View source for Quantum gravity

{{short description|Description of gravity using discrete values}}
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|caption1=A depiction of the [[cGh physics|''cGh'' cube]]
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'''Quantum gravity''' ('''QG''') is a field of [[theoretical physics]] that seeks [[Unification of theories in physics|unification]] of the theory of [[gravity]] with the principles of [[quantum mechanics]]. It deals with environments in which neither gravitational nor quantum effects can be ignored,<ref name="scholarpedia">{{cite journal | last = Rovelli | first = Carlo | author-link = Carlo Rovelli | year = 2008| title = Quantum gravity | journal = [[Scholarpedia]] | volume = 3 | issue = 5| page = 7117 | doi = 10.4249/scholarpedia.7117 | bibcode = 2008SchpJ...3.7117R | doi-access = free }}</ref> such as in the vicinity of [[black holes]] or similar compact astrophysical objects, as well as in the early stages of the universe moments after the [[Big Bang]].<ref>{{Cite book |last=Kiefer |first=Claus |title=Quantum gravity |date=2012 |publisher=Oxford University Press |isbn=978-0-19-958520-5 |edition=3rd |series=International series of monographs on physics |location=Oxford |pages=1–4 |language=en}}</ref>

Three of the four [[fundamental force]]s of nature are described within the framework of quantum mechanics and [[quantum field theory]]: the [[Electromagnetism|electromagnetic interaction]], the [[Strong interaction|strong force]], and the [[Weak interaction|weak force]]; this leaves gravity as the only interaction that has not been fully accommodated. The current understanding of gravity is based on [[Albert Einstein]]'s [[general theory of relativity]], which incorporates his theory of special relativity and deeply modifies the understanding of concepts like time and space. Although general relativity is highly regarded for its elegance and accuracy, it has limitations: the [[Gravitational singularity|gravitational singularities]] inside black holes, the ad hoc postulation of [[dark matter]], as well as [[dark energy]] and its relation to the [[cosmological constant]] are among the current unsolved mysteries regarding gravity,<ref>{{Cite journal |last=Mannheim |first=Philip |date=2006 |title=Alternatives to dark matter and dark energy |journal=Progress in Particle and Nuclear Physics |language=en |volume=56 |issue=2 |pages=340–445 |doi=10.1016/j.ppnp.2005.08.001|arxiv=astro-ph/0505266 |bibcode=2006PrPNP..56..340M |s2cid=14024934 }}</ref> all of which signal the collapse of the general theory of relativity at different scales and highlight the need for a gravitational theory that goes into the quantum realm. At distances close to the [[Planck length]], like those near the center of a black hole, [[quantum fluctuations]] of spacetime are expected to play an important role.<ref>{{cite web
 | url = https://www.quantamagazine.org/black-hole-singularities-are-as-inescapable-as-expected-20191202/
 | title = Black Hole Singularities Are as Inescapable as Expected
 | last = Nadis
 | first = Steve
 | date = 2 December 2019
 | website = quantamagazine.org
 | publisher = [[Quanta Magazine]]
 | access-date = 22 April 2020
 | archive-date = 14 April 2020
 | archive-url = https://web.archive.org/web/20200414150244/https://www.quantamagazine.org/black-hole-singularities-are-as-inescapable-as-expected-20191202/
 | url-status = live
 }}</ref> Finally, the discrepancies between the predicted value for the [[vacuum energy]] and the observed values (which, depending on considerations, can be of 60 or 120 orders of magnitude)<ref>{{cite journal|last=Bousso |first=Raphael |title=The cosmological constant |journal=General Relativity and Gravitation |volume=40 |year=2008 |issue=2–3 |pages=607–637 |arxiv=0708.4231 |doi=10.1007/s10714-007-0557-5|bibcode=2008GReGr..40..607B }}</ref><ref>{{cite journal|doi=10.1088/2058-7058/34/03/32 |first=Rob |last=Lea |title=A new generation takes on the cosmological constant |journal=Physics World |volume=34 |number=3 |page=42 |year=2021|bibcode=2021PhyW...34c..42L }}</ref> highlight the necessity for a quantum theory of gravity.

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]] and [[loop quantum gravity]].<ref>{{cite book |last=Penrose |first=Roger |title=The road to reality: a complete guide to the laws of the universe |url=https://archive.org/details/roadtoreality00penr_319 |url-access=limited |date=2007 |publisher=Vintage |oclc=716437154 |page=[https://archive.org/details/roadtoreality00penr_319/page/n1045 1017]|isbn=978-0-679-77631-4 }}</ref> All of these approaches aim to describe the quantum behavior of the [[gravitational field]], which does not necessarily include [[Theory of everything|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]]. Some of the approaches, 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. Other lesser-known but no less important theories include [[causal dynamical triangulation]], [[Noncommutative geometry#Applications in mathematical physics|noncommutative geometry]], and [[twistor theory]].<ref>{{Cite arXiv |last=Rovelli |first=Carlo |date=2001 |title=Notes for a brief history of quantum gravity |eprint=gr-qc/0006061 }}</ref>

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<sup>−35</sup> meters, a scale far smaller, and hence only accessible with far higher energies, than those currently available in high energy [[particle accelerator]]s. Therefore, physicists lack experimental data which could distinguish between the competing theories which have been proposed.<ref group="n.b.">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.</ref><ref group="n.b.">On the quantization of the geometry of spacetime, see also in the article [[Planck length]], in the examples</ref>

