Entropic gravity

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The theory of entropic gravity abides by Newton's law of universal gravitation on earth and at interplanetary distances but diverges from this classic nature at interstellar distances.

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 1.2×10−10 meters/second2, gravitational strength begins to vary inversely (linearly) with distance from a mass rather than the normal inverse-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.[1] Subsequently, other physicists, most notably Thanu Padmanabhan, began to explore links between gravity and entropy.[2][3]

Erik Verlinde's theory[edit]

In 2009, Erik Verlinde disclosed a conceptual model that describes gravity as an entropic force.[4] He argues (similar to Jacobson's result) that gravity is a consequence of the "information associated with the positions of material bodies".[5] 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."[6]

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.[7]

Verlinde's article also attracted a large amount of media exposure,[8][9] and led to immediate follow-up work in cosmology,[10][11] the dark energy hypothesis,[12] cosmological acceleration,[13][14] cosmological inflation,[15] and loop quantum gravity.[16] Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales.[17]

Derivation of the law of gravitation[edit]

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

where is the Planck length. The statistical equipartition theorem relates the temperature of a system with its average energy

where is the Boltzmann constant. This energy is identified with a mass by the mass–energy equivalence relation


The effective temperature experienced by a uniformly accelerating detector in a vacuum field is given by the Unruh effect. This temperature is

where is the reduced Planck constant, and is the local acceleration, which is related to a force by Newton's second law of motion


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[edit]

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" [18] 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 [26] 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 [19] 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.

A team from the Leiden Observatory testing the lensing effect of gravity around more than 33,000 galaxies concluded that Verlinde's theory agreed with the measured gravity distribution.[20][21][22]

Entropic gravity and quantum coherence[edit]

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.[23] Luboš Motl gives popular explanations of this position in his blog.[24][25]

See also[edit]


  1. ^ Jacobson, Theodore (4 April 1995). "Thermodynamics of Spacetime: The Einstein Equation of State". Phys. Rev. Lett. 75 (7): 1260–1263. arXiv:gr-qc/9504004Freely accessible. Bibcode:1995PhRvL..75.1260J. doi:10.1103/PhysRevLett.75.1260. 
  2. ^ Padmanabhan, Thanu (26 November 2009). "Thermodynamical Aspects of Gravity: New insights". Rep. Prog. Phys. 73 (4): 6901. arXiv:0911.5004Freely accessible. Bibcode:2010RPPh...73d6901P. doi:10.1088/0034-4885/73/4/046901. 
  3. ^ Mok, H.M. (13 August 2004). "Further Explanation to the Cosmological Constant Problem by Discrete Space-time Through Modified Holographic Principle". arXiv:physics/0408060Freely accessible [physics.gen-ph]. 
  4. ^ van Calmthout, Martijn (12 December 2009). "Is Einstein een beetje achterhaald?". de Volkskrant (in Dutch). Retrieved 6 September 2010. 
  5. ^ E.P. Verlinde. "On the Origin of Gravity and the Laws of Newton". JHEP. arXiv:1001.0785Freely accessible. Bibcode:2011JHEP...04..029V. doi:10.1007/JHEP04(2011)029. 
  6. ^ Overbye, Dennis (12 July 2010). "A Scientist Takes On Gravity". The New York Times. Retrieved 6 September 2010. 
  7. ^ E. Verlinde, The Hidden Phase Space of our Universe, Strings 2011, Uppsala, 1 July 2011.
  8. ^ The entropy force: a new direction for gravity, New Scientist, 20 January 2010, issue 2744
  9. ^ Gravity is an entropic form of holographic information, Wired Magazine, 20 January 2010
  10. ^ Fu-Wen Shu; Yungui Gong (2010). "Equipartition of energy and the first law of thermodynamics at the apparent horizon". arXiv:1001.3237Freely accessible [gr-qc]. 
  11. ^ Rong-Gen Cai; Li-Ming Cao; Nobuyoshi Ohta (2010). "Friedmann Equations from Entropic Force". Phys. Rev. D. 81 (6). arXiv:1001.3470Freely accessible. Bibcode:2010PhRvD..81f1501C. doi:10.1103/PhysRevD.81.061501. 
  12. ^ It from Bit: How to get rid of dark energy, Johannes Koelman, 2010
  13. ^ Easson; Frampton; Smoot (2010). "Entropic Accelerating Universe". Phys. Lett. B. 696 (3): 273–277. arXiv:1002.4278Freely accessible. Bibcode:2011PhLB..696..273E. doi:10.1016/j.physletb.2010.12.025. 
  14. ^ Yi-Fu Cai; Jie Liu; Hong Li (2010). "Entropic cosmology: a unified model of inflation and late-time acceleration". Phys. Lett. B. 690 (3): 213–219. arXiv:1003.4526Freely accessible. Bibcode:2010PhLB..690..213C. doi:10.1016/j.physletb.2010.05.033. 
  15. ^ Yi Wang (2010). "Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics". arXiv:1001.4786Freely accessible [hep-th]. 
  16. ^ Lee Smolin (2010). "Newtonian gravity in loop quantum gravity". arXiv:1001.3668Freely accessible [gr-qc]. 
  17. ^ Jarmo Mäkelä (2010). "Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde". arXiv:1001.3808Freely accessible [gr-qc]. 
  18. ^ Visser, Matt. "Conservative entropic forces". arXiv:1108.5240Freely accessible. 
  19. ^ Wang, Tower. "Modified entropic gravity revisited". arXiv:1211.5722Freely accessible. 
  20. ^ "Verlinde's new theory of gravity passes first test". December 16, 2016. 
  21. ^ Brouwer, Margot M.; et al. (11 December 2016). "First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements". Monthly Notices of the Royal Astronomical Society (to appear). arXiv:1612.03034Freely accessible. doi:10.1093/mnras/stw3192. 
  22. ^ https://www.newscientist.com/article/2116446-first-test-of-rival-to-einsteins-gravity-kills-off-dark-matter/
  23. ^ Kobakhidze, Archil. "Gravity is not an entropic force". arXiv:1009.5414Freely accessible. 
  24. ^ Motl, Luboš. "Why gravity can't be entropic". The Reference Frame. Retrieved 10 March 2015. 
  25. ^ Motl, Luboš. "Once more: gravity is not an entropic force". The Reference Frame. Retrieved 29 April 2015. 

Further reading[edit]