Entropic gravity: Difference between revisions
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==Origin== |
==Origin== |
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The thermodynamic description of gravity has a history that goes back at least to research on [[black hole thermodynamics]] by [[Jacob Bekenstein|Bekenstein]] and [[Stephen Hawking|Hawking]] in the mid-1970s. These studies suggest a deep connection between [[gravity]] and thermodynamics, which describes the behavior of heat. In 1995, [[Theodore Jacobson|Jacobson]] demonstrated that the [[Einstein field equations]] describing relativistic gravitation can be derived by combining general thermodynamic considerations with the [[equivalence principle]].<ref>{{cite journal|last=Jacobson|first=Theodore|title=Thermodynamics of Spacetime: The Einstein Equation of State|doi=10.1103/PhysRevLett.75.1260|date=4 April 1995|pages=1260–1263|issue=7|volume=75|journal=Phys. Rev. Lett.|arxiv=gr-qc/9504004|bibcode=1995PhRvL..75.1260J}}</ref> Subsequently, other physicists, most notably [[Thanu Padmanabhan]], began to explore links between gravity and [[entropy]].<ref>{{cite journal|last=Padmanabhan|first=Thanu|title=Thermodynamical Aspects of Gravity: New insights|date=26 November 2009|pages=6901|issue=4|volume=73|journal=Rep. Prog. Phys. |arxiv=0911.5004|doi=10.1088/0034-4885/73/4/046901|bibcode=2010RPPh...73d6901P}}</ref><ref>{{cite arXiv|last=Mok|first=H.M.|title=Further Explanation to the Cosmological Constant Problem by Discrete Space-time Through Modified Holographic Principle|eprint=physics/0408060|date=13 August 2004|class=physics.gen-ph}}</ref> |
The thermodynamic description of gravity has a history that goes back at least to research on [[black hole thermodynamics]] by [[Jacob Bekenstein|Bekenstein]] and [[Stephen Hawking|Hawking]] in the mid-1970s. These studies suggest a deep connection between [[gravity]] and thermodynamics, which describes the behavior of heat. In 1995, [[Theodore Jacobson|Jacobson]] demonstrated that the [[Einstein field equations]] describing relativistic gravitation can be derived by combining general thermodynamic considerations with the [[equivalence principle]].<ref>{{cite journal|last=Jacobson|first=Theodore|title=Thermodynamics of Spacetime: The Einstein Equation of State|doi=10.1103/PhysRevLett.75.1260|date=4 April 1995|pages=1260–1263|issue=7|volume=75|journal=Phys. Rev. Lett.|arxiv=gr-qc/9504004|bibcode=1995PhRvL..75.1260J}}</ref> Subsequently, other physicists, Mario J. Pinheiro<ref>{{Cite journal|last=Pinheiro|first=M. J|date=2002-02-01|title=An information-theoretic formulation of Newton's second law|url=https://doi.org/10.1209/epl/i2002-00459-5|journal=Europhysics Letters (EPL)|language=en|volume=57|issue=3|pages=305–309|doi=10.1209/epl/i2002-00459-5|issn=0295-5075}}</ref> and most notably [[Thanu Padmanabhan]], began to explore links between gravity and [[entropy]].<ref>{{cite journal|last=Padmanabhan|first=Thanu|title=Thermodynamical Aspects of Gravity: New insights|date=26 November 2009|pages=6901|issue=4|volume=73|journal=Rep. Prog. Phys. |arxiv=0911.5004|doi=10.1088/0034-4885/73/4/046901|bibcode=2010RPPh...73d6901P}}</ref><ref>{{cite arXiv|last=Mok|first=H.M.|title=Further Explanation to the Cosmological Constant Problem by Discrete Space-time Through Modified Holographic Principle|eprint=physics/0408060|date=13 August 2004|class=physics.gen-ph}}</ref> |
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==Erik Verlinde's theory== |
==Erik Verlinde's theory== |
Revision as of 19:22, 3 February 2017
![](http://upload.wikimedia.org/wikipedia/commons/thumb/0/0e/NewtonsLawOfUniversalGravitation.svg/200px-NewtonsLawOfUniversalGravitation.svg.png)
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.