[[Thought experiment]] approaches have been suggested as a testing tool for quantum gravity theories.<ref>
{{cite journal
|last1 = Lindner
|first1 = Nethanel H.
|last2 = Peres
|first2 = Asher
|title = Testing quantum superpositions of the gravitational field with Bose-Einstein condensates
|date = 2005
|journal = [[Physical Review A]]
|volume = 71
|issue = 2
|article-number = 024101
|doi = 10.1103/PhysRevA.71.024101
|arxiv = gr-qc/0410030
|bibcode = 2005PhRvA..71b4101L
}}</ref><ref>
{{cite arXiv
|last1 = Kafri
|first1 = Dvir
|last2 = Taylor
|first2 = Jacob M
|title = A noise inequality for classical forces
|date = 2013
|class = quant-ph
|eprint = 1311.4558
}}</ref> In the field of quantum gravity there are several open questions – e.g., it is not known how the spin of elementary particles sources gravity, and thought experiments could provide a pathway to explore possible resolutions to these questions,<ref name="Spin-Spacetime Censorship AdP">{{cite journal|journal=Annalen der Physik|first1=J.|last1=Nemirovsky|first2=E.|last2=Cohen|title=Spin Spacetime Censorship|volume = 534|issue = 1|doi = 10.1002/andp.202100348|date=5 November 2021|last3=Kaminer|first3=I.|article-number=2100348 |arxiv=1812.11450|s2cid=119342861}}</ref> 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.<ref name="nautilus">{{cite web |last1=Hossenfelder |first1=Sabine |title=What Quantum Gravity Needs Is More Experiments |url=http://nautil.us/issue/45/power/what-quantum-gravity-needs-is-more-experiments |website=Nautilus |access-date=21 September 2020 |date=2 February 2017 |archive-date=28 January 2018 |archive-url=https://web.archive.org/web/20180128021051/http://nautil.us/issue/45/power/what-quantum-gravity-needs-is-more-experiments }}</ref><ref name="springer1">{{cite book |title=Experimental search for quantum gravity |date=2017 |publisher=Springer |location=Cham |isbn=978-3-319-64536-0}}</ref><ref name="tabletop">{{cite journal |last1=Carney |first1=Daniel |last2=Stamp |first2=Philip C. E. |last3=Taylor |first3=Jacob M. |title=Tabletop experiments for quantum gravity: a user's manual |journal=Classical and Quantum Gravity |page=034001 |doi=10.1088/1361-6382/aaf9ca |date=7 February 2019 |volume=36 |issue=3 |arxiv=1807.11494 |bibcode=2019CQGra..36c4001C |s2cid=119073215 }}</ref><ref>{{Cite journal |last1=Danielson |first1=Daine L. |last2=Satishchandran |first2=Gautam |last3=Wald |first3=Robert M. |date=2022-04-05 |title=Gravitationally mediated entanglement: Newtonian field versus gravitons |url=https://link.aps.org/doi/10.1103/PhysRevD.105.086001 |journal=Physical Review D |volume=105 |issue=8 |article-number=086001 |arxiv=2112.10798 |doi=10.1103/PhysRevD.105.086001 |bibcode=2022PhRvD.105h6001D |s2cid=245353748 |access-date=2022-12-11 |archive-date=2023-01-22 |archive-url=https://web.archive.org/web/20230122174555/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.086001 |url-status=live }}</ref> This field of study is called [[phenomenological quantum gravity]].

== Overview ==
{{unsolved|physics|How can the theory of quantum mechanics be merged with the theory of [[general relativity]] / [[gravitation]]al force and remain correct at microscopic length scales? What verifiable predictions does any theory of quantum gravity make?}}

[[File:Quantum gravity.svg|thumb|upright=1.4|Diagram showing the place of quantum gravity in the hierarchy of physics theories]]

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 the slogan of [[John Archibald Wheeler]], "Spacetime tells matter how to move; matter tells spacetime how to curve."<ref>{{cite book|first=John Archibald|last=Wheeler|title=Geons, Black Holes, and Quantum Foam: A Life in Physics|year=2010|publisher=[[W. W. Norton & Company]]|isbn=978-0-393-07948-7|pages=235}}</ref> On the other hand, quantum field theory is typically formulated in the ''flat'' spacetime used in [[special relativity]]. 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 [[renormalization|renormalizable]].<ref name=":1">{{cite book|title=Quantum Field Theory in a Nutshell|last=Zee|first=Anthony|publisher=[[Princeton University Press]]|year=2010|isbn=978-0-691-14034-6|edition=second|pages=[https://archive.org/details/isbn_9780691140346/page/172 172,434&ndash;435]|oclc=659549695|author-link=Anthony Zee|title-link=Quantum Field Theory in a Nutshell}}</ref> 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.<ref name="Wald 1994">{{cite book |last=Wald |first=Robert M. |title= Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics |date=1994 |publisher=University of Chicago Press |isbn=978-0-226-87027-4}}</ref>

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 hole]]s, and the [[Big Bang|origin of the universe]].<ref name="scholarpedia"/>

One major obstacle is that for [[quantum field theory in curved spacetime]] with a fixed metric, [[Boson|bosonic]]/[[Fermion|fermionic]] operator fields [[Lie superalgebra|supercommute]] for [[Causal structure|spacelike separated points]]. (This is a way of imposing a [[principle of locality#Relativistic quantum mechanics|principle of locality]].) However, in quantum gravity, the metric is dynamical, so that whether two points are spacelike separated depends on the state. In fact, they can be in a [[quantum superposition]] of being spacelike and not spacelike separated.{{cn|date=June 2024}}

