Quantum gravity (QG) is a field of
theoretical physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...
that seeks to describe gravity according to the principles of
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
; it deals with environments in which neither
gravitational
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stron ...
nor quantum effects can be ignored,
such as in the vicinity of
black holes or similar compact astrophysical objects, such as
neutron stars
A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
.
Three of the four
fundamental force
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
s of physics are described within the framework of
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistr ...
and
quantum field theory. The current understanding of the fourth force,
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
, is based on
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's
general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
, which is formulated within the entirely different framework of
classical physics. However, that description is incomplete: describing the gravitational field of a black hole in the general theory of relativity leads physical quantities, such as the
spacetime curvature
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. G ...
, to diverge at the center of the black hole.
This signals the breakdown of the general theory of relativity and the need for a theory that goes beyond general relativity into the quantum realm. At distances very close to the center of the black hole (closer than the
Planck length),
quantum fluctuations
In quantum physics, a quantum fluctuation (also known as a vacuum state fluctuation or vacuum fluctuation) is the temporary random change in the amount of energy in a point in space, as prescribed by Werner Heisenberg's uncertainty principle. ...
of spacetime are expected to play an important role. To describe these quantum effects a theory of quantum gravity is needed. Such a theory should allow the description to be extended closer to the center and might even allow an understanding of physics at the center of a black hole. On more formal grounds, one can argue that a classical system cannot consistently be coupled to a quantum one.
The field of quantum gravity is actively developing, and theorists are exploring a variety of approaches to the problem of quantum gravity, the most popular being
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
and
loop quantum gravity.
All of these approaches aim to describe the quantum behavior of the
gravitational field. This does not necessarily include
unifying all fundamental interactions into a single mathematical framework. However, many approaches to quantum gravity, such as
string theory, try to develop a framework that describes all fundamental forces. Such a theory is often referred to as a
theory of everything
A theory of everything (TOE or TOE/ToE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all asp ...
. Others, such as loop quantum gravity, make no such attempt; instead, they make an effort to quantize the gravitational field while it is kept separate from the other forces.
One of the difficulties of formulating a quantum gravity theory is that direct observation of quantum gravitational effects is thought to only appear at length scales near the
Planck scale, around 10
−35 meters, a scale far smaller, and hence only accessible with far higher energies, than those currently available in high energy
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
s. Therefore, physicists lack experimental data which could distinguish between the competing theories which have been proposed.
[Quantum effects in the early universe might have an observable effect on the structure of the present universe, for example, or gravity might play a role in the unification of the other forces. Cf. the text by Wald cited above.][On the quantization of the geometry of spacetime, see also in the article Planck length, in the examples]
Thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anc ...
approaches have been suggested as a testing tool for quantum gravity theories. In the field of quantum gravity there are several open questions - e.g., it is not known how spin of elementary particles sources gravity, and thought experiments could provide a pathway to explore possible resolutions to these questions,
even in the absence of lab experiments or physical observations.
In the early 21st century, new experiment designs and technologies have arisen which suggest that indirect approaches to testing quantum gravity may be feasible over the next few decades.
This field of study is called
phenomenological quantum gravity
Phenomenological quantum gravity is the research field that deals with phenomenology of quantum gravity. The relevance of this research area derives from the fact that none of the candidate theories for quantum gravity has yielded experimentally te ...
.
Overview
![Quantum gravity](https://upload.wikimedia.org/wikipedia/commons/6/64/Quantum_gravity.svg)
Much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. General relativity models gravity as curvature of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
: in the slogan of
John Archibald Wheeler
John Archibald Wheeler (July 9, 1911April 13, 2008) was an American theoretical physicist. He was largely responsible for reviving interest in general relativity in the United States after World War II. Wheeler also worked with Niels Bohr in ...
, "Spacetime tells matter how to move; matter tells spacetime how to curve." On the other hand, quantum field theory is typically formulated in the ''flat'' spacetime used in
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
. No theory has yet proven successful in describing the general situation where the dynamics of matter, modeled with quantum mechanics, affect the curvature of spacetime. If one attempts to treat gravity as simply another quantum field, the resulting theory is not
renormalizable
Renormalization is a collection of techniques in quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, that are used to treat infinities arising in calculated quantities by altering va ...
.