Origin
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, Mario J. Pinheiro[2] and most notably Thanu Padmanabhan, began to explore links between gravity and entropy.[3][4]
Erik Verlinde's theory
In 2009, Erik Verlinde disclosed a conceptual model that describes gravity as an entropic force.[5] He argues (similar to Jacobson's result) that gravity is a consequence of the "information associated with the positions of material bodies".[6] 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."[7]
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.[8]
Verlinde's article also attracted a large amount of media exposure,[9][10] and led to immediate follow-up work in cosmology,[11][12] the dark energy hypothesis,[13] cosmological acceleration,[14][15] cosmological inflation,[16] and loop quantum gravity.[17] Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales.[18]
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
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
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" [19] 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 [20] 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.[21][22][23]
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.[24] Luboš Motl gives popular explanations of this position in his blog.[25][26]
See also
References
- ^ Jacobson, Theodore (4 April 1995). "Thermodynamics of Spacetime: The Einstein Equation of State". Phys. Rev. Lett. 75 (7): 1260–1263. arXiv:gr-qc/9504004. Bibcode:1995PhRvL..75.1260J. doi:10.1103/PhysRevLett.75.1260.
- ^ Pinheiro, M. J (1 February 2002). "An information-theoretic formulation of Newton's second law". Europhysics Letters (EPL). 57 (3): 305–309. doi:10.1209/epl/i2002-00459-5. ISSN 0295-5075.
- ^ Padmanabhan, Thanu (26 November 2009). "Thermodynamical Aspects of Gravity: New insights". Rep. Prog. Phys. 73 (4): 6901. arXiv:0911.5004. Bibcode:2010RPPh...73d6901P. doi:10.1088/0034-4885/73/4/046901.
- ^ Mok, H.M. (13 August 2004). "Further Explanation to the Cosmological Constant Problem by Discrete Space-time Through Modified Holographic Principle". arXiv:physics/0408060.
{{cite arXiv}}
:|class=
ignored (help) - ^ van Calmthout, Martijn (12 December 2009). "Is Einstein een beetje achterhaald?". de Volkskrant (in Dutch). Retrieved 6 September 2010.
- ^ E.P. Verlinde. "On the Origin of Gravity and the Laws of Newton". JHEP. arXiv:1001.0785. Bibcode:2011JHEP...04..029V. doi:10.1007/JHEP04(2011)029.
- ^ Overbye, Dennis (12 July 2010). "A Scientist Takes On Gravity". The New York Times. Retrieved 6 September 2010.
- ^ E. Verlinde, The Hidden Phase Space of our Universe, Strings 2011, Uppsala, 1 July 2011.
- ^ The entropy force: a new direction for gravity, New Scientist, 20 January 2010, issue 2744
- ^ Gravity is an entropic form of holographic information, Wired Magazine, 20 January 2010
- ^ Fu-Wen Shu; Yungui Gong (2010). "Equipartition of energy and the first law of thermodynamics at the apparent horizon". arXiv:1001.3237 [gr-qc].
- ^ Rong-Gen Cai; Li-Ming Cao; Nobuyoshi Ohta (2010). "Friedmann Equations from Entropic Force". Phys. Rev. D. 81 (6). arXiv:1001.3470. Bibcode:2010PhRvD..81f1501C. doi:10.1103/PhysRevD.81.061501.
- ^ It from Bit: How to get rid of dark energy, Johannes Koelman, 2010
- ^ Easson; Frampton; Smoot (2010). "Entropic Accelerating Universe". Phys. Lett. B. 696 (3): 273–277. arXiv:1002.4278. Bibcode:2011PhLB..696..273E. doi:10.1016/j.physletb.2010.12.025.
- ^ 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:1003.4526. Bibcode:2010PhLB..690..213C. doi:10.1016/j.physletb.2010.05.033.
- ^ Yi Wang (2010). "Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics". arXiv:1001.4786 [hep-th].
- ^ Lee Smolin (2010). "Newtonian gravity in loop quantum gravity". arXiv:1001.3668 [gr-qc].
- ^ Jarmo Mäkelä (2010). "Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde". arXiv:1001.3808 [gr-qc].
- ^ Visser, Matt. "Conservative entropic forces". arXiv:1108.5240.
- ^ Wang, Tower. "Modified entropic gravity revisited". arXiv:1211.5722.
- ^ "Verlinde's new theory of gravity passes first test". 16 December 2016.
- ^ 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:1612.03034. doi:10.1093/mnras/stw3192.
{{cite journal}}
: CS1 maint: unflagged free DOI (link) - ^ https://www.newscientist.com/article/2116446-first-test-of-rival-to-einsteins-gravity-kills-off-dark-matter/
- ^ Kobakhidze, Archil. "Gravity is not an entropic force". arXiv:1009.5414.
- ^ Motl, Luboš. "Why gravity can't be entropic". The Reference Frame. Retrieved 10 March 2015.
- ^ Motl, Luboš. "Once more: gravity is not an entropic force". The Reference Frame. Retrieved 29 April 2015.