== Quantum mechanics and general relativity ==

=== Graviton ===
{{Main|Graviton}}
The observation that all [[fundamental forces]] 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]] 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.<ref name=Kraichnan1955>{{cite journal
|last = Kraichnan
|first = R. H.
|author-link = Robert Kraichnan
|title = Special-Relativistic Derivation of Generally Covariant Gravitation Theory
|date = 1955
|journal = [[Physical Review]]
|volume = 98
|issue = 4
|pages = 1118–1122
|doi = 10.1103/PhysRev.98.1118
|bibcode = 1955PhRv...98.1118K }}</ref><ref name=Gupta1954>{{cite journal
|last = Gupta
|first = S. N.
|author-link = Suraj N. Gupta
|title = Gravitation and Electromagnetism
|date = 1954
|journal = [[Physical Review]]
|volume = 96
|issue = 6
|pages = 1683–1685
|doi = 10.1103/PhysRev.96.1683
|bibcode = 1954PhRv...96.1683G }}</ref><ref name=Gupta1957>{{cite journal
|last = Gupta
|first = S. N.
|author-link = Suraj N. Gupta
|title = Einstein's and Other Theories of Gravitation
|date = 1957
|journal = [[Reviews of Modern Physics]]
|volume = 29
|issue = 3
|pages = 334–336
|doi = 10.1103/RevModPhys.29.334
|bibcode=1957RvMP...29..334G
}}</ref><ref name=Gupta1962>{{cite book
|first = S. N.
|last = Gupta
|author-link = Suraj N. Gupta
|title = Recent Developments in General Relativity
|contribution = Quantum Theory of Gravitation
|date = 1962
|pages = 251–258
|publisher = Pergamon Press
}}</ref><ref name=Deser1970>{{cite journal
|last = Deser
|first = S.
|author-link = Stanley Deser
|title = Self-Interaction and Gauge Invariance
|date = 1970
|journal = [[General Relativity and Gravitation]]
|volume = 1
|issue = 1
|pages = 9–18
|doi = 10.1007/BF00759198
|bibcode=1970GReGr...1....9D
|arxiv = gr-qc/0411023 |s2cid = 14295121
}}</ref> 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]] places some constraints on theories in which [[composite gravity|the graviton is a composite particle]].<ref>{{cite journal|first1=Steven|last1=Weinberg|first2=Edward|last2=Witten|author-link1=Steven Weinberg|author-link2=Edward Witten|title=Limits on massless particles|journal=[[Physics Letters B]]|volume=96|issue=1–2|year=1980|pages=59&ndash;62|doi=10.1016/0370-2693(80)90212-9|bibcode=1980PhLB...96...59W}}</ref><ref>{{cite book|first1=Gary T.|last1=Horowitz|first2=Joseph|last2=Polchinski|author-link2=Joseph Polchinski|chapter=Gauge/gravity duality|title=Approaches to Quantum Gravity|publisher=[[Cambridge University Press]]|editor-last=Oriti|editor-first=Daniele|isbn=978-0-511-57554-9|oclc=873715753|arxiv=gr-qc/0602037|bibcode=2006gr.qc.....2037H|year=2006}}</ref> 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.<ref>{{cite journal
 |last1        = Rothman
 |first1       = Tony
 |last2        = Boughn
 |first2       = Stephen
 |date         = 2006
 |title        = Can Gravitons be Detected?
 |url          = https://link.springer.com/article/10.1007/s10701-006-9081-9
 |journal      = Foundations of Physics
 |volume       = 36
 |issue        = 12
 |pages        = 1801–1825
 |doi          = 10.1007/s10701-006-9081-9
 |arxiv        = gr-qc/0601043
 |bibcode      = 2006FoPh...36.1801R
 |s2cid        = 14008778
 |access-date  = 2020-05-15
 |archive-date = 2020-08-06
 |archive-url  = https://web.archive.org/web/20200806234929/https://link.springer.com/article/10.1007/s10701-006-9081-9
 |url-status   = live
}}</ref>

=== Nonrenormalizability of gravity ===
{{Further|Renormalization|Asymptotic safety in quantum gravity}}
General relativity, like [[electromagnetism]], 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]].<ref>{{Cite book |last=Feynman |first=Richard P. |title=Feynman Lectures on Gravitation |publisher=Addison-Wesley |year=1995 |isbn=978-0-201-62734-3 |location=Reading, Massachusetts |pages=xxxvi–xxxviii, 211–212 |language=en-us}}</ref><ref>{{ cite book | last= Hamber | first= H. W. | title= Quantum Gravitation – The Feynman Path Integral Approach | publisher = Springer Nature | date=2009 | isbn=978-3-540-85292-6 }}</ref> For a quantum field theory to be well defined according to this understanding of the subject, it must be [[asymptotic freedom|asymptotically free]] or [[asymptotic safety|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]] 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]], ''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]] 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.<ref>{{Cite journal|doi=10.1016/0370-2693(85)91470-4|last1=Goroff|first1=Marc H.|last2=Sagnotti|first2=Augusto|last3=Sagnotti|first3=Augusto|title=Quantum gravity at two loops|date=1985|journal=[[Physics Letters B]]|volume=160|issue=1–3|pages=81–86|bibcode = 1985PhLB..160...81G }}</ref>

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]] is not a reliable guide to the renormalizability of the theory, and that there really ''is'' a [[UV fixed point]] for gravity. Since this is a question of [[non-perturbative]] quantum field theory, finding a reliable answer is difficult, pursued in the [[Asymptotic safety in quantum gravity|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.<ref>{{Cite web|url=https://golem.ph.utexas.edu/~distler/blog/archives/000639.html|title=Motivation|last=Distler|first=Jacques|author-link=Jacques Distler|date=2005-09-01|website=golem.ph.utexas.edu|language=en|access-date=2018-02-24|archive-date=2019-02-11|archive-url=https://web.archive.org/web/20190211070351/https://golem.ph.utexas.edu/~distler/blog/archives/000639.html|url-status=live}}</ref>{{Better source needed|date=February 2019}}

=== Quantum gravity as an effective field theory ===
{{Main|Effective field theory}}
In an [[effective field theory]], 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.<ref name=":0">{{cite book
|author1-link=John Francis Donoghue (physicist)
|last = Donoghue
|first=John F. 
|contribution=Introduction to the Effective Field Theory Description of Gravity
|date=1995
|arxiv=gr-qc/9512024
|editor-last=Cornet
|editor-first=Fernando
|title=Effective Theories: Proceedings of the Advanced School, Almunecar, Spain, 26 June–1 July 1995
|isbn=978-981-02-2908-5
|publisher = [[World Scientific]]
|location = Singapore
|bibcode=1995gr.qc....12024D
}}</ref> 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.<ref>{{Cite book|title=Phase transitions and renormalization group|last=Zinn-Justin|first=Jean|date=2007|publisher=[[Oxford University Press]]|isbn=978-0-19-966516-7|location=Oxford|oclc=255563633|author-link=Jean Zinn-Justin}}</ref>

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.<ref name=":0" /> Another example is the calculation of the corrections to the Bekenstein-Hawking entropy formula.<ref>{{cite journal |last1=Calmet |last2=Kuipers |first1=Xavier |first2=Folkert |title=Quantum gravitational corrections to the entropy of a Schwarzschild black hole |journal=Phys. Rev. D|year=2021 |volume=104 |issue=6 |page=6 |doi=10.1103/PhysRevD.104.066012 |arxiv=2108.06824 |bibcode=2021PhRvD.104f6012C |s2cid=237091145 }}</ref><ref>{{cite journal |last1=Campos Delgado|first1=Ruben |title=Quantum gravitational corrections to the entropy of a Reissner-Nordström black hole |journal=Eur. Phys. J. C|year=2022 |volume=82 |issue=3 |article-number=272 |doi=10.1140/epjc/s10052-022-10232-0|arxiv=2201.08293 |bibcode=2022EPJC...82..272C |s2cid=247824137 |doi-access=free }}</ref>

