Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes gravity as an entropic force—a force with macro-scale homogeneity but which is subject to quantum-level disorder—and not a fundamental interaction. The theory, based on string theory, black hole physics, and quantum information theory, describes gravity as an emergent phenomenon that springs from the quantum entanglement of small bits of spacetime information. As such, entropic gravity is said to abide by the second law of thermodynamics under which the entropy of a physical system tends to increase over time.
At its simplest, the theory holds that when gravity becomes vanishingly weak—levels usually seen only at interstellar distances—it diverges from its classically understood nature and its strength begins to decay linearly with distance from a mass.
Entropic gravity provides the underlying framework to explain Modified Newtonian Dynamics, or MOND, which holds that at a gravitational acceleration threshold of approximately ×10−10 meters/second2, gravitational strength begins to vary inversely (linearly) with distance from a mass rather than the normal 1.2inverse-square law of the distance. This is an exceedingly low threshold; it is 12 trillionths gravity’s strength at earth’s surface and is over 3000 times less than exists at the point where Voyager 1 crossed our solar system’s heliopause and entered interstellar space.
The theory claims to be consistent with both the macro-level observations of Newtonian gravity as well as Einstein's theory of general relativity and its gravitational distortion of spacetime. Importantly, the theory also explains—without invoking the existence of dark matter and its accompanying math featuring new free parameters that are tweaked to obtain the desired outcome—why galactic rotation curves differ from the profile expected with visible matter.
The theory of entropic gravity posits that what has been interpreted as unobserved dark matter is actually the product of quantum effects that can be regarded as a form of positive dark energy that lifts the vacuum energy of space from its ground state value. A central tenet of the theory is that the positive dark energy leads to a thermal volume law contribution to entropy that overtakes the area law of anti-de Sitter space precisely at the cosmological horizon.
The proposal has been intensely contested in the physics community, but it has also sparked a new line of research into thermodynamic properties of gravity.
The thermodynamic description of gravity has a history that goes back at least to research on black hole thermodynamics by Bekenstein and Hawking in the mid-1970s. These studies suggest a deep connection between gravity and thermodynamics, which describes the behavior of heat. In 1995, Jacobson demonstrated that the Einstein field equations describing relativistic gravitation can be derived by combining general thermodynamic considerations with the equivalence principle. Subsequently, other physicists, most notably Thanu Padmanabhan, began to explore links between gravity and entropy.
Erik Verlinde's theory
In 2009, Erik Verlinde disclosed a conceptual model that describes gravity as an entropic force. He argues (similar to Jacobson's result) that gravity is a consequence of the "information associated with the positions of material bodies". This model combines the thermodynamic approach to gravity with Gerard 't Hooft's holographic principle. It implies that gravity is not a fundamental interaction, but an emergent phenomenon which arises from the statistical behavior of microscopic degrees of freedom encoded on a holographic screen. The paper drew a variety of responses from the scientific community. Andrew Strominger, a string theorist at Harvard said “Some people have said it can’t be right, others that it’s right and we already knew it — that it’s right and profound, right and trivial."
In July 2011 Verlinde presented the further development of his ideas in a contribution to the Strings 2011 conference, including an explanation for the origin of dark matter.
Verlinde's article also attracted a large amount of media exposure, and led to immediate follow-up work in cosmology, the dark energy hypothesis, cosmological acceleration, cosmological inflation, and loop quantum gravity. Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales.
Derivation of the law of gravitation
The law of gravitation is derived from classical statistical mechanics applied to the holographic principle, that states that the description of a volume of space can be thought of as bits of binary information, encoded on a boundary to the region, a surface of area . The information is evenly distributed on the surface and each bit is stored on an elementary surface of area
By assuming that the holographic screen is a sphere of radius , its surface is given by
and one derives from these principles Newton's law of universal gravitation
Criticism and experimental tests
Entropic gravity, as proposed by Verlinde in his original article, reproduces Einstein field equations and, in a Newtonian approximation, a 1/r potential for gravitational forces. Since it does not make new physical predictions, it cannot be falsified with existing experimental methods any more than Newtonian gravity and general relativity.
Even so, entropic gravity in its current form has been severely challenged on formal grounds. Matt Visser, professor of mathematics at Victoria University of Wellington, NZ in "Conservative Entropic Forces"  has shown that the attempt to model conservative forces in the general Newtonian case (i.e. for arbitrary potentials and an unlimited number of discrete masses) leads to unphysical requirements for the required entropy and involves an unnatural number of temperature baths of differing temperatures. Visser concludes:
There is no reasonable doubt concerning the physical reality of entropic forces, and no reasonable doubt that classical (and semi-classical) general relativity is closely related to thermodynamics [52–55]. Based on the work of Jacobson [1–6], Thanu Padmanabhan [7– 12], and others, there are also good reasons to suspect a thermodynamic interpretation of the fully relativistic Einstein equations might be possible. Whether the specific proposals of Verlinde  are anywhere near as fundamental is yet to be seen — the rather baroque construction needed to accurately reproduce n-body Newtonian gravity in a Verlinde-like setting certainly gives one pause.
For the derivation of Einstein's equations from an entropic gravity perspective, Tower Wang shows  that the inclusion of energy-momentum conservation and cosmological homogeneity and isotropy requirements severely restrict a wide class of potential modifications of entropic gravity, some of which have been used to generalize entropic gravity beyond the singular case of an entropic model of Einstein's equations. Wang asserts that:
As indicated by our results, the modified entropic gravity models of form (2), if not killed, should live in a very narrow room to assure the energy-momentum conservation and to accommodate a homogeneous isotropic universe.
Entropic gravity and quantum coherence
Another criticism of entropic gravity is that entropic processes should, as critics argue, break quantum coherence. Experiments with ultra-cold neutrons in the gravitational field of Earth are claimed to show that neutrons lie on discrete levels exactly as predicted by the Schrödinger equation considering the gravitation to be a conservative potential field without any decoherent factors. Archil Kobakhidze argues that this result disproves entropic gravity. Luboš Motl gives popular explanations of this position in his blog.
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