Editing Complementarity (physics) (section)

== Continuous complementarity ==
{{Main | Wave–particle duality relation }}
While the concept of complementarity can be discussed via two experimental extremes, continuous tradeoff is also possible.<ref name=Zeilinger/><ref>{{Cite journal |last=Englert |first=Berthold-Georg |date=1999-01-01 |title=Remarks on Some Basic Issues in Quantum Mechanics |journal=Zeitschrift für Naturforschung A |language=en |volume=54 |issue=1 |pages=11–32 |doi=10.1515/zna-1999-0104 |issn=1865-7109|doi-access=free |bibcode=1999ZNatA..54...11E }}</ref> 
In 1979 Wooters and Zurek introduced an information-theoretic treatment of the [[double-slit experiment]] providing on approach to a quantiative model of complementarity.<ref>{{Cite journal |last=Wootters |first=William K. |last2=Zurek |first2=Wojciech H. |date=1979-01-15 |title=Complementarity in the double-slit experiment: Quantum nonseparability and a quantitative statement of Bohr's principle |url=https://link.aps.org/doi/10.1103/PhysRevD.19.473 |journal=Physical Review D |language=en |volume=19 |issue=2 |pages=473–484 |doi=10.1103/PhysRevD.19.473 |issn=0556-2821|url-access=subscription }}</ref><ref>{{Cite journal |last=Bartell |first=L. S. |date=1980-03-15 |title=Complementarity in the double-slit experiment: On simple realizable systems for observing intermediate particle-wave behavior |url=https://link.aps.org/doi/10.1103/PhysRevD.21.1698 |journal=Physical Review D |language=en |volume=21 |issue=6 |pages=1698–1699 |doi=10.1103/PhysRevD.21.1698 |issn=0556-2821|url-access=subscription }}</ref>
The wave-particle relation, introduced by [[Daniel Greenberger]] and Allaine Yasin in 1988, and since then refined by others,<ref name=Sen2014>{{Cite journal |last1 = Sen | first1 = D. | title = The Uncertainty relations in quantum mechanics | url = https://www.jstor.org/stable/24103129 | journal = Current Science | volume = 107| issue = 2| year = 2014| pages = 203–218 | jstor = 24103129 }}</ref> quantifies the trade-off between measuring particle path distinguishability, <math>D</math>, and wave interference fringe visibility, <math>V</math>:
<math display=block>D^2 + V^2\ \le\ 1</math>
The values of <math>D</math> and <math>V</math> can vary between 0 and 1 individually, but any experiment that combines particle and wave detection will limit one or the other, or both. The detailed definition of the two terms vary among applications,<ref name=Sen2014/> but the relation expresses the verified constraint that efforts to detect particle paths will result in less visible wave interference.