=== Spacetime background dependence ===
{{Main|Background independence}}
A fundamental lesson of general relativity is that there is no fixed spacetime background, as found in [[Newtonian mechanics]] and [[special relativity]]; 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]],<ref>{{cite book
|last = Smolin
|first = Lee
|author-link= Lee Smolin
|title = Three Roads to Quantum Gravity
|publisher = [[Basic Books]]
|date = 2001
|pages = [https://archive.org/details/threeroadstoquan00smol_0/page/20 20–25]
|isbn = 978-0-465-07835-6|title-link = Three Roads to Quantum Gravity
}} Pages 220–226 are annotated references and guide for further reading.</ref> in which the only physically relevant information is the relationship between different events in spacetime.

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]] is the fixed background of the theory.

==== String theory ====
[[File:Point&string.png|right|thumb|class=skin-invert-image|Interaction in the subatomic world: [[world line]]s of point-like [[Subatomic particle|particles]] in the [[Standard Model]] or a [[world sheet]] swept up by closed [[string (physics)|strings]] in 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 dynamic way.
Although string theory had its origins in the study of [[quark confinement]] and not of quantum gravity, it was soon discovered that the string spectrum contains the [[graviton]], 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 that may exhibit a strong dependence on asymptotics (as seen, for example, in the [[AdS/CFT]] correspondence) which is a weak form of [[Background independence|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]] 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]]s.{{Citation needed|date=September 2020}}

=== Semi-classical quantum gravity ===
{{Main article|Quantum field theory in curved spacetime|Semiclassical 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]], 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 ===
{{Main|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 (quantum mechanics)|Hamiltonian operator]] acting as the [[Translation operator (quantum mechanics)|generator of infinitesimal translations]] of quantum states through time.<ref>{{Cite book|title=Modern Quantum Mechanics|last1=Sakurai|first1=J. J.|last2=Napolitano|first2=Jim J.|date=2010-07-14|publisher=Pearson|isbn=978-0-8053-8291-4|edition=2|page=68|language=en}}</ref> In contrast, general relativity [[Einstein field equations|treats time as a dynamical variable]] which relates directly with matter and moreover requires the Hamiltonian constraint to vanish.<ref>{{Cite book|url=https://books.google.com/books?id=vDWvUBiNgNkC|title=Cosmology and Gravitation: Xth Brazilian School of Cosmology and Gravitation; 25th Anniversary (1977–2002), Mangaratiba, Rio de Janeiro, Brazil|last1=Novello|first1=Mario|last2=Bergliaffa|first2=Santiago E.|date=2003-06-11|publisher=Springer Science & Business Media|isbn=978-0-7354-0131-0|page=95|language=en}}</ref> Because this variability of time has been [[Gravitational time dilation#Experimental confirmation|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.<ref>A timeline and overview can be found in {{Cite arXiv
|last=Rovelli
|first=Carlo
|author-link=Carlo Rovelli
|date=2000
|title=Notes for a brief history of quantum gravity
|eprint=gr-qc/0006061
}} (verify against {{ISBN|9789812777386}})</ref> 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.<ref>{{cite conference
|last=Ashtekar |first=Abhay
|author-link=Abhay Ashtekar
|date=2007
|title=Loop Quantum Gravity: Four Recent Advances and a Dozen Frequently Asked Questions
|conference=The Eleventh Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity
|page=126
|arxiv=0705.2222
|doi=10.1142/9789812834300_0008
|bibcode=2008mgm..conf..126A
|isbn=978-981-283-426-3
|s2cid=119663169
}}</ref><ref>{{cite journal
|last=Schwarz
|first=John H.
|title=String Theory: Progress and Problems
|journal=[[Progress of Theoretical Physics Supplement]]
|volume=170
|pages=214–226
|date=2007
|arxiv=hep-th/0702219
|doi=10.1143/PTPS.170.214
|bibcode=2007PThPS.170..214S
|s2cid=16762545
}}</ref>

=== String theory ===
{{Main|String theory}}
[[File:Calabi-Yau.png|thumb|Projection of a [[Calabi–Yau manifold]], one of the ways of [[Compactification (physics)|compactifying]] the extra dimensions posited by string theory]]

The central idea of string theory is to replace the classical concept of a [[point particle]] in quantum field theory with a quantum theory of one-dimensional extended objects: string theory.<ref>An accessible introduction at the undergraduate level can be found in {{Cite book
|last=Zwiebach
|first=Barton
|author-link= Barton Zwiebach
|title=A First Course in String Theory
|publisher=[[Cambridge University Press]]
|date=2004
|isbn=978-0-521-83143-7
}}, and more complete overviews in {{Cite book
|last=Polchinski
|first=Joseph
|author-link=Joseph Polchinski
|date=1998
|title=String Theory Vol. I: An Introduction to the Bosonic String
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-63303-1
}} and {{Cite book
|last=Polchinski
|first=Joseph
|author-link=Joseph Polchinski
|date=1998b
|title=String Theory Vol. II: Superstring Theory and Beyond
|publisher=[[Cambridge University Press]]
|isbn=978-0-521-63304-8
}}</ref> At the energies reached in current experiments, these strings are indistinguishable from point-like particles, but, crucially, different [[Normal mode|modes]] of oscillation of one and the same type of fundamental string appear as particles with different ([[electric]] and other) [[charge (physics)|charges]]. In this way, string theory promises to be a [[theory of everything|unified description]] of all particles and interactions.<ref>{{Cite journal
|last=Ibanez
|first=L. E.
|title=The second string (phenomenology) revolution
|journal=[[Classical and Quantum Gravity]]
|volume=17
|issue=5
|date=2000
|pages=1117–1128
|arxiv=hep-ph/9911499
|doi=10.1088/0264-9381/17/5/321
|bibcode = 2000CQGra..17.1117I |s2cid=15707877
}}</ref> The theory is successful in that one mode will always correspond to a [[graviton]], the [[messenger particle]] 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.<ref>For the graviton as part of the string spectrum, e.g. {{Harvnb|Green|Schwarz|Witten|2012|loc=sec. 2.3 and 5.3}}; for the extra dimensions, ibid sec. 4.2.</ref>

