Entropic gravity

Entropic gravity is a physical theory that describes gravity as an entropic force . This means that it is not understood as a fundamental interaction that acts through exchange particles . Rather, a mass-containing space tries to reach a state of higher entropy according to the second law of thermodynamics , which leads to an entropic force . The theory has its roots in string theory , black hole thermodynamics and the theory of quantum information . ${\displaystyle F=T\nabla S}$

The theory agrees over many orders of magnitude with the macroscopic observations of Newton's gravitation and Albert Einstein's general theory of relativity , especially the space-time curvature described by the latter . It is subject to quantum fluctuations on small length scales , which leads to the fact that the gravitation in areas of vanishingly small gravitational acceleration (less than a threshold value of approximately ) does not decrease with , but with (linear-inverse instead of quadratic-inverse). It is therefore one of the possible explanations of Modified Newtonian Dynamics (MOON) and can explain without dark matter why the rotation curve of galaxies deviates from the profile that is expected from visible matter. ${\displaystyle 1{,}2\cdot 10^{-10}\,\mathrm {m/s^{2}} \ }$ ${\displaystyle 1/r^{2}}$ ${\displaystyle 1/r}$

A postulate of entropic gravity is therefore that what was interpreted as unobservable dark matter is rather a result of quantum effects, i.e. positive dark energy that shifts the zero point energy of spacetime above that of its ground state. The contributions of dark energy to entropy increase proportionally to the volume, while an area law is expected in the anti-de-sitter space . It is one of the statements of the theory that the former contributions become stronger than the latter, especially on the cosmological horizon .

The theory is controversial among physicists and has stimulated numerous research ideas and experiments that are intended to test its validity.

Historical classification

The thermodynamic description of gravity goes back to the research of Jacob Bekenstein and Stephen Hawking on the thermodynamics of black holes in the mid-1970s (see also Bekenstein-Hawking entropy ). Their work establishes a fundamental connection between gravity and thermodynamics. Theodore Jacobson showed in 1995 that Einstein's field equations , which describe relativistic gravity , can be derived by combining general thermodynamic considerations with the principle of equivalence . In the late 1990s, Gerardus' t Hooft and Leonard Susskind in particular developed the holographic principle . In the following years, other physicists, such as Thanu Padmanabhan , began to investigate the connection between gravity and entropy .

Erik Verlinde's theory

In 2009 Erik Verlinde published the conceptual model that describes gravity as an entropic force. He argues, similar to Jacobson's earlier, that gravity is a consequence of the “ information that is associated with the positions of material bodies . “Verlinde's 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 that arises from the statistical behavior of microscopic degrees of freedom . Just as the event horizon of a black hole separates the inner degrees of freedom from the macroscopically observed quantities, a holographic screen is thought around a mass, which separates the inner degrees of freedom from the macroscopically observable space-time coordinates. The work generated a variety of responses from the scientific community. Andrew Strominger , a string theorist at Harvard University, 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 further ideas at the Strings 2011 conference in Uppsala, including a comparison with the theories for dark matter and dark energy.

Verlinde's article generated a lot of media coverage and led to immediate follow-up work in related research areas: in cosmology, in the theory of dark energy, in considerations of the acceleration of the expansion of the universe and cosmological inflation, and in loop quantum gravity . A special microscopic model has also been proposed that actually results in entropic gravity emerging on larger scales.

Derivation of the law of gravitation

Verlinde's derivation of Newton's law of gravitation initially follows a thought experiment that Bekenstein used for a test particle near the horizon of a black hole. However, Verlinde uses this reasoning in flat space. A holographic screen separates two regions: one looks at macroscopic properties, such as the positions of particles, while the other only looks at microscopic degrees of freedom. A particle of the mass is within a distance of its Compton wavelength from the holographic screen. The holographic principle says that the entropy of the screen changes by when the particle falls into the screen and its information is combined with the microscopic degrees of freedom. Here are the reduced Planck quantum of action , the speed of light and the Boltzmann constant . This results in ${\displaystyle m}$ ${\displaystyle \Delta x=\hbar /mc}$ ${\displaystyle \Delta S=2\pi k_{\text{B}}}$ ${\displaystyle \hbar }$ ${\displaystyle c}$ ${\displaystyle k_{\text{B}}}$