Even in the simpler case where the curvature of spacetime is fixed ''a priori,'' developing quantum field theory becomes more mathematically challenging, and many ideas physicists use in quantum field theory on flat spacetime are no longer applicable.
It is widely hoped that a theory of quantum gravity would allow us to understand problems of very high energy and very small dimensions of space, such as the behavior of
black holes, and the
origin of the universe
Cosmogony is any model concerning the origin of the cosmos or the universe.
Overview
Scientific theories
In astronomy, cosmogony refers to the study of the origin of particular astrophysical objects or systems, and is most commonly used i ...
.
Quantum mechanics and general relativity
Graviton
The observation that all
fundamental forces
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist: the gravitational and electro ...
except gravity have one or more known
messenger particles leads researchers to believe that at least one must exist for gravity. This hypothetical particle is known as the ''graviton''. These particles act as a
force particle similar to the
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
of the electromagnetic interaction. Under mild assumptions, the structure of general relativity requires them to follow the quantum mechanical description of interacting theoretical spin-2 massless particles.
Many of the accepted notions of a unified theory of physics since the 1970s assume, and to some degree depend upon, the existence of the graviton.
The
Weinberg–Witten theorem
In theoretical physics, the Weinberg–Witten (WW) theorem, proved by Steven Weinberg and Edward Witten, states that massless particles (either composite or elementary) with spin ''j'' > 1/2 cannot carry a
Lorentz-covariant current, while massle ...
places some constraints on theories in which
the graviton is a composite particle.
While gravitons are an important theoretical step in a quantum mechanical description of gravity, they are generally believed to be undetectable because they interact too weakly.
Nonrenormalizability of gravity
General relativity, like
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
, is a
classical field theory. One might expect that, as with electromagnetism, the gravitational force should also have a corresponding
quantum field theory.
However, gravity is perturbatively
nonrenormalizable. For a quantum field theory to be well defined according to this understanding of the subject, it must be
asymptotically free
In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases.
Asymptotic fr ...
or
asymptotically safe. The theory must be characterized by a choice of ''finitely many'' parameters, which could, in principle, be set by experiment. For example, in
quantum electrodynamics
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and spec ...
these parameters are the charge and mass of the electron, as measured at a particular energy scale.
On the other hand, in quantizing gravity there are, in
perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...
, ''infinitely many independent parameters'' (counterterm coefficients) needed to define the theory. For a given choice of those parameters, one could make sense of the theory, but since it is impossible to conduct infinite experiments to fix the values of every parameter, it has been argued that one does not, in perturbation theory, have a meaningful physical theory. At low energies, the logic of the
renormalization group
In theoretical physics, the term renormalization group (RG) refers to a formal apparatus that allows systematic investigation of the changes of a physical system as viewed at different scales. In particle physics, it reflects the changes in the ...
tells us that, despite the unknown choices of these infinitely many parameters, quantum gravity will reduce to the usual Einstein theory of general relativity. On the other hand, if we could probe very high energies where quantum effects take over, then ''every one'' of the infinitely many unknown parameters would begin to matter, and we could make no predictions at all.
It is conceivable that, in the correct theory of quantum gravity, the infinitely many unknown parameters will reduce to a finite number that can then be measured. One possibility is that normal
perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...
is not a reliable guide to the renormalizability of the theory, and that there really ''is'' a
UV fixed point
In a quantum field theory, one may calculate an effective or running coupling constant that defines the coupling of the theory measured at a given momentum scale. One example of such a coupling constant is the electric charge.
In approximate cal ...
for gravity. Since this is a question of
non-perturbative
In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. An example is the function
: f(x) = e^,
which does not have a Taylor series at ''x'' = 0. Every coefficient of the Taylor ...
quantum field theory, finding a reliable answer is difficult, pursued in the
asymptotic safety program. Another possibility is that there are new, undiscovered symmetry principles that constrain the parameters and reduce them to a finite set. This is the route taken by
string theory, where all of the excitations of the string essentially manifest themselves as new symmetries.
Quantum gravity as an effective field theory
In an
effective field theory, not all but the first few of the infinite set of parameters in a nonrenormalizable theory are suppressed by huge energy scales and hence can be neglected when computing low-energy effects. Thus, at least in the low-energy regime, the model is a predictive quantum field theory.
