Entropic gravity, also known as emergent gravity, is a theory in modern physics that describes
gravity as an ''
entropic force
In physics, an entropic force acting in a system is an emergent phenomenon resulting from the entire system's statistical tendency to increase its entropy, rather than from a particular underlying force on the atomic scale.
Mathematical formula ...
''—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
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can defo ...
physics, and
quantum information theory
Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both t ...
, describes gravity as an ''emergent'' phenomenon that springs from the
quantum entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...
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.
The theory has been controversial within the physics community but has sparked research and experiments to test its validity.
Significance
At its simplest, the theory holds that when gravity becomes vanishingly weak—levels 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 an underlying framework to explain
Modified Newtonian Dynamics
Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. It is an alternative to the hypothesis of dark matter in terms of explaini ...
, or MOND, which holds that at a
gravitational acceleration threshold of approximately , 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, measuring only 12 trillionths
gravity's strength at Earth's surface; an object dropped from a height of one meter would fall for 36 hours were Earth's gravity this weak. It is also 3,000 times less than the remnant of Earth's gravitational field that exists at the point where crossed the solar system's
heliopause and entered interstellar space.
The theory claims to be consistent with both the macro-level observations of
Newtonian gravity
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...
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 tweaking of its new
free parameter
A free parameter is a variable in a mathematical model which cannot be predicted precisely or constrained by the model and must be estimated experimentally or theoretically. A mathematical model, theory, or conjecture
In mathematics, a conje ...
s) 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 the product of quantum effects that can be regarded as a form of ''positive
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
'' that lifts the
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experimental ...
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
In mathematics and physics, ''n''-dimensional anti-de Sitter space (AdS''n'') is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are named after Willem de Sitter (1872� ...
precisely at
the
cosmological horizon
A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Co ...
.
Thus this theory provides an alternative explanation for what mainstream physics currently attributes to
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...
. Since dark matter is believed to compose the vast majority of the universe's mass, a theory in which it is absent has huge implications for
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
. In addition to continuing theoretical work in various directions, there are many experiments planned or in progress to actually detect or better determine the properties of dark matter (beyond its gravitational attraction), all of which would be undermined by an alternative explanation for the gravitational effects currently attributed to this elusive entity.
Origin
The thermodynamic description of gravity has a history that goes back at least to research on
black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons. As the study of the statistical mechanics of black-body radiation led to the development ...
by
Bekenstein and
Hawking
Hawking may refer to:
People
* Stephen Hawking (1942–2018), English theoretical physicist and cosmologist
* Hawking (surname), a family name (including a list of other persons with the name)
Film
* ''Hawking'' (2004 film), about Stephen Ha ...
in the mid-1970s. These studies suggest a deep connection between
gravity and thermodynamics, which describes the behavior of heat. In 1995,
Jacobson
Jacobson may refer to:
* Jacobson (surname), including a list of people with the name
* Jacobson, Minnesota, a place in the United States
* Jacobson's, an American regional department store chain
See also
* Jacobsen (disambiguation)
* Jakob ...
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 proposed 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
Gerardus (Gerard) 't Hooft (; born July 5, 1946) is a Dutch theoretical physicist and professor at Utrecht University, the Netherlands. He shared the 1999 Nobel Prize in Physics with his thesis advisor Martinus J. G. Veltman "for elucidating th ...
's
holographic principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a ...
. It implies that gravity is not a
fundamental interaction, but an
emergent phenomenon
In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole.
Emergen ...
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
Andrew Eben Strominger (; born 1955) is an American theoretical physicist who is the director of Harvard's Center for the Fundamental Laws of Nature. He has made significant contributions to quantum gravity and string theory. These include his ...
, 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
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from seconds after the conjectured Big Bang singularity ...
, and
loop quantum gravity
Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...
. Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales. Entropic gravity can emerge from quantum entanglement of local
Rindler horizons.
Derivation of the law of gravitation
The law of gravitation is derived from classical statistical mechanics applied to the
holographic principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a ...
, that states that the description of a volume of space can be thought of as
bits of binary information, encoded on a boundary to that region, a closed surface of area
. The information is evenly distributed on the surface with each bit requiring an area equal to
, the so-called ''Planck area'', from which
can thus be computed:
:
where
is the
Planck length. The Planck length is defined as:
:
where
is the
universal gravitational constant
The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
,
is the speed of light, and
is the reduced
Planck constant. When substituted in the equation for
we find:
:
The statistical
equipartition theorem defines the temperature
of a system with
degrees of freedom in terms of its energy
such that:
:
where
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constan ...
. This is the
equivalent energy for a mass
according to:
:
.
The effective temperature experienced due to a uniform acceleration in a
vacuum field according to the
Unruh effect
The Unruh effect (also known as the Fulling–Davies–Unruh effect) is a kinematic prediction of quantum field theory that an accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe ...
is:
:
,
where
is that acceleration, which for a mass
would be attributed to a force
according to
Newton's second law
Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:
# A body remains at rest, or in motion ...
of motion:
:
.
