Editing Momentum (section)

===Symmetry and conservation===
Conservation of momentum is a mathematical consequence of the [[Homogeneity (physics)|homogeneity]] (shift [[symmetry]]) of space (position in space is the [[canonical conjugate]] quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of [[Noether's theorem]].<ref>{{cite book|last1=Hand|first1=Louis N. |last2=Finch |first2=Janet D. |title=Analytical mechanics|date=1998|publisher=Cambridge University Press|location=Cambridge|isbn=978-0-521-57572-0|edition=7th print |pages=Chapter 4 |no-pp=true}}</ref> For systems that do not have this symmetry, it may not be possible to define conservation of momentum. Examples where conservation of momentum does not apply include [[curved space]]times in [[general relativity]]<ref>{{cite journal|last1=Witten|first1=Edward|title=A new proof of the positive energy theorem|journal=Communications in Mathematical Physics|volume=80|issue=3|year=1981|pages=381–402|issn=0010-3616|doi=10.1007/BF01208277|bibcode=1981CMaPh..80..381W|s2cid=1035111|url=https://www.sns.ias.edu/ckfinder/userfiles/files/%5B32%5DCMP_80_1981.pdf|access-date=2020-12-17|archive-date=2016-11-25|archive-url=https://web.archive.org/web/20161125044504/https://www.sns.ias.edu/ckfinder/userfiles/files/%5B32%5DCMP_80_1981.pdf}}</ref> or [[time crystals]] in [[condensed matter physics]].<ref name="Grossman 2012">{{cite magazine|last1=Grossman|first1=Lisa|title=Death-defying time crystal could outlast the universe|url=https://www.newscientist.com/article/mg21328484-000-death-defying-time-crystal-could-outlast-the-universe/|magazine=New Scientist|archive-url=https://archive.today/20170202104619/https://www.newscientist.com/article/mg21328484-000-death-defying-time-crystal-could-outlast-the-universe/|archive-date=2017-02-02|date=18 January 2012}}</ref><ref name="Cowen 2012">{{cite magazine|last1=Cowen|first1=Ron|title='Time Crystals' Could Be a Legitimate Form of Perpetual Motion|url=https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|magazine=Scientific American|archive-url=https://archive.today/20170202101455/https://www.scientificamerican.com/article/time-crystals-could-be-legitimate-form-perpetual-motion/|archive-date=2017-02-02|date=27 February 2012}}</ref><ref name="Powell 2013">{{cite journal|last1=Powell|first1=Devin|title=Can matter cycle through shapes eternally?|journal=Nature|year=2013|issn=1476-4687|doi=10.1038/nature.2013.13657|s2cid=181223762|url=http://www.nature.com/news/can-matter-cycle-through-shapes-eternally-1.13657|archive-url=https://archive.today/20170203080014/http://www.nature.com/news/can-matter-cycle-through-shapes-eternally-1.13657|archive-date=2017-02-03}}</ref><ref name="Gibney 2017">{{cite journal|last1=Gibney|first1=Elizabeth|title=The quest to crystallize time|journal=Nature|volume=543|issue=7644|year=2017|pages=164–166|issn=0028-0836|doi=10.1038/543164a|pmid=28277535|url=http://www.nature.com/news/the-quest-to-crystallize-time-1.21595|archive-url=https://archive.today/20170313115721/http://www.nature.com/news/the-quest-to-crystallize-time-1.21595|archive-date=2017-03-13|bibcode=2017Natur.543..164G|s2cid=4460265}}</ref>