Furthermore, many theorists argue that the Standard Model should be regarded as an effective field theory itself, with "nonrenormalizable" interactions suppressed by large energy scales and whose effects have consequently not been observed experimentally.
Works pioneered by Barvinsky and Vilkovisky suggest as a starting point up to second order in curvature the following action, consisting of local and non-local terms:
:
where
is an energy scale. The exact values of the coefficients
are unknown, as they depend on the nature of the ultra-violet theory of quantum gravity.
is an operator with the integral representation
:
By treating general relativity as an
effective field theory, one can actually make legitimate predictions for quantum gravity, at least for low-energy phenomena. An example is the well-known calculation of the tiny first-order quantum-mechanical correction to the classical Newtonian gravitational potential between two masses.
Moreover, one can compute the quantum gravitational corrections to classical thermodynamic properties of black holes, most importantly the entropy. A rigorous derivation of the quantum gravitational corrections to the entropy of Schwarzschild black holes was provided by Calmet and Kuipers. A generalisation for charged (Reissner–Nordström) black holes was subsequently carried out by Campos Delgado.
Spacetime background dependence
A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in
Newtonian mechanics and
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws ...
; the spacetime geometry is dynamic. While simple to grasp in principle, this is a complex idea to understand about general relativity, and its consequences are profound and not fully explored, even at the classical level. To a certain extent, general relativity can be seen to be a
relational theory
Relationalism is any theoretical position that gives importance to the relational nature of things. For relationalism, things exist and function only as relational entities. Relationalism may be contrasted with relationism, which tends to emphasize ...
, in which the only physically relevant information is the relationship between different events in space-time.
On the other hand, quantum mechanics has depended since its inception on a fixed background (non-dynamic) structure. In the case of quantum mechanics, it is time that is given and not dynamic, just as in Newtonian classical mechanics. In relativistic quantum field theory, just as in classical field theory,
Minkowski spacetime
In mathematical physics, Minkowski space (or Minkowski spacetime) () is a combination of Three-dimensional space, three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two Event (rel ...
is the fixed background of the theory.
String theory
String theory can be seen as a generalization of
quantum field theory where instead of point particles, string-like objects propagate in a fixed spacetime background, although the interactions among closed strings give rise to
space-time in a dynamical way.
Although string theory had its origins in the study of
quark confinement
In quantum chromodynamics (QCD), color confinement, often simply called confinement, is the phenomenon that color-charged particles (such as quarks and gluons) cannot be isolated, and therefore cannot be directly observed in normal conditions ...
and not of quantum gravity, it was soon discovered that the string spectrum contains the
graviton
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathem ...
, and that "condensation" of certain vibration modes of strings is equivalent to a modification of the original background. In this sense, string perturbation theory exhibits exactly the features one would expect of a
perturbation theory
In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...
that may exhibit a strong dependence on asymptotics (as seen, for example, in the
AdS/CFT
In theoretical physics, the anti-de Sitter/conformal field theory correspondence, sometimes called Maldacena duality or gauge/gravity duality, is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter s ...
correspondence) which is a weak form of
background dependence.
Background independent theories
Loop quantum gravity is the fruit of an effort to formulate a
background-independent quantum theory.
Topological quantum field theory
In gauge theory and mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory which computes topological invariants.
Although TQFTs were invented by physicists, they are also of mathe ...
provided an example of background-independent quantum theory, but with no local degrees of freedom, and only finitely many degrees of freedom globally. This is inadequate to describe gravity in 3+1 dimensions, which has local degrees of freedom according to general relativity. In 2+1 dimensions, however, gravity is a topological field theory, and it has been successfully quantized in several different ways, including
spin network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear f ...
s.
Semi-classical quantum gravity
Quantum field theory on curved (non-Minkowskian) backgrounds, while not a full quantum theory of gravity, has shown many promising early results. In an analogous way to the development of quantum electrodynamics in the early part of the 20th century (when physicists considered quantum mechanics in classical electromagnetic fields), the consideration of quantum field theory on a curved background has led to predictions such as black hole radiation.
Phenomena such as 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 ...