${\displaystyle \Delta S=2\pi k_{\text{B}}{\frac {mc}{\hbar }}\Delta x\ .}$

The entropic force is explained using a particle on a semipermeable membrane : if the particle prefers one side of the membrane for entropy reasons and this has a temperature , the particle will experience an effective force that is sufficient. With the above equation we get: ${\displaystyle T}$ ${\displaystyle F}$ ${\displaystyle F\Delta x=T\Delta S}$

${\displaystyle F\ =\ T{\frac {\Delta S}{\Delta x}}\ =\ 2\pi k_{\text{B}}{\frac {mc}{\hbar }}T\ .}$

Verlinde notes here that a linear relationship between temperature and acceleration is also known from the Unruh effect , whereby he emphasizes that the temperature causes an acceleration and not how often the temperature is caused by the acceleration. ${\displaystyle T=\hbar a/(2\pi ck_{\text{B}})}$ ${\displaystyle T}$ ${\displaystyle a}$

If you now take the holographic screen from the above thought experiment as part of the surface of a sphere with a radius and assume that each bit of holographic information requires an area , where the Planck length and the gravitational constant are, then the entire surface of the sphere bears one number of ${\displaystyle r}$ ${\displaystyle \ell _{\text{P}}^{2}}$ ${\displaystyle \ell _{\text{P}}={\sqrt {\hbar G/c^{3}}}}$ ${\displaystyle G}$ ${\displaystyle A=4\pi r^{2}}$

${\displaystyle N\ =\ {\frac {A}{\ell _{\text{P}}^{2}}}\ =\ {\frac {Ac^{3}}{\hbar G}}\ =\ {\frac {4\pi r^{2}c^{3}}{\hbar G}}}$

Bits of information. According to the uniform distribution theorem , these degrees of freedom carry an energy at temperature ${\displaystyle N}$ ${\displaystyle T}$

${\displaystyle E\ =\ {\frac {1}{2}}Nk_{\text{B}}T\ ,}$

which, according to the equivalence of mass and energy , corresponds to a mass with . After resolved it results ${\displaystyle M}$ ${\displaystyle E=Mc^{2}}$ ${\displaystyle T}$

${\displaystyle T\ =\ {\frac {2}{k_{\text{B}}N}}E\ =\ {\frac {2}{k_{\text{B}}{\frac {4\pi r^{2}c^{3}}{\hbar G}}}}Mc^{2}\ =\ {\frac {\hbar GM}{2\pi ck_{\text{B}}r^{2}}}\ .}$

Inserted into the above formula for the force one obtains

${\displaystyle F\ =\ 2\pi k_{\text{B}}{\frac {mc}{\hbar }}\cdot {\frac {\hbar GM}{2\pi ck_{\text{B}}r^{2}}}\ =\ G{\frac {Mm}{r^{2}}}\ ,}$

thus Newton's law of gravitation .

Criticism and experimental testing

The theory of entropic gravity, as proposed by Verlinde in the original article, reproduces Einstein's field equations and, in Newton's approximation, the potential for the gravitational force. Since the results deviate from Newtonian gravity only in areas of extremely small gravitational fields, tests in laboratories on Earth do not seem feasible. Laboratories in spaceships, e.g. B. at Lagrange points in the solar system would be very expensive and complex. ${\displaystyle 1/r}$

Nevertheless (or precisely because of this) entropic gravity in its current form was questioned on a formal basis:

• The mathematics professor Matt Visser from the Victoria University of Wellington (New Zealand) showed that the attempt to model conservative forces in the general Newtonian case (i.e. with arbitrary potentials and an unlimited number of discrete masses (??) ) too unphysical demands on the necessary Entropy and leads to an unnaturally high number of heat baths at different 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. "

- Matt Visser

• Concerning the derivation of Einstein's field equations from the perspective of entropic gravity, Tower Wang showed that the demands of conservation of the energy-momentum tensor , cosmic homogeneity, and isotropy seriously limit the large number of possible modifications of entropic gravity, although some of them Modifications were used to generalize entropic gravity beyond a simple model of the Einstein equations. Wang notes:

"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."

