Universe

=== Spacetime ===
{{Main|Spacetime|World line}}
{{See also|Lorentz transformation}}
Modern physics regards [[event (relativity)|events]] as being organized into [[spacetime]].<ref>{{Cite book
 |author=Schutz, Bernard
 |title=A First Course in General Relativity
 |publisher=Cambridge University Press
 |edition=2nd
 |date= 2009
 |isbn=978-0-521-88705-2
 |pages=[https://archive.org/details/firstcourseingen00bern_0/page/142 142, 171]
 |author-link=Bernard Schutz
 |url=https://archive.org/details/firstcourseingen00bern_0/page/142
 }}</ref> This idea originated with the [[special theory of relativity]], which predicts that if one observer sees two events happening in different places at the same time, a second observer who is moving relative to the first will see those events happening at different times.<ref name="Mermin2005">{{cite book|first=N. David |last=Mermin |author-link=N. David Mermin |title=It's About Time: Understanding Einstein's Relativity |publisher=Princeton University Press |year=2021 |orig-year=2005 |edition=Princeton Science Library paperback |isbn=978-0-691-12201-4 |oclc=1193067111}}</ref>{{rp|45–52}} The two observers will disagree on the time <math>T</math> between the events, and they will disagree about the distance <math>D</math> separating the events, but they will agree on the [[speed of light]] <math>c</math>, and they will measure the same value for the combination <math>c^2T^2 - D^2</math>.<ref name="Mermin2005"/>{{rp|80}} The square root of the [[absolute value]] of this quantity is called the ''interval'' between the two events. The interval expresses how widely separated events are, not just in space or in time, but in the combined setting of spacetime.<ref name="Mermin2005"/>{{rp|84,136}}<ref>{{cite journal |doi=10.1007/s10714-006-0254-9 |bibcode=2006GReGr..38..643B |arxiv=gr-qc/0407022 |title=Spacetime and Euclidean geometry |journal=General Relativity and Gravitation |volume=38 |issue=4 |year=2006 |pages=643–651 |last1=Brill |first1=Dieter |last2=Jacobsen |first2=Ted |citeseerx=10.1.1.338.7953 |s2cid=119067072 }}</ref>

The special theory of relativity cannot account for [[gravity]]. Its successor, the [[general theory of relativity]], explains gravity by recognizing that spacetime is not fixed but instead dynamical. In general relativity, gravitational force is reimagined as curvature of [[spacetime]]. A curved path like an orbit is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by [[John Archibald Wheeler]] that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve",<ref name="Wheeler">{{Cite book|last=Wheeler|first=John Archibald|url=https://books.google.com/books?id=zGFkK2tTXPsC&pg=PA235|title=Geons, Black Holes, and Quantum Foam: A Life in Physics|date=2010|publisher=W. W. Norton & Company|isbn=978-0-393-07948-7|language=en|author-link=John Archibald Wheeler|access-date=February 17, 2023|archive-date=February 17, 2023|archive-url=https://web.archive.org/web/20230217135729/https://books.google.com/books?id=zGFkK2tTXPsC&pg=PA235|url-status=live}}</ref><ref>{{Cite journal|last=Kersting|first=Magdalena|date=May 2019|title=Free fall in curved spacetime – how to visualise gravity in general relativity|journal=[[Physics Education]] |volume=54|issue=3|pages=035008|doi=10.1088/1361-6552/ab08f5|bibcode=2019PhyEd..54c5008K |s2cid=127471222 |issn=0031-9120|doi-access=free|hdl=10852/74677|hdl-access=free}}</ref> and therefore there is no point in considering one without the other.<ref name="Hawking" /> The [[Newton's law of universal gravitation|Newtonian theory of gravity]] is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.<ref>{{Cite book |last1=Goldstein |first1=Herbert |title=Classical Mechanics |title-link=Classical Mechanics (Goldstein) |last2=Poole |first2=Charles P. |last3=Safko |first3=John L. |date=2002 |publisher=Addison Wesley |isbn=0-201-31611-0 |edition=3rd |location=San Francisco |oclc=47056311 |author-link=Herbert Goldstein |author2-link=Charles P. Poole}}</ref>{{Rp|page=327}}<ref>{{Cite book |last=Goodstein |first=Judith R. |url=https://www.worldcat.org/oclc/1020305599 |title=Einstein's Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity |date=2018 |publisher=American Mathematical Society |isbn=978-1-4704-2846-4 |location=Providence, Rhode Island |pages=143 |oclc=1020305599 |author-link=Judith R. Goodstein}}</ref>