, in which particles exist in certain accelerating frames but not in stationary ones, do not pose any difficulty when considered on a curved background (the Unruh effect occurs even in flat Minkowskian backgrounds). The vacuum state is the state with the least energy (and may or may not contain particles).
Problem of time
A conceptual difficulty in combining quantum mechanics with general relativity arises from the contrasting role of time within these two frameworks. In quantum theories time acts as an independent background through which states evolve, with the
Hamiltonian operator
Hamiltonian may refer to:
* Hamiltonian mechanics, a function that represents the total energy of a system
* Hamiltonian (quantum mechanics), an operator corresponding to the total energy of that system
** Dyall Hamiltonian, a modified Hamiltonia ...
acting as the
generator of infinitesimal translations of quantum states through time. In contrast, general relativity
treats time as a dynamical variable which relates directly with matter and moreover requires the Hamiltonian constraint to vanish. Because this variability of time has been
observed macroscopically, it removes any possibility of employing a fixed notion of time, similar to the conception of time in quantum theory, at the macroscopic level.
Candidate theories
There are a number of proposed quantum gravity theories. Currently, there is still no complete and consistent quantum theory of gravity, and the candidate models still need to overcome major formal and conceptual problems. They also face the common problem that, as yet, there is no way to put quantum gravity predictions to experimental tests, although there is hope for this to change as future data from cosmological observations and particle physics experiments become available.
String theory
![Calabi-Yau](https://upload.wikimedia.org/wikipedia/commons/d/d4/Calabi-Yau.png)
The central idea of string theory is to replace the classical concept of a
point particle
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up ...
in
quantum field theory with a quantum theory of one-dimensional extended objects:
string theory. At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different
modes
Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to:
Arts and entertainment
* '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine
* ''Mode'' magazine, a fictional fashion magazine which is ...
of oscillation of one and the same type of fundamental string appear as particles with different (
electric
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and other)
charges
Charge or charged may refer to:
Arts, entertainment, and media Films
* ''Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* '' Charge!!'', an album by The Aqu ...
. In this way, string theory promises to be a
unified description of all particles and interactions. The theory is successful in that one mode will always correspond to a
graviton
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathem ...
, the
messenger particle In quantum field theory, a force carrier, also known as messenger particle or intermediate particle, is a type of particle that gives rise to forces between other particles. These particles serve as the quanta of a particular kind of physical fi ...
of gravity; however, the price of this success is unusual features such as six extra dimensions of space in addition to the usual three for space and one for time.
In what is called the
second superstring revolution
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum ...
, it was conjectured that both string theory and a unification of general relativity and
supersymmetry known as
supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
form part of a hypothesized eleven-dimensional model known as
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's ...
, which would constitute a uniquely defined and consistent theory of quantum gravity. As presently understood, however, string theory admits a very large number (10
500 by some estimates) of consistent vacua, comprising the so-called "
string landscape". Sorting through this large family of solutions remains a major challenge.
Loop quantum gravity
![Spin network](https://upload.wikimedia.org/wikipedia/commons/5/52/Spin_network.svg)
Loop quantum gravity seriously considers general relativity's insight that spacetime is a dynamical field and is therefore a quantum object. Its second idea is that the quantum discreteness that determines the particle-like behavior of other field theories (for instance, the photons of the electromagnetic field) also affects the structure of space.
The main result of loop quantum gravity is the derivation of a granular structure of space at the Planck length. This is derived from following considerations: In the case of electromagnetism, the
quantum operator
In physics, an operator is a function over a space of physical states onto another space of physical states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Bec ...
representing the energy of each frequency of the field has a discrete spectrum. Thus the energy of each frequency is quantized, and the quanta are the photons. In the case of gravity, the operators representing the area and the volume of each surface or space region likewise have discrete spectra. Thus area and volume of any portion of space are also quantized, where the quanta are elementary quanta of space. It follows, then, that spacetime has an elementary quantum granular structure at the Planck scale, which cuts off the ultraviolet infinities of quantum field theory.
The quantum state of spacetime is described in the theory by means of a mathematical structure called
spin network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear f ...
s. Spin networks were initially introduced by
Roger Penrose in abstract form, and later shown by
Carlo Rovelli and
Lee Smolin
Lee Smolin (; born June 6, 1955) is an American theoretical physicist, a faculty member at the Perimeter Institute for Theoretical Physics, an adjunct professor of physics at the University of Waterloo and a member of the graduate faculty of the ...
to derive naturally from a non-perturbative quantization of general relativity. Spin networks do not represent quantum states of a field in spacetime: they represent directly quantum states of spacetime.
