Editing Universe (section)

=== 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 describes a flat spacetime. Its successor, the [[general theory of relativity]], explains [[gravity]] as curvature of [[spacetime]] arising due to its energy content. 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 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 be identified by a set of four coordinates: {{nowrap begin}}(''x'', ''y'', ''z'', ''t''){{nowrap end}}.