In what is called the [[History of string theory#1984–1989: first superstring revolution|second superstring revolution]], it was conjectured that both string theory and a unification of general relativity and [[supersymmetry]] known as [[supergravity]]<ref>{{Cite book
|last=Weinberg
|first=Steven
|chapter=Chapter 31
|author-link=Steven Weinberg
|title=The Quantum Theory of Fields II: Modern Applications
|publisher=Cambridge University Press
|date=2000
|chapter-url=https://books.google.com/books?id=aYDDRKqODpUC
|isbn=978-0-521-55002-4
|url-access=registration
|url=https://archive.org/details/quantumtheoryoff00stev
}}</ref> form part of a hypothesized eleven-dimensional model known as [[M-theory]], which would constitute a uniquely defined and consistent theory of quantum gravity.<ref>{{Cite journal
|last=Townsend
|first=Paul K.
|title=Four Lectures on M-Theory
|journal=High Energy Physics and Cosmology
|volume=13
|series=ICTP Series in Theoretical Physics
|page=385
|date=1996
|arxiv=hep-th/9612121
|bibcode=1997hepcbconf..385T
}}</ref><ref>{{Cite journal
|last=Duff
|first=Michael
|author-link=Michael Duff (physicist)
|title=M-Theory (the Theory Formerly Known as Strings)
|journal=[[International Journal of Modern Physics A]]
|volume=11 |issue=32
|date=1996
|pages=5623–5642
|doi=10.1142/S0217751X96002583
|arxiv=hep-th/9608117
|bibcode=1996IJMPA..11.5623D
|s2cid=17432791
}}</ref> As presently understood, however, string theory admits a very large number (10<sup>500</sup> 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 ===
{{Main|Loop quantum gravity}}
[[File:Spin network.svg|thumb|upright=1|Simple [[spin network]] of the type used in loop quantum gravity]]
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 that there is a granular structure of space at the Planck length. This is derived from the following considerations: In the case of electromagnetism, the [[quantum operator]] 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]]s. Spin networks were initially introduced by [[Roger Penrose]] in abstract form, and later shown by [[Carlo Rovelli]] and [[Lee Smolin]] 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]], which represent geometric gravity using mathematical analogues of [[electric field|electric]] and [[magnetic field]]s.<ref>{{Cite journal
|last=Ashtekar
|first=Abhay
|author-link=Abhay Ashtekar
|title=New variables for classical and quantum gravity
|journal=[[Physical Review Letters]]
|volume=57
|pages=2244–2247
|date=1986
|doi=10.1103/PhysRevLett.57.2244
|pmid=10033673
|issue=18
|bibcode=1986PhRvL..57.2244A
}}</ref><ref>{{Cite journal
|last=Ashtekar
|first=Abhay
|author-link=Abhay Ashtekar
|title=New Hamiltonian formulation of general relativity
|journal=[[Physical Review D]]
|volume=36|issue=6|pages=1587–1602
|date=1987
|doi=10.1103/PhysRevD.36.1587
|pmid=9958340
|bibcode = 1987PhRvD..36.1587A }}</ref> In the quantum theory, space is represented by a network structure called a spin network, evolving over time in discrete steps.<ref>{{Cite book|last=Thiemann|first=Thomas|title=Approaches to Fundamental Physics|year=2007|isbn=978-3-540-71115-5|series=Lecture Notes in Physics|volume=721|pages=185–263|chapter=Loop Quantum Gravity: An Inside View|bibcode=2007LNP...721..185T|doi=10.1007/978-3-540-71117-9_10|arxiv=hep-th/0608210|s2cid=119572847}}</ref><ref>{{cite journal
|last=Rovelli
|first=Carlo
|author-link=Carlo Rovelli
|title=Loop Quantum Gravity
|journal=[[Living Reviews in Relativity]]
|volume=1
|date=1998
|issue=1
|article-number=1
|doi=10.12942/lrr-1998-1
|doi-access=free
|pmid=28937180
|pmc=5567241
|arxiv=gr-qc/9710008
|bibcode=1998LRR.....1....1R
}}</ref><ref>{{cite journal
 | last1=Ashtekar
 | first1=Abhay
 | author-link=Abhay Ashtekar
 | first2=Jerzy
 | last2=Lewandowski
 | title=Background Independent Quantum Gravity: A Status Report
 | journal=[[Classical and Quantum Gravity]]
 | volume=21
 | date=2004
 | issue=15
 | pages=R53–R152
 | arxiv=gr-qc/0404018
 | doi=10.1088/0264-9381/21/15/R01
 |bibcode = 2004CQGra..21R..53A | s2cid=119175535
 }}</ref><ref>{{Cite book
|last=Thiemann
|first=Thomas
|chapter=Lectures on Loop Quantum Gravity
|date=2003
|volume=631
|pages=41–135
|arxiv=gr-qc/0210094
|bibcode=2003LNP...631...41T
|doi = 10.1007/978-3-540-45230-0_3 |series=Lecture Notes in Physics
|isbn=978-3-540-40810-9
|title=Quantum Gravity
|s2cid=119151491
}}</ref>