The theory is based on the reformulation of general relativity known as
Ashtekar variables
In the ADM formulation of general relativity, spacetime is split into spatial slices and a time axis. The basic variables are taken to be the induced metric q_ (x) on the spatial slice and the metric's conjugate momentum K^ (x), which is related ...
, which represent geometric gravity using mathematical analogues of
electric
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by ...
and
magnetic fields.
In the quantum theory, space is represented by a network structure called a
spin network
In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear f ...
, evolving over time in discrete steps.
The dynamics of the theory is today constructed in several versions. One version starts with the
canonical quantization of general relativity. The analogue of the
Schrödinger equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...
is a
Wheeler–DeWitt equation
The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general ...
, which can be defined within the theory.
In the covariant, or
spinfoam
In physics, the topological structure of spinfoam or spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman's path integral description of quantum gravity. These structu ...
formulation of the theory, the quantum dynamics is obtained via a sum over discrete versions of spacetime, called spinfoams. These represent histories of spin networks.
Other theories
There are a number of other approaches to quantum gravity. The theories differ depending on which features of general relativity and quantum theory are accepted unchanged, and which features are modified. Examples include:
*
Asymptotic safety in quantum gravity
*
Euclidean quantum gravity
In theoretical physics, Euclidean quantum gravity is a version of quantum gravity. It seeks to use the Wick rotation to describe the force of gravity according to the principles of quantum mechanics.
Introduction in layperson's terms
The W ...
* Integral method
*
Causal dynamical triangulation
Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent.
This means that it does not assum ...
*
Causal fermion system
The theory of causal fermion systems is an approach to describe fundamental physics. It provides a unification of the weak, the strong and the electromagnetic forces with gravity at the level of classical field theory. Moreover, it gives qu ...
s
*
Causal Set Theory
* Covariant Feynman
path integral approach
*
Dilatonic quantum gravity
*
Double copy theory
Double copy theory is a theory in theoretical physics, specifically in quantum gravity, that hypothesizes a perturbative Duality (mathematics), duality between gauge theory and gravity. The theory says that scattering amplitudes in Non-abelian gau ...
*
Group field theory
Group field theory (GFT) is a quantum field theory in which the base manifold is taken to be a Lie group. It is closely related to background independent quantum gravity approaches such as loop quantum gravity, the spin foam formalism and ca ...
*
Wheeler–DeWitt equation
The Wheeler–DeWitt equation for theoretical physics and applied mathematics, is a field equation attributed to John Archibald Wheeler and Bryce DeWitt. The equation attempts to mathematically combine the ideas of quantum mechanics and general ...
*
Geometrodynamics
In theoretical physics, geometrodynamics is an attempt to describe spacetime and associated phenomena completely in terms of geometry. Technically, its goal is to grand unification, unify the fundamental forces and reformulate general relativity ...
*
Hořava–Lifshitz gravity
Hořava–Lifshitz gravity (or Hořava gravity) is a theory of quantum gravity proposed by Petr Hořava in 2009. It solves the problem of different concepts of time in quantum field theory and general relativity by treating the quantum concept as ...
*
MacDowell–Mansouri action
*
Noncommutative geometry
Noncommutative geometry (NCG) is a branch of mathematics concerned with a geometric approach to noncommutative algebras, and with the construction of ''spaces'' that are locally presented by noncommutative algebras of functions (possibly in some g ...
*
Path-integral based models of
quantum cosmology
Quantum cosmology is the attempt in theoretical physics to develop a quantum theory of the universe. This approach attempts to answer open questions of classical physical cosmology, particularly those related to the first phases of the universe.
...
*
Regge calculus In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961. Available ...
*
Shape Dynamics
In theoretical physics, shape dynamics is a theory of gravity that implements Mach's principle, developed with the specific goal to obviate the problem of time and thereby open a new path toward the resolution of incompatibilities between general ...