Taking the holographic screen to be a sphere of radius
, the surface area would be given by:
:
.
From algebraic substitution of these into the above relations, one derives
Newton's law of universal gravitation:
:
.
Note that this derivation assumes that the number of the binary bits of information is equal to the number of the degrees of freedom.
:
Criticism and experimental tests
Entropic gravity, as proposed by Verlinde in his original article, reproduces the
Einstein field equations and, in a Newtonian approximation, a
potential for gravitational forces. Since its results do not differ from Newtonian gravity except in regions of extremely small gravitational fields, testing the theory with earth-based laboratory experiments does not appear feasible. Spacecraft-based experiments performed at
Lagrangian point
In celestial mechanics, the Lagrange points (; also Lagrangian points or libration points) are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Mathematically, this involves the solution of ...
s within our solar system would be expensive and challenging.
Even so, entropic gravity in its current form has been severely challenged on formal grounds.
Matt Visser
Matt Visser is a mathematics Professor at Victoria University of Wellington, in New Zealand.
Work
Visser's research interests include general relativity, quantum field theory and cosmology.
Visser has produced a large number of research paper ...
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:
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 restricts 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:
Cosmological observations using available technology can be used to test the theory. On the basis of lensing by the galaxy cluster Abell 1689, Nieuwenhuizen concludes that EG is strongly ruled out unless additional (dark) matter-like eV neutrinos is added. A team from
Leiden Observatory
Leiden Observatory ( nl, Sterrewacht Leiden) is an astronomical institute of Leiden University, in the Netherlands. Established in 1633 to house the quadrant of Rudolph Snellius, it is the oldest operating university observatory in the world, with ...
statistically observing the
lensing effect of gravitational fields at large distances from the centers of more than 33,000 galaxies found that those gravitational fields were consistent with Verlinde's theory. Using conventional gravitational theory, the fields implied by these observations (as well as from measured
galaxy rotation curves) could only be ascribed to a particular distribution of
dark matter
Dark matter is a hypothetical form of matter thought to account for approximately 85% of the matter in the universe. Dark matter is called "dark" because it does not appear to interact with the electromagnetic field, which means it does not a ...
. In June 2017, a study by
Princeton University researcher Kris Pardo asserted that Verlinde's theory is inconsistent with the observed rotation velocities of
dwarf galaxies.
[ arXiv accessed 2017-06-22.] Another theory of entropy based on geometric considerations (Quantitative Geometrical Thermodynamics, QGT
) provides an entropic basis for the holographic principle and also offers another explanation for galaxy rotation curves as being due to the entropic influence
of the central supermassive blackhole found in the centre of a spiral galaxy.
Sabine Hossenfelder
Sabine Hossenfelder (born 1976) is a German theoretical physicist, author, musician and YouTuber. She is currently employed as a research fellow at the Frankfurt Institute for Advanced Studies. She is the author of ''Lost in Math: How Beauty L ...
argues that "one should interpret these studies
omparing dark matter gravitational studies with EGwith caution" because "approximations must be made to arrive at
he to be tested EGequation
and it's not yet clear that the approximations are themselves correct.
In 2018, Zhi-Wei Wang and Samuel L. Braunstein showed that, while spacetime surfaces near black holes (called stretched horizons) do obey an analog of the first law of thermodynamics, ordinary spacetime surfaces — including holographic screens — generally do not, thus undermining the key thermodynamic assumption of the emergent gravity program.
In his 1964 lecture on the Relation of Mathematics and Physics,
Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ...
describes a related theory for gravity where the gravitational force is explained due to an entropic force due to unspecified microscopic degrees of freedom. However, he immediately points out that the resulting theory cannot be correct as the
fluctuation-dissipation theorem would also lead to friction which would slow down the motion of the planets which contradicts observations.
Entropic gravity and quantum coherence
Another criticism of entropic gravity is that entropic processes should, as critics argue, break
quantum coherence. There is no theoretical framework quantitatively describing the strength of such decoherence effects, though. The temperature of the gravitational field in earth gravity well is very small (on the order of 10K).
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, while Chaichian ''et al''. suggest a potential loophole in the argument in weak gravitational fields such as those affecting Earth-bound experiments.
See also
*
*
*
*
*
*
*
*
*
*
Footnotes
References
Further reading
It from bit – Entropic gravity for pedestrians J. Koelman
Gravity: the inside story T Padmanabhan
Experiments Show Gravity Is Not an Emergent Phenomenon
{{Portal bar, Physics, Mathematics, Astronomy, Stars, Spaceflight, Outer space, Solar System, Science
Theories of gravity
Gravity As An Entropic Force
Gravity As An Entropic Force
Emergence
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