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]] is a [[Wheeler–DeWitt equation]], which can be defined within the theory.<ref>{{Cite book
|last=Rovelli
|first=Carlo
|title=Quantum Gravity
|date=2004
|publisher=Cambridge University Press
|isbn=978-0-521-71596-6
}}</ref> In the covariant, or [[spinfoam]] 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 proposals ===
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.<ref>{{Cite book
|last=Isham
|first=Christopher J.
|title=Canonical Gravity: From Classical to Quantum
|author-link=Christopher Isham
|contribution=Prima facie questions in quantum gravity
|editor-last=Ehlers
|editor-first=Jürgen
|editor2-last=Friedrich
|editor2-first=Helmut
|volume=434
|pages=1–21
|date=1994
|publisher=Springer
|arxiv=gr-qc/9310031
|isbn=978-3-540-58339-4
|bibcode=1994LNP...434....1I
|doi=10.1007/3-540-58339-4_13
|series=Lecture Notes in Physics
|s2cid=119364176
}}</ref><ref>{{Cite journal
|last=Sorkin
|first=Rafael D.
|author-link= Rafael Sorkin
|title=Forks in the Road, on the Way to Quantum Gravity
|arxiv=gr-qc/9706002
|journal=[[International Journal of Theoretical Physics]]
|volume=36
|date=1997
|issue=12
|pages=2759–2781
|doi=10.1007/BF02435709
|bibcode = 1997IJTP...36.2759S |s2cid=4803804
}}</ref> Such approaches include:
{{columns-list|colwidth=17em|
* [[Asymptotic safety in quantum gravity]]
* [[Euclidean quantum gravity]]
* [[Virtual black hole|Integral method]]<ref>{{Cite web |last=Klimets |first=A. P. |date=2017 |title=Philosophy Documentation Center, Western University – Canada |url=https://philpapers.org/archive/ALXOTF.pdf |url-status=live |archive-url=https://web.archive.org/web/20190701011840/https://philpapers.org/archive/ALXOTF.pdf |archive-date=2019-07-01 |access-date=2020-04-24 |publisher=Philosophy Documentation Center, Western University – Canada |pages=25–32}}</ref>
* [[Causal dynamical triangulation]]<ref>{{Cite journal
|last=Loll
|first=Renate
|title=Discrete Approaches to Quantum Gravity in Four Dimensions
|journal=[[Living Reviews in Relativity]]
|volume=1
|issue=1
|article-number=13
|date=1998
|bibcode=1998LRR.....1...13L
|arxiv = gr-qc/9805049 |doi = 10.12942/lrr-1998-13 |doi-access=free
|pmid=28191826
 |pmc=5253799
}}</ref>
* [[Causal fermion system]]s
* [[causal sets|Causal Set Theory]]
* Covariant Feynman [[path integral formulation|path integral]] approach
* [[Dilaton#The dilaton in quantum gravity|Dilatonic quantum gravity]]
*[[Double copy theory]]
* [[Group field theory]]
* [[Wheeler–DeWitt equation]]
* [[Geometrodynamics]]
* [[Hořava–Lifshitz gravity]]
* [[MacDowell–Mansouri action]]
* [[noncommutative standard model|Noncommutative geometry]]
* [[path integral formulation|Path-integral]] based models of [[quantum cosmology]]<ref>{{Cite book
|last=Hawking
|first=Stephen W.
|author-link=Stephen Hawking
|contribution=Quantum cosmology
|pages =631–651
|editor2-last=Israel
|editor2-first=Werner
|editor1-last=Hawking
|editor1-first=Stephen W.
|title=300 Years of Gravitation
|publisher=Cambridge University Press
|date=1987
|isbn=978-0-521-37976-2
}}</ref>
* [[Regge calculus]]
* [[Shape dynamics|Shape Dynamics]]
* [[String-net]]s and [[quantum graphity]]
* [[Supergravity]]
* [[Twistor theory]]<ref>See ch. 33 in {{Harvnb|Penrose|2005}} and references therein.</ref>
* [[Canonical quantum gravity]]
*[[An Exceptionally Simple Theory of Everything]] (Garret Lisi's E8 model)


}}

== 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, since the 2000s, 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]], which studies the possibility of experimental tests, has obtained increased attention.<ref>{{cite book |last=Hossenfelder |first=Sabine |title=Classical and Quantum Gravity: Theory, Analysis and Applications |date=2011 |publisher=Nova Publishers |isbn=978-1-61122-957-8 |editor=Frignanni |editor-first=V. R. |chapter=Experimental Search for Quantum Gravity |access-date=2012-04-01 |chapter-url=https://www.novapublishers.com/catalog/product_info.php?products_id=15903 |archive-url=https://web.archive.org/web/20170701040647/https://www.novapublishers.com/catalog/product_info.php?products_id=15903 |archive-date=2017-07-01 }}</ref>

