Editing Gravity (section)

== General relativity ==
{{see also | Introduction to general relativity}}
In [[modern physics]], general relativity is considered the most successful theory of gravitation.<ref>{{Cite book |last=Stephani |first=Hans |title=Exact Solutions to Einstein's Field Equations |year=2003 |isbn=978-0-521-46136-8 |pages=1 |publisher=Cambridge University Press |language=en}}</ref> Physicists continue to work to find [[Solutions of the Einstein field equations|solutions]] to the [[Einstein field equations]] that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases.<ref name="ScienceNews2019">{{cite web
  | title = Einstein's general relativity theory is questioned but still stands for now
  | work = Science News
  | publisher = Science Daily
  | date = 25 July 2019
| url = https://www.sciencedaily.com/releases/2019/07/190725150408.htm
  | doi = 
  | accessdate = 11 August 2024}}</ref><ref name="Lea">{{cite web
  | last = Lea
  | first = Robert 
  | title = Einstein's greatest theory just passed its most rigorous test yet
  | website = Scientific American
  | publisher = Springer Nature America, Inc.
  | date = 15 September 2022
| url = https://www.scientificamerican.com/article/einsteins-greatest-theory-just-passed-its-most-rigorous-test-yet/
  | format = 
  | doi = 
  | accessdate = 11 August 2024}}</ref><ref name="Will"/>{{rp|p.9}}

=== General characteristics ===
Unlike Newton's formula with one parameter, {{math|''G''}}, force in general relativity is terms of 10 numbers formed in to a [[metric tensor]].<ref name=Weinberg-1972/>{{rp|70}}
In general relativity the effects of gravitation are described in different ways in different frames of reference. In a free-falling or co-moving coordinate system, an object travels in a straight line. In other coordinate systems, the object accelerates and thus is seen to move under a force. The path in [[spacetime]] (not 3D space) taken by a free-falling object is called a [[geodesic]] and the length of that path as measured by time in the objects frame is the shortest (or rarely the longest) one. Consequently the effect of gravity can be described as curving spacetime. In a weak stationary gravitational field, general relativity reduces to Newton's equations. The corrections introduced by general relativity on Earth are on the order of 1 part in a billion.<ref name=Weinberg-1972/>{{rp|77}}

=== Einstein field equations ===
{{main| Einstein field equations}}
The Einstein field equations are a [[System of equations|system]] of 10 [[partial differential equation]]s which describe how matter affects the curvature of spacetime. The system is may be expressed in the form
<math display="block">G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu},</math>
where {{mvar|G{{sub|μν}}}} is the [[Einstein tensor]], {{mvar|g{{sub|μν}}}} is the [[metric tensor (general relativity)|metric tensor]], {{mvar|T{{sub|μν}}}} is the [[stress–energy tensor]], {{math|Λ}} is the [[cosmological constant]], <math>G</math> is the Newtonian constant of gravitation and <math>c</math> is the [[speed of light]].<ref>{{Cite web |title=Einstein Field Equations (General Relativity) |url=https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/generalrelativity/ |access-date=24 May 2022 |website=University of Warwick |language=en |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525140036/https://warwick.ac.uk/fac/sci/physics/intranet/pendulum/generalrelativity/ |url-status=live }}</ref> The constant <math>\kappa = \frac{8\pi G}{c^4}</math> is referred to as the Einstein gravitational constant.<ref>{{Cite web |title=How to understand Einstein's equation for general relativity |url=https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/ |access-date=24 May 2022 |website=Big Think |date=15 September 2021 |language=en-US |archive-date=26 May 2022 |archive-url=https://web.archive.org/web/20220526023430/https://bigthink.com/starts-with-a-bang/einstein-general-theory-relativity-equation/ |url-status=live }}</ref>