The relation between matter distribution and spacetime curvature is given by the [[Einstein field equations]], which require [[tensor calculus]] to express.<ref>{{Cite book |last=Choquet-Bruhat |first=Yvonne |url=https://www.worldcat.org/oclc/317496332 |title=General Relativity and the Einstein Equations |date=2009 |publisher=Oxford University Press |isbn=978-0-19-155226-7 |location=Oxford |oclc=317496332 |author-link=Yvonne Choquet-Bruhat}}</ref>{{Rp|page=43}}<ref>{{Cite book |last=Prescod-Weinstein |first=Chanda |url=https://www.worldcat.org/oclc/1164503847 |title=The Disordered Cosmos: A Journey into Dark Matter, Spacetime, and Dreams Deferred |date=2021 |publisher=Bold Type Books |isbn=978-1-5417-2470-9 |location=New York, New York |language=en-us |oclc=1164503847 |author-link=Chanda Prescod-Weinstein |access-date=February 17, 2023 |archive-date=February 21, 2022 |archive-url=https://web.archive.org/web/20220221214240/http://www.worldcat.org/oclc/1164503847 |url-status=live }}</ref> The solutions to these equations include not only the spacetime of special relativity, [[Minkowski spacetime]], but also [[Schwarzschild metric|Schwarzschild spacetimes]], which describe [[black hole]]s; [[Friedmann–Lemaître–Robertson–Walker metric|FLRW spacetime]], which describes an expanding universe; and more.

The universe appears to be a smooth spacetime continuum consisting of three [[space|spatial]] [[dimension]]s and one temporal ([[time]]) dimension. Therefore, an event in the spacetime of the physical universe can therefore be identified by a set of four coordinates: {{nowrap begin}}(''x'', ''y'', ''z'', ''t''){{nowrap end}}. On average, [[3-space|space]] is observed to be very nearly [[Shape of the universe|flat]] (with a [[curvature]] close to zero), meaning that [[Euclidean geometry]] is empirically true with high accuracy throughout most of the universe.<ref name="Shape">{{Cite web |title=WMAP Mission – Age of the Universe |url=https://map.gsfc.nasa.gov/m_mm/mr_content.html |access-date=February 14, 2023 |website=map.gsfc.nasa.gov |archive-date=December 4, 2022 |archive-url=https://web.archive.org/web/20221204182149/https://map.gsfc.nasa.gov/m_mm/mr_content.html |url-status=live }}</ref> Spacetime also appears to have a [[simply connected space|simply connected]] [[topology]], in analogy with a sphere, at least on the length scale of the observable universe. However, present observations cannot exclude the possibilities that the universe has more dimensions (which is postulated by theories such as the [[string theory]]) and that its spacetime may have a multiply connected global topology, in analogy with the cylindrical or [[toroid]]al topologies of two-dimensional [[space]]s.<ref name="Nat03">{{cite journal
 |last1        = Luminet
 |first1       = Jean-Pierre
 |author-link  = Jean-Pierre Luminet
 |last2        = Weeks
 |first2       = Jeffrey R.
 |last3        = Riazuelo
 |first3       = Alain
 |last4        = Lehoucq
 |first4       = Roland
 |last5        = Uzan
 |first5       = Jean-Philippe
 |title        = Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
 |journal      = [[Nature (journal)|Nature]]
 |volume       = 425
 |issue        = 6958
 |pages        = 593–595
 |date         = October 9, 2003
|pmid         = 14534579
 |arxiv        = astro-ph/0310253
 |doi          = 10.1038/nature01944
 |bibcode      = 2003Natur.425..593L
 |s2cid        = 4380713
 |url          = https://cds.cern.ch/record/647738
 |type         = Submitted manuscript
 |access-date  = August 21, 2018
|archive-date = May 17, 2021
|archive-url  = https://web.archive.org/web/20210517180259/https://cds.cern.ch/record/647738
 |url-status   = live
}}</ref><ref name="_spacetime_topology">{{cite conference
|first1=Jean-Pierre
|last1=Luminet
|first2=Boudewijn F.
 |last2=Roukema
 |title=Topology of the Universe: Theory and Observations
|book-title=Proceedings of Cosmology School held at Cargese, Corsica, August 1998
|date=1999
|arxiv=astro-ph/9901364
|bibcode=1999ASIC..541..117L }}</ref>