The most widely pursued possibilities for quantum gravity phenomenology include gravitationally mediated entanglement,<ref>
{{cite journal
|last1 = Lindner
|first1 = Nethanel H.
|last2 = Peres
|first2 = Asher
|title = Testing quantum superpositions of the gravitational field with Bose-Einstein condensates
|date = 2005
|journal = [[Physical Review A]]
|volume = 71
|issue = 2
|article-number = 024101
|doi = 10.1103/PhysRevA.71.024101
|arxiv = gr-qc/0410030
|bibcode = 2005PhRvA..71b4101L
}}</ref><ref>
{{cite arXiv
|last1 = Kafri
|first1 = Dvir
|last2 = Taylor
|first2 = Jacob M
|title = A noise inequality for classical forces
|date = 2013
|class = quant-ph
|eprint = 1311.4558
}}</ref>
violations of [[Lorentz covariance|Lorentz invariance]], imprints of quantum gravitational effects in the [[cosmic microwave background]] (in particular its polarization), and decoherence induced by fluctuations<ref>{{Cite journal|last1=Oniga|first1=Teodora|last2=Wang|first2=Charles H.-T.|date=2016-02-09|title=Quantum gravitational decoherence of light and matter|url=https://link.aps.org/doi/10.1103/PhysRevD.93.044027|journal=Physical Review D|volume=93|issue=4|article-number=044027|doi=10.1103/PhysRevD.93.044027|arxiv=1511.06678|bibcode=2016PhRvD..93d4027O|hdl=2164/5830|s2cid=119210226|hdl-access=free|access-date=2021-01-01|archive-date=2023-01-22|archive-url=https://web.archive.org/web/20230122174605/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.93.044027|url-status=live}}</ref><ref>{{Cite journal|last1=Oniga|first1=Teodora|last2=Wang|first2=Charles H.-T.|date=2017-10-05|title=Quantum coherence, radiance, and resistance of gravitational systems|url=https://link.aps.org/doi/10.1103/PhysRevD.96.084014|journal=Physical Review D|volume=96|issue=8|article-number=084014|doi=10.1103/PhysRevD.96.084014|arxiv=1701.04122|bibcode=2017PhRvD..96h4014O|hdl=2164/9320|s2cid=54777871|hdl-access=free|access-date=2021-01-01|archive-date=2023-01-22|archive-url=https://web.archive.org/web/20230122174600/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.084014|url-status=live}}</ref><ref>{{Cite journal|last1=Quiñones|first1=D. A.|last2=Oniga|first2=T.|last3=Varcoe|first3=B. T. H.|last4=Wang|first4=C. H.-T.|date=2017-08-15|title=Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological stochastic background of spacetime|url=https://link.aps.org/doi/10.1103/PhysRevD.96.044018|journal=Physical Review D|volume=96|issue=4|article-number=044018|doi=10.1103/PhysRevD.96.044018|arxiv=1702.03905|bibcode=2017PhRvD..96d4018Q|hdl=2164/9150|s2cid=55056264|hdl-access=free|access-date=2021-01-02|archive-date=2023-01-22|archive-url=https://web.archive.org/web/20230122174603/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.96.044018|url-status=live}}</ref> in the [[space-time foam]].<ref>{{Cite journal|last1=Oniga|first1=Teodora|last2=Wang|first2=Charles H.-T.|date=2016-09-19|title=Spacetime foam induced collective bundling of intense fields|url=https://link.aps.org/doi/10.1103/PhysRevD.94.061501|journal=Physical Review D|volume=94|issue=6|article-number=061501|doi=10.1103/PhysRevD.94.061501|arxiv=1603.09193|bibcode=2016PhRvD..94f1501O|hdl=2164/7434|s2cid=54872718|hdl-access=free|access-date=2021-01-02|archive-date=2023-01-22|archive-url=https://web.archive.org/web/20230122174605/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.94.061501|url-status=live}}</ref> The latter scenario has been searched for in light from [[gamma-ray burst]]s and both astrophysical and atmospheric [[neutrino]]s, placing limits on phenomenological quantum gravity parameters.<ref>{{Cite journal |last1=Vasileiou |first1=Vlasios |last2=Granot |first2=Jonathan |last3=Piran |first3=Tsvi |last4=Amelino-Camelia |first4=Giovanni |date=2015-03-16 |title=A Planck-scale limit on spacetime fuzziness and stochastic Lorentz invariance violation |journal=Nature Physics |volume=11 |issue=4 |pages=344–346 |doi=10.1038/nphys3270 |bibcode=2015NatPh..11..344V |s2cid=54727053 |issn=1745-2473|doi-access=free }}</ref><ref>{{Cite journal |last1=The IceCube Collaboration |last2=Abbasi |first2=R. |last3=Ackermann |first3=M. |last4=Adams |first4=J. |last5=Aguilar |first5=J. A. |last6=Ahlers |first6=M. |last7=Ahrens |first7=M. |last8=Alameddine |first8=J. M. |last9=Alispach |first9=C. |last10=Alves Jr |first10=A. A. |last11=Amin |first11=N. M. |last12=Andeen |first12=K. |last13=Anderson |first13=T. |last14=Anton |first14=G. |last15=Argüelles |first15=C. |date=2022-11-01 |title=Search for quantum gravity using astrophysical neutrino flavour with IceCube |url=https://www.nature.com/articles/s41567-022-01762-1 |journal=Nature Physics |language=en |volume=18 |issue=11 |pages=1287–1292 |doi=10.1038/s41567-022-01762-1 |bibcode=2022NatPh..18.1287I |s2cid=243848123 |issn=1745-2473|arxiv=2111.04654 }}</ref><ref>{{cite journal | arxiv=2308.00105 | doi=10.1038/s41567-024-02436-w | title=Search for decoherence from quantum gravity with atmospheric neutrinos | date=2024 | last1=Abbasi | first1=R. | last2=Ackermann | first2=M. | last3=Adams | first3=J. | last4=Agarwalla | first4=S. K. | last5=Aguilar | first5=J. A. | last6=Ahlers | first6=M. | last7=Alameddine | first7=J. M. | last8=Amin | first8=N. M. | last9=Andeen | first9=K. | last10=Anton | first10=G. | last11=Argüelles | first11=C. | last12=Ashida | first12=Y. | last13=Athanasiadou | first13=S. | last14=Ausborm | first14=L. | last15=Axani | first15=S. N. | last16=Bai | first16=X. | last17=Balagopal v | first17=A. | last18=Baricevic | first18=M. | last19=Barwick | first19=S. W. | last20=Basu | first20=V. | last21=Bay | first21=R. | last22=Beatty | first22=J. J. | last23=Tjus | first23=J. Becker | last24=Beise | first24=J. | last25=Bellenghi | first25=C. | last26=Benning | first26=C. | last27=Benzvi | first27=S. | last28=Berley | first28=D. | last29=Bernardini | first29=E. | last30=Besson | first30=D. Z. | journal=Nature Physics | volume=20 | issue=6 | pages=913–920 | bibcode=2024NatPh..20..913T | display-authors=1 }}</ref>

[[ESA]]'s [[INTEGRAL]] 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<sup>−48</sup>&nbsp;m, or 13 orders of magnitude below the Planck scale.<ref>{{Cite web|date=2011-06-30|title=Integral challenges physics beyond Einstein|url=https://www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein|url-status=live|access-date=2021-11-06|website=European Space Agency|archive-date=2021-11-13|archive-url=https://web.archive.org/web/20211113230038/https://www.esa.int/Science_Exploration/Space_Science/Integral_challenges_physics_beyond_Einstein}}</ref><ref>{{Cite journal|last1=Laurent|first1=P.|last2=Götz|first2=D.|last3=Binétruy|first3=P.|last4=Covino|first4=S.|last5=Fernandez-Soto|first5=A.|date=2011-06-28|title=Constraints on Lorentz Invariance Violation using integral/IBIS observations of GRB041219A|url=https://link.aps.org/doi/10.1103/PhysRevD.83.121301|journal=Physical Review D|language=en|volume=83|issue=12|article-number=121301|doi=10.1103/PhysRevD.83.121301|arxiv=1106.1068|bibcode=2011PhRvD..83l1301L|hdl=10261/37661 |s2cid=53603505|issn=1550-7998|access-date=2021-11-06|archive-date=2023-01-22|archive-url=https://web.archive.org/web/20230122175047/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.83.121301|url-status=live}}</ref>{{better source needed|date=September 2024}}

