Editing Uncertainty principle (section)

{{Short description|Foundational principle in quantum physics}}
{{Other uses}}
{{Use American English|date=January 2019}}
{{Quantum mechanics}}

[[File:Werner Heisenberg - Canonical commutation rule for position and momentum variables of a particle - Uncertainty principle, 1927.jpg|thumb|Canonical commutation rule for position ''q'' and momentum ''p'' variables of a particle, 1927. ''pq'' − ''qp'' = ''h''/(2''πi''). Uncertainty principle of Heisenberg, 1927.]]

The '''uncertainty principle''', also known as '''Heisenberg's indeterminacy principle''', is a fundamental concept in [[quantum mechanics]]. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and [[momentum]], can be simultaneously known. In other words, the more accurately one property is measured, the less accurately the other property can be known.

More formally, the uncertainty principle is any of a variety of [[Inequality (mathematics)|mathematical inequalities]] asserting a fundamental limit to the product of the accuracy of certain related pairs of measurements on a quantum system, such as [[Position (vector)|position]], ''x'', and momentum, ''p''.<ref name=Sen2014>{{Cite journal | last1 = Sen | first1 = D. | title = The Uncertainty relations in quantum mechanics | url = http://www.currentscience.ac.in/Volumes/107/02/0203.pdf | journal = Current Science | volume = 107 | issue = 2 | year = 2014 | pages = 203–218 | access-date = 2016-02-14 | archive-date = 2019-09-24 | archive-url = https://web.archive.org/web/20190924115453/https://www.currentscience.ac.in/Volumes/107/02/0203.pdf | url-status = live }}</ref> Such paired-variables are known as [[Complementarity (physics)|complementary variables]] or [[Canonical coordinates|canonically conjugate variables]].

First introduced in 1927 by German physicist [[Werner Heisenberg]],<ref name=":0">{{Cite journal |last=Heisenberg |first=W. |orig-date=1927-03-01 |title=Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik |url=https://doi.org/10.1007/BF01397280 |journal=Zeitschrift für Physik |date=1927 |language=de |volume=43 |issue=3 |pages=172–198 |bibcode=1927ZPhy...43..172H |doi=10.1007/BF01397280 |issn=0044-3328 |s2cid=122763326 }}{{Cite journal |last=Heisenberg |first=W |year=1983 |orig-date=1927 |title=The actual content of quantum theoretical kinematics and mechanics |url=https://ntrs.nasa.gov/citations/19840008978 |journal=No. NAS 1.15: 77379. 1983. |volume=43 |issue=3–4 |page=172 |bibcode=1983ZhPhy..43..172H |quote=English translation of Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik |access-date=2023-08-28 |archive-date=2023-09-02 |archive-url=https://web.archive.org/web/20230902112403/https://ntrs.nasa.gov/citations/19840008978 |url-status=live }}</ref><ref>Werner Heisenberg (1989), ''Encounters with Einstein and Other Essays on People, Places and Particles'',  [[Princeton University Press]], p. 53. {{ISBN?}}</ref><ref>{{cite book | doi=10.1515/9781400889167 | title=The Tests of Time | year=2003 | isbn=978-1400889167 | editor-last1=Dolling | editor-last2=Gianelli | editor-last3=Statile | editor-first1=Lisa M. | editor-first2=Arthur F. | editor-first3=Glenn N. }}</ref><ref>Kumar, Manjit. ''Quantum: Einstein, Bohr, and the great debate about the nature of reality.'' 1st American ed., 2008. Chap. 10, Note 37. {{ISBN?}}</ref> the formal inequality relating the [[standard deviation]] of position ''σ<sub>x</sub>'' and the standard deviation of momentum ''σ<sub>p</sub>'' was derived by [[Earle Hesse Kennard]]<ref name="Kennard">{{Citation |first=E. H. |last=Kennard |title=Zur Quantenmechanik einfacher Bewegungstypen |language=de|journal=Zeitschrift für Physik |volume=44 |issue=4–5 |year=1927 |pages=326–352 |doi=10.1007/BF01391200 |postscript=. |bibcode = 1927ZPhy...44..326K |s2cid=121626384 }}</ref> later that year and by [[Hermann Weyl]]<ref name="Weyl1928">{{Cite book |last=Weyl |first=H. |title=Gruppentheorie und Quantenmechanik |lang=de |year=1928 |publisher=Hirzel |location=Leipzig}}{{page?|date=February 2024}}</ref> in 1928:
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|equation = <math> \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2}</math>
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where <math>\hbar = \frac{h}{2\pi}</math> is the [[reduced Planck constant]].

The quintessentially quantum mechanical uncertainty principle comes in many forms other than position–momentum. The energy–time relationship is widely used to relate quantum state lifetime to measured energy widths but its formal derivation is fraught with confusing issues about the nature of time. The basic principle has been extended in numerous directions; it must be considered in many kinds of fundamental physical measurements.