=== Solutions ===
{{main|Solutions of the Einstein field equations}}
The non-linear second-order Einstein field equations are extremely complex and have been solved in only a few special cases.<ref>{{Cite web |last=Siegel |first=Ethan |title=This Is Why Scientists Will Never Exactly Solve General Relativity |url=https://www.forbes.com/sites/startswithabang/2019/12/04/this-is-why-scientists-will-never-exactly-solve-general-relativity/ |access-date=27 May 2022 |website=Forbes |language=en |archive-date=27 May 2022 |archive-url=https://web.archive.org/web/20220527212804/https://www.forbes.com/sites/startswithabang/2019/12/04/this-is-why-scientists-will-never-exactly-solve-general-relativity/ |url-status=live }}</ref> These cases however has been transformational in our understanding of the cosmos. Several solutions are the basis for understanding [[black holes]] and for our modern model of the evolution of the universe since the [[Big Bang]].<ref name="Longair-2009">{{Cite book|date=2008 |title=Galaxy Formation 
|author=Malcolm S. Longair
|url=http://link.springer.com/10.1007/978-3-540-73478-9 |series=Astronomy and Astrophysics Library |language=en |location=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-540-73478-9 |isbn=978-3-540-73477-2}}</ref>{{rp|227}}

=== Tests of general relativity ===
{{main | Tests of general relativity}}
[[File:1919 eclipse positive.jpg|thumb|The 1919 [[total solar eclipse]] provided one of the first opportunities to test the predictions of general relativity.]]

Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses.<ref name="NASA-2022">{{Cite web |title=Testing General Relativity |url=https://asd.gsfc.nasa.gov/blueshift/index.php/2015/11/27/testing-general-relativity/ |access-date=29 May 2022 |website=NASA Blueshift |language=en-US |archive-date=16 May 2022 |archive-url=https://web.archive.org/web/20220516115115/https://asd.gsfc.nasa.gov/blueshift/index.php/2015/11/27/testing-general-relativity/ |url-status=live }}</ref>
A wide range of experiments provided support of general relativity.<ref name="Will">{{cite book
  | last = Will
  | first = Clifford M.
  | title = Theory and Experiment in Gravitational Physics
  | publisher = Cambridge Univ. Press
  | date = 2018
  | location = 
  | language = 
  | url = https://books.google.com/books?id=gf1uDwAAQBAJ
  | archive-url= 
  | archive-date=
  | doi = 
  | id = 
  | isbn = 9781107117440
  | mr = 
  | zbl = 
  | jfm =}}</ref>{{rp|p.1–9}}<ref>{{Cite journal |last=Lindley |first=David |date=12 July 2005 |title=The Weight of Light |url=https://physics.aps.org/story/v16/st1 |journal=Physics |language=en |volume=16 |access-date=22 May 2022 |archive-date=25 May 2022 |archive-url=https://web.archive.org/web/20220525201415/https://physics.aps.org/story/v16/st1 |url-status=live }}</ref><ref>{{Cite web |title=Hafele-Keating Experiment |url=http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html |access-date=22 May 2022 |website=hyperphysics.phy-astr.gsu.edu |archive-date=18 April 2017 |archive-url=https://web.archive.org/web/20170418005731/http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/airtim.html |url-status=live }}</ref><ref>{{Cite web |title=How the 1919 Solar Eclipse Made Einstein the World's Most Famous Scientist |url=https://www.discovermagazine.com/the-sciences/how-the-1919-solar-eclipse-made-einstein-the-worlds-most-famous-scientist |access-date=22 May 2022 |website=Discover Magazine |language=en |archive-date=22 May 2022 |archive-url=https://web.archive.org/web/20220522141013/https://www.discovermagazine.com/the-sciences/how-the-1919-solar-eclipse-made-einstein-the-worlds-most-famous-scientist |url-status=live }}</ref><ref>{{Cite web |title=At Long Last, Gravity Probe B Satellite Proves Einstein Right |url=https://www.science.org/content/article/long-last-gravity-probe-b-satellite-proves-einstein-right |access-date=22 May 2022 |website=www.science.org |language=en |archive-date=22 May 2022 |archive-url=https://web.archive.org/web/20220522141013/https://www.science.org/content/article/long-last-gravity-probe-b-satellite-proves-einstein-right |url-status=live }}</ref> Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations.<ref name="Will" />{{rp|79}}<ref name="Hassani">{{cite book
  | last = Hassani
  | first = Sadri
  | title = From Atoms to Galaxies: A conceptual physics approach to scientific awareness
  | publisher = CRC Press
  | date = 2010
  | location = 
  | pages = 131
  | language = 
  | url = https://books.google.com/books?id=oypZ_a9pqdsC&pg=PA131
  | archive-url= 
  | archive-date=
  | doi = 
  | id = 
  | isbn = 9781439808504
  | mr = 
  | zbl = 
  | jfm =}}</ref>