*
String-net
In condensed matter physics, a string-net is an extended object whose collective behavior has been proposed as a physical mechanism for topological order by Michael A. Levin and Xiao-Gang Wen. A particular string-net model may involve only closed ...
s and
quantum graphity
*
Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
*
Twistor theory
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic are ...
*
Canonical quantum gravity
In physics, canonical quantum gravity is an attempt to quantize the canonical formulation of general relativity (or canonical gravity). It is a Hamiltonian formulation of Einstein's general theory of relativity. The basic theory was outlined by ...
Experimental tests
As was emphasized above, quantum gravitational effects are extremely weak and therefore difficult to test. For this reason, the possibility of experimentally testing quantum gravity had not received much attention prior to the late 1990s. However, in the past decade, physicists have realized that evidence for quantum gravitational effects can guide the development of the theory. Since theoretical development has been slow, the field of
phenomenological quantum gravity
Phenomenological quantum gravity is the research field that deals with phenomenology of quantum gravity. The relevance of this research area derives from the fact that none of the candidate theories for quantum gravity has yielded experimentally te ...
, which studies the possibility of experimental tests, has obtained increased attention.
The most widely pursued possibilities for quantum gravity phenomenology include gravitationally mediated entanglement, violations of
Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
, imprints of quantum gravitational effects in the
cosmic microwave background
In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
(in particular its polarization), and decoherence induced by fluctuations in the
space-time foam.
ESA
, owners =
, headquarters = Paris, Île-de-France, France
, coordinates =
, spaceport = Guiana Space Centre
, seal = File:ESA emblem seal.png
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, image = Views in the Main Control Room (120 ...
's
INTEGRAL
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along wit ...
satellite measured polarization of photons of different wavelengths and was able to place a limit in the granularity of space that is less than 10
−48m, or 13 orders of magnitude below the Planck scale.
The
BICEP2 experiment detected what was initially thought to be primordial
B-mode polarization caused by
gravitational waves in the early universe. Had the signal in fact been primordial in origin, it could have been an indication of quantum gravitational effects, but it soon transpired that the polarization was due to
interstellar dust
Cosmic dust, also called extraterrestrial dust, star dust or space dust, is dust which exists in outer space, or has fallen on Earth. Most cosmic dust particles measure between a few molecules and 0.1 mm (100 micrometers). Larger particles are c ...
interference.
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See also
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De Sitter relativity
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Dilaton
In particle physics, the hypothetical dilaton particle is a particle of a scalar field \varphi that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theor ...
*
Doubly special relativity
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Gravitational decoherence
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Gravitomagnetism
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain ...
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Hawking radiation
Hawking radiation is theoretical black body radiation that is theorized to be released outside a black hole's event horizon because of relativistic quantum effects. It is named after the physicist Stephen Hawking, who developed a theoretical a ...
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List of quantum gravity researchers
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Orders of magnitude (length)
The following are examples of orders of magnitude for different lengths.
__TOC__
Overview
Detailed list
To help compare different orders of magnitude, the following list describes various lengths between 1.6 \times 10^ metres and 10 ...
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Penrose interpretation
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Planck epoch
The chronology of the universe describes the history and future of the universe according to Big Bang cosmology.
Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, wit ...
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Planck units
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Swampland (physics)
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Virtual black hole
Virtual may refer to:
* Virtual (horse), a thoroughbred racehorse
* Virtual channel, a channel designation which differs from that of the actual radio channel (or range of frequencies) on which the signal travels
* Virtual function, a programming ...
*
Weak Gravity Conjecture
Notes
References
Further reading
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External links
"Planck Era" and "Planck Time"(up to 10
−43 seconds after
birth
Birth is the act or process of bearing or bringing forth offspring, also referred to in technical contexts as parturition. In mammals, the process is initiated by hormones which cause the muscular walls of the uterus to contract, expelling the f ...
of
Universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...
) (
University of Oregon
The University of Oregon (UO, U of O or Oregon) is a public research university in Eugene, Oregon. Founded in 1876, the institution is well known for its strong ties to the sports apparel and marketing firm Nike, Inc, and its co-founder, billion ...
).
"Quantum Gravity" BBC Radio 4 discussion with John Gribbin, Lee Smolin and Janna Levin (''In Our Time'', Feb. 22, 2001)
{{portal bar, Physics, Science
General relativity
Physics beyond the Standard Model
Theories of gravity