on the screen would describe the emergent space inside, which would be "viewed" as equivalent to a mass M at its center. The attractive force between the the mass and the screen—what we would commonly call gravity—becomes, as Verlinde describes it, an entropic force due to the different informational densities between the two regions.
Not being content to leave it there, Verlinde goes further and rederives Newton's famous second law, F=ma (fun historical note: F=ma appears exactly zero times in Newton's famous Principia). Through that derivation, Verlinde is able to associate acceleration with an entropy gradient. According to his work, a particle at rest will stay at rest because there is no entropy gradient around it. This allows him to identify Newton's potential—the negative of the gradient, which is the acceleration a particle feels—as a potential that "keeps track of the depletion of the entropy per bit."
With such a description, extending the idea further becomes feasible. The entropic potential previously identified is shown to follow the common Poisson equation that describes the distribution of matter about a system. So he concludes that, if temperature and informational density on the holographic screen are chosen properly, then the laws of gravity fall out of this theory in a straightforward fashion.
Up to this point in the manuscript, everything Verlinde has derived applies to non-relativistic cases. How well does such a radical departure hold up when viewed through the lens of relativity theory? Here, Verlinde starts with the general relativistic description of Newton's potential. He then goes on to derive the force required to hold a particle a fixed distance away from a holographic screen, and again is able to derive the commonly accepted equation with force now described by a difference in entropy between the point and the screen. Furthermore, the manuscript lays out a path—but does not explicitly follow it—for one to rederive the full set of Einstein's field equations that form the cornerstone of general relativity using the fact that gravity, in Verlinde's work, is an "entropic force."