===Gravity and quantum mechanics===
{{Main|Graviton|Quantum gravity}}

Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with [[quantum mechanics]]. This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as [[quantum|quanta]]. This contradiction is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago.<ref>{{Cite web |title=Gravity Probe B – Special & General Relativity Questions and Answers |url=https://einstein.stanford.edu/content/relativity/a11758.html#:~:text=Quantum%20mechanics%20is%20incompatible%20with,exchange%20of%20well-defined%20quanta. |access-date=1 August 2022 |website=einstein.stanford.edu |archive-date=6 June 2022 |archive-url=https://web.archive.org/web/20220606161408/https://einstein.stanford.edu/content/relativity/a11758.html#:~:text=Quantum%20mechanics%20is%20incompatible%20with,exchange%20of%20well-defined%20quanta. |url-status=live }}</ref> As a result, modern researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework.<ref>{{Cite book |last1=Huggett |first1=Nick |title=Beyond Spacetime: The Foundations of Quantum Gravity |last2=Matsubara |first2=Keizo |last3=Wüthrich |first3=Christian |publisher=[[Cambridge University Press]] |year=2020 |isbn=9781108655705 |pages=6 |language=en}}</ref>

One path is to describe gravity in the framework of [[quantum field theory]], which has been successful to accurately describe the other [[fundamental interaction]]s. The electromagnetic force arises from an exchange of virtual [[photon]]s, where the QFT description of gravity is that there is an exchange of [[virtual particle|virtual]] [[graviton]]s.<ref>{{cite book |last= Feynman |first= R.P. |author2=Morinigo, F.B. |author3=Wagner, W.G. |author4=Hatfield, B.  |title= Feynman lectures on gravitation |url= https://archive.org/details/feynmanlectureso0000feyn_g4q1 |url-access= registration |publisher= Addison-Wesley |date= 1995 |isbn=978-0-201-62734-3 }}</ref><ref>{{cite book | author=Zee, A. |title=Quantum Field Theory in a Nutshell | publisher = Princeton University Press | date=2003 | isbn=978-0-691-01019-9}}</ref> This description reproduces general relativity in the [[classical limit]]. However, this approach fails at short distances of the order of the [[Planck length]],<ref name="Randall, Lisa 2005">{{cite book | author=Randall, Lisa | title=Warped Passages: Unraveling the Universe's Hidden Dimensions | publisher=Ecco | date=2005 | isbn=978-0-06-053108-9 | url=https://archive.org/details/warpedpassagesun00rand_1 }}</ref> where a more complete theory of [[quantum gravity]] (or a new approach to quantum mechanics) is required.

