Editing Quantum gravity (section)

== 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=9780511575549|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=978-0201627343 |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]], 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.<ref name=":0">{{cite book
|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=9780199665167|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 |page=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.