- Tower Wang

• A major test of the theory is cosmological observations with available technologies. A research group at the Leiden Observatory , which observes the gravitational lensing effect on over 33,000 galaxies, found that their gravitational fields agree with Verlinde's theory. With conventional gravitation theory, the fields there and the measured galactic rotation curves could only be explained with a special distribution of dark matter.

• In June 2017, Princeton University's Kris Pardo found that Verlinde's theory is inconsistent with the observed rotational speeds of dwarf galaxies .

• Another point of criticism of entropic gravity is based on the fact that entropic processes should actually break quantum coherence . However, experiments with neutrons at ultra-low temperatures in the Earth's gravitational field determine that the neutrons are at precisely the discrete levels predicted by the Schrödinger equation of conventional gravitational potential without decoherent factors. Archil Kobakhidze therefore argues that this speaks against the correctness of entropic gravity. Luboš Motl explains some of Kobakhidze's criticisms in his blog.

literature

• It from bit - Entropic gravity for pedestrians , J. Koelman
• Gravity: the inside story , T Padmanabhan

Individual evidence

1. ↑ ^{a b} The threshold value for the linear-inverse behavior of entropic gravitation is very small: It is 12 trillionths of the acceleration due to gravity on the earth's surface. Even at the point where Voyager 1 has crossed the heliopause to interstellar space , the Sun's gravitational field is 3,000 times as strong. ${\displaystyle 1{,}2\cdot 10^{-10}\,\mathrm {m/s^{2}} }$
2. ↑ ^{a b c d} Erik P. Verlinde: Emergent Gravity and the Dark Universe . In: SciPost Physics . tape 2 , no. 3 , May 16, 2017, p. 16 , doi : 10.21468 / SciPostPhys.2.3.016 , arxiv : 1611.02269 .
3. ^ Theodore Jacobson: Thermodynamics of Spacetime: The Einstein Equation of State . In: Phys. Rev. Lett. tape 75 , no. 7 , April 4, 1995, 10060248, pp. 1260–1263 , doi : 10.1103 / PhysRevLett.75.1260 , PMID 10060248 , arxiv : gr-qc / 9504004 , bibcode : 1995PhRvL..75.1260J .
4. ^ Gerardus' t Hooft : Dimensional Reduction in Quantum Gravity . In: Salamfest 1993: 0284-296 . October 19, 1993, arxiv : gr-qc / 9310026 .
5. ^ Leonard Susskind : The World as a Hologram . In: Journal of Mathematical Physics . tape 36 , September 15, 1995, pp. 6377 , arxiv : hep-th / 9409089 .
6. ^ Edward Witten : Anti-de Sitter Space and Holography . In: Adv. Theor. Math. Phys. tape 2 , February 20, 1998, p. 253-291 , arxiv : hep-th / 9802150 .
7. ^ Gerardus' t Hooft : The Holographic Principle . March 1, 2000, arxiv : hep-th / 0003004 .
8. ^ Thanu Padmanabhan: Thermodynamical Aspects of Gravity: New Insights . In: Rep. Prog. Phys. tape 73 , no. 4 , November 26, 2009, p. 6901 , doi : 10.1088 / 0034-4885 / 73/4/046901 , arxiv : 0911.5004 , bibcode : 2010RPPh ... 73d6901P .
9. ^ HM Mok: Further Explanation to the Cosmological Constant Problem by Discrete Space-time Through Modified Holographic Principle . August 13, 2004, arxiv : physics / 0408060 .
10. ↑ Erik Verlinde : On the origin of gravity and the laws of Newton . In: Journal of High Energy Physics . tape 04 , no. 29 , 2011, doi : 10.1007 / JHEP04 (2011) 029 , arxiv : 1001.0785 .