===Alternative theories===
{{Main|Alternatives to general relativity}}
General relativity has withstood many [[tests of general relativity|tests]] over a large range of mass and size scales.<ref name=WillReview2014>{{cite journal | last=Will | first=Clifford M. | title=The Confrontation between General Relativity and Experiment | journal=Living Reviews in Relativity | volume=17 | issue=1 | date=2014-12-01 | issn=2367-3613 | doi=10.12942/lrr-2014-4 | pages=4 | pmid=28179848 | pmc=5255900 | arxiv=1403.7377 | bibcode=2014LRR....17....4W | doi-access=free}}</ref><ref>{{cite arXiv |eprint=1705.04397v1|last1= Asmodelle|first1= E.|title= Tests of General Relativity: A Review|class= physics.class-ph|year= 2017}}</ref> When applied to interpret astronomical observations, cosmological models based on general relativity introduce two components to the universe,<ref name="k889">{{cite book | last=Ryden | first=Barbara Sue | title=Introduction to cosmology | publisher=Cambridge University Press | publication-place=Cambridge | date=2017 | isbn=978-1-316-65108-7 | page=}}</ref> [[dark matter]]<ref name="dm">{{cite journal | last1=Garrett | first1=Katherine | last2=Duda | first2=Gintaras | title=Dark Matter: A Primer | journal=Advances in Astronomy | volume=2011 | date=2011 | issn=1687-7969 | doi=10.1155/2011/968283 | doi-access=free | pages=1–22| arxiv=1006.2483 | bibcode=2011AdAst2011E...8G }}</ref> and [[dark energy]],<ref name="de">{{cite journal | last1=Li | first1=Miao | last2=Li | first2=Xiao-Dong | last3=Wang | first3=Shuang | last4=Wang | first4=Yi | title=Dark energy: A brief review | journal=Frontiers of Physics | volume=8 | issue=6 | date=2013 | issn=2095-0462 | doi=10.1007/s11467-013-0300-5 | pages=828–846| arxiv=1209.0922 | bibcode=2013FrPhy...8..828L }}</ref> the nature of which is currently an [[List of unsolved problems in physics#Cosmology and general relativity|unsolved problem in physics]].  The many successful, high precision predictions of the [[Lambda-CDM model|standard model of cosmology]] has led astrophysicists to conclude it and thus general relativity will be the basis for future progress.<ref name=Turner-2022>{{Cite journal |last=Turner |first=Michael S. |date=2022-09-26 |title=The Road to Precision Cosmology |url=https://www.annualreviews.org/content/journals/10.1146/annurev-nucl-111119-041046 |journal=Annual Review of Nuclear and Particle Science |language=en |volume=72 |issue=2022 |pages=1–35 |doi=10.1146/annurev-nucl-111119-041046 |issn=0163-8998|arxiv=2201.04741 |bibcode=2022ARNPS..72....1T }}</ref><ref name=Intertwined-2022>{{Cite journal |last1=Abdalla |first1=Elcio |last2=Abellán |first2=Guillermo Franco |last3=Aboubrahim |first3=Amin |last4=Agnello |first4=Adriano |last5=Akarsu |first5=Özgür |last6=Akrami |first6=Yashar |last7=Alestas |first7=George |last8=Aloni |first8=Daniel |last9=Amendola |first9=Luca |last10=Anchordoqui |first10=Luis A. |last11=Anderson |first11=Richard I. |last12=Arendse |first12=Nikki |last13=Asgari |first13=Marika |last14=Ballardini |first14=Mario |last15=Barger |first15=Vernon |date=2022-06-01 |title=Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies |url=https://linkinghub.elsevier.com/retrieve/pii/S2214404822000179 |journal=Journal of High Energy Astrophysics |volume=34 |pages=49–211 |doi=10.1016/j.jheap.2022.04.002 |issn=2214-4048|arxiv=2203.06142 |bibcode=2022JHEAp..34...49A }}</ref> However, dark matter is not supported by the [[standard model of particle physics]], physical models for dark energy do not match cosmological data, and some cosmological observations are inconsistent.<ref name=Intertwined-2022/> These issues have led to the study of 
alternative theories of gravity.<ref name="physicsworld">{{cite web|url=https://physicsworld.com/a/cosmic-combat-delving-into-the-battle-between-dark-matter-and-modified-gravity|title=Cosmic combat: delving into the battle between dark matter and modified gravity|date=6 February 2024|author=Keith Cooper|publisher=physicsworld}}</ref>