The [[BICEP and Keck Array|BICEP2 experiment]] detected what was initially thought to be primordial [[B-modes|B-mode polarization]] caused by [[gravitational wave]]s 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 [[cosmic dust|interstellar dust]] interference.<ref name="nature-20150130">
{{cite journal
 |last=Cowen |first=Ron
 |date=30 January 2015
 |title=Gravitational waves discovery now officially dead
 |journal=[[Nature (journal)|Nature]]
 |doi=10.1038/nature.2015.16830
|s2cid=124938210
 }}</ref>

== See also ==
{{cols|colwidth=16em}}
* [[De Sitter relativity]]
* [[Dilaton]]
* [[Doubly special relativity]]
* [[Gravitational decoherence]]
* [[Gravitomagnetism]]
* [[Hawking radiation]]
* [[List of quantum gravity researchers]]
* [[Orders of magnitude (length)]]
* [[Penrose interpretation]]
* [[Planck epoch]]
* [[Planck units]]
* [[Swampland (physics)]]
* [[Virtual black hole]]
* [[Weak Gravity Conjecture]]
{{colend}}

== Notes ==
{{Reflist|group=n.b.}}

== References ==
{{Reflist|30em}}

== Sources ==
*{{Cite book |last1=Green |first1=Michael B. |title=Superstring theory. 1: Introduction |last2=Schwarz |first2=John H. |last3=Witten |first3=Edward |date=2012 |publisher=Cambridge University Press |isbn=978-1-107-02911-8 |edition=25th Anniversary |volume=l |orig-date=1987 |author-link1=Michael Green (physicist) |author-link2=John Henry Schwarz |author-link3=Edward Witten}}
* {{Cite book |last=Penrose |first=Roger |author-link=Roger Penrose |url=https://archive.org/details/roadtorealitycom00penr_0 |title=The road to reality: a complete guide to the laws of the universe |date=2005 |publisher=Knopf |isbn=978-0-679-45443-4 |location=New York}}

== Further reading ==
* {{Cite journal
|last=Ahluwalia
|first=D. V.
|title=Interface of Gravitational and Quantum Realms
|arxiv=gr-qc/0205121
|date=2002
|journal=[[Modern Physics Letters A]]
|doi=10.1142/S021773230200765X
|volume=17
|issue=15–17
|bibcode=2002MPLA...17.1135A
|pages=1135–1145
|s2cid=119358167
}}
* {{Cite journal
|last=Ashtekar
|first=Abhay
|author-link=Abhay Ashtekar
|title=The winding road to quantum gravity
|url= http://pubman.mpdl.mpg.de/pubman/item/escidoc:150927:1/component/escidoc:150926/2064.pdf
|journal=[[Current Science]]
|volume=89
|pages=2064–2074
|date=2005
|issue=12
|jstor=24111069
}}
* {{Cite journal
|last=Carlip
|first=Steven
|author-link= Steve Carlip
|title=Quantum Gravity: a Progress Report
|journal=[[Reports on Progress in Physics]]
|volume=64
|issue=8
|date=2001
|pages=885–942
|arxiv=gr-qc/0108040
 |doi=10.1088/0034-4885/64/8/301
|bibcode = 2001RPPh...64..885C |s2cid=118923209
}}
* {{Cite book |last=Hamber |first=H. W. |editor-first1=Herbert W. |editor-last1=Hamber |url=https://cds.cern.ch/record/1233211 |title=Quantum gravitation: the Feynman path integral approach |date=2009 |publisher=Springer |isbn=978-3-540-85292-6 |location=Berlin |doi=10.1007/978-3-540-85293-3 |hdl=11858/00-001M-0000-0013-471D-A |oclc=248994165}}
* {{Cite book
|last=Kiefer
|first=Claus
|title=Quantum Gravity
|date=2007
|publisher=Oxford University Press
|isbn=978-0-19-921252-1
}}
* {{Cite journal
|last=Kiefer
|first=Claus
|title=Quantum Gravity: General Introduction and Recent Developments
|date=2005
|journal=[[Annalen der Physik]]
|volume=15
|issue=1
|arxiv=gr-qc/0508120
|doi=10.1002/andp.200510175
|pages=129–148
|bibcode = 2006AnP...518..129K |s2cid=12984346
}}
* {{Cite book
|editor-last=Lämmerzahl
|editor-first=Claus
|title= Quantum Gravity: From Theory to Experimental Search
|series=[[Lecture Notes in Physics]]
|date=2003
|publisher= Springer
|isbn=978-3-540-40810-9
}}
* {{Cite book
|last=Rovelli
|first=Carlo
|author-link=Carlo Rovelli
|title=Quantum Gravity
|date=2004
|publisher=Cambridge University Press
|isbn=978-0-521-83733-0
}}

== External links ==
{{Wikiquote}}
* {{iep|url-id=m-quantum-gravity|title=Metaphysics of Quantum Gravity}}
* {{cite SEP|url-id=quantum-gravity|title=Quantum Gravity|author-last1=Weinstein|author-first1=Steven|author-last2=Rickles|first2=Dean}}
* [http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html "Planck Era" and "Planck Time"] {{Webarchive|url=https://web.archive.org/web/20181128045313/http://abyss.uoregon.edu/~js/cosmo/lectures/lec20.html |date=2018-11-28 }} (up to 10<sup>−43</sup> seconds after [[Big Bang|birth]] of [[Universe]]) ([[University of Oregon]]).
* [https://www.bbc.co.uk/programmes/p00547c4 "Quantum Gravity"], BBC Radio 4 discussion with John Gribbin, Lee Smolin and Janna Levin (''In Our Time'', February 22, 2001)

{{Quantum gravity}}
{{Theories of gravitation}}
{{Relativity}}
{{Standard model of physics}}
{{Quantum mechanics topics}}
{{Authority control}}
{{portal bar|Physics|Science}}

[[Category:Quantum gravity| ]]
[[Category:General relativity]]
[[Category:Physics beyond the Standard Model]]
[[Category:Theories of gravity]]