11. ↑ Martijn van Calmthout: Is Einstein een beetje achterhaald? Ed .: de Volkskrant. December 12, 2009 (Dutch, no longer available online.).
12. ↑ Dennis Overbye: A Scientist Takes On Gravity. The New York Times , July 2, 2017, accessed July 2, 2017 . 
13. ↑ Erik Verlinde: The Hidden Phase Space of our Universe. (PDF) Strings 2011, Uppsala, July 1, 2011, accessed July 6, 2017 . 
14. ↑ Martijn van Calmthout: The entropy force: a new direction for gravity. New Scientist , issue 2744, January 20, 2010, accessed July 6, 2017 . 
15. ↑ Fu-Wen Shu, Yungui Gong: Equipartition of energy and the first law of thermodynamics at the apparent horizon . 2010, arxiv : 1001.3237 .
16. ^ Rong-Gen Cai, Li-Ming Cao, Nobuyoshi Ohta: Friedmann Equations from Entropic Force . In: Phys. Rev. D . tape 81 , no. 6 , 2010, doi : 10.1103 / PhysRevD.81.061501 , arxiv : 1001.3470 , bibcode : 2010PhRvD..81f1501C .
17. ^ Damien A. Easson, Paul H. Frampton, George F. Smoot: Entropic Accelerating Universe . In: Phys. Lett. B . tape 696 , no. 3 , 2010, p. 273–277 , doi : 10.1016 / j.physletb.2010.12.025 , arxiv : 1002.4278 , bibcode : 2011PhLB..696..273E .
18. ↑ Yi-Fu Cai, Jie Liu, Hong Li: Entropic cosmology: a unified model of inflation and late-time acceleration . In: Phys. Lett. B . tape 690 , no. 3 , 2010, p. 213–219 , doi : 10.1016 / j.physletb.2010.05.033 , arxiv : 1003.4526 , bibcode : 2010PhLB..690..213C .
19. ^ Yi Wang: Towards a Holographic Description of Inflation and Generation of Fluctuations from Thermodynamics . 2010, arxiv : 1001.4786 .
20. ↑ Lee Smolin: Newtonian gravity in loop quantum gravity . 2010, arxiv : 1001.3668 .
21. ^ Jarmo Mäkelä: Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde . 2010, arxiv : 1001.3808 .
22. ^ Jacob Bekenstein: Black holes and entropy . In: Phys. Rev. D . tape 7 , no. 8 , April 15, 1973, doi : 10.1103 / PhysRevD.7.2333 .
23. ↑ Matt Visser: Conservative entropic forces . August 26, 2011, arxiv : 1108.5240 .
24. ^ ^{A b} Tower Wang: Modified entropic gravity revisited . November 25, 2012, arxiv : 1211.5722 .
25. ^ Verlinde's new theory of gravity passes first test. phys.org, December 16, 2016, accessed July 2, 2017 . 
26. ^ Margot M. Brouwer et al .: First test of Verlinde's theory of Emergent Gravity using Weak Gravitational Lensing measurements . In: Monthly Notices of the Royal Astronomical Society . tape 466 , December 11, 2016, p. 2547-2559 , doi : 10.1093 / mnras / stw3192 , arxiv : 1612.03034 .
27. ↑ Mark Anderson: First test of rival to Einstein's gravity kills off dark matter. New Scientist, December 15, 2016, accessed July 2, 2017 . 
28. ^ Kris Pardo: Testing Emergent Gravity with Isolated Dwarf Galaxies . June 2, 2017, arxiv : 1706.00785 .
29. ↑ Archil Kobakhidze: Gravity is not an entropic force . September 27, 2010, arxiv : 1009.5414 .
30. ↑ Archil Kobakhidze: Once more: gravity is not to force entropic . August 21, 2011, arxiv : 1108.4161 .
31. ↑ Experiments Show Gravity Is Not an Emergent Phenomenon. MIT Technology Review, August 24, 2011, accessed July 7, 2017 . 
32. ^ Luboš Motl: Why gravity can't be entropic. The Reference Frame, accessed July 2, 2017 . 
33. ^ Luboš Motl: Once more: gravity is not an entropic force. The Reference Frame, accessed July 2, 2017 .