Physics:Quantum Zeno effect - Revision history

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 == See also ==

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	Another crucial problem related to the effect is strictly connected to the ~~[[Physics:Uncertainty principle#Time–energy uncertainty relation\|~~time–energy indeterminacy relation]] (part of the indeterminacy principle). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state in which reduction occurs becomes increasingly large. However, the deviations from the exponential decay law for small times is crucially related to the inverse of the energy spread, so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect.<ref name=Ghirardi>		Another crucial problem related to the effect is strictly connected to the time–energy indeterminacy relation (part of the indeterminacy principle). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the energy spread of the state in which reduction occurs becomes increasingly large. However, the deviations from the exponential decay law for small times is crucially related to the inverse of the energy spread, so that the region in which the deviations are appreciable shrinks when one makes the measurement process duration shorter and shorter. An explicit evaluation of these two competing requests shows that it is inappropriate, without taking into account this basic fact, to deal with the actual occurrence and emergence of Zeno's effect.<ref name=Ghirardi>
	{{cite journal		{{cite journal
	\|last1=Ghirardi \|first1=G. C.		\|last1=Ghirardi \|first1=G. C.
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	}}</ref> By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.		}}</ref> By its nature, the effect appears only in systems with distinguishable quantum states, and hence is inapplicable to classical phenomena and macroscopic bodies.

	The idea is implicit in John von Neumann's early work ''Mathematical Foundations of Quantum Mechanics'', and in particular the rule sometimes called the ''~~[[Physics:Wave function collapse#History and context\|~~reduction postulate]]''.<ref name="vonNeumann">{{cite book \|title=Mathematische Grundlagen der Quantenmechanik \|publisher=Springer \|year=1932 \|isbn=978-3-540-59207-5 \|page=Chapter V.2 \|no-pp=true \|last1=von Neumann \|first1=J.}} See also {{cite book \|title=Mathematical Foundations of Quantum Mechanics \|url=https://archive.org/details/mathematicalfoun0613vonn \|url-access=registration \|publisher=Princeton University Press \|year=1955 \|isbn=978-0-691-02893-4 \|page=[https://archive.org/details/mathematicalfoun0613vonn/page/366 366] \|last1=von Neumann \|first1=J.}}); {{cite book \|url=https://books.google.com/books?id=Bo7jujlMqL8C&pg=PA80 \|title=Quantum Measurements and Decoherence \|publisher=Springer \|year=2000 \|isbn=978-0-7923-6227-2 \|page=§4.1.1, pp. 315 ff \|no-pp=yes \|last1=Menskey \|first1=M. B.}}; {{cite book \|url=https://books.google.com/books?id=mmhJ37o8fdwC&pg=PA315 \|title=Quantum Measurements and New Concepts for Experiments with Trapped Ions \|last2=Balzer \|first2=C. \|publisher=Academic Press \|year=2003 \|isbn=978-0-12-003849-7 \|series=Advances in Atomic, Molecular, and Optical Physics \|volume=49 \|page=315 \|last1=Wunderlich \|first1=C. \|editor1-last=Bederson \|editor1-first=B. \|editor2-last=Walther \|editor2-first=H.}}</ref> It was later shown that the quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system.<ref>{{Cite journal \|date=April 1997 \|title=Quantum Zeno Effect and the Impossibility of Determining the Quantum State of a Single System \|journal=Phys. Rev. A \|volume=55 \|issue=5 \|pages=R2499–R2502 \|bibcode=1997PhRvA..55.2499A \|doi=10.1103/PhysRevA.55.R2499 \|author=Orly Alter and Yoshihisa Yamamoto}}</ref><ref>{{Cite book \|chapter-url=http://www.alterlab.org/publications/Alter_Yamamoto_Quantum_Interferometry_1996.pdf \|title=Quantum Interferometry \|date=October 1996 \|publisher=Wiley-VCH \|pages=539–544 \|chapter=The quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system \|author=Orly Alter and Yoshihisa Yamamoto \|editor=F. De Martini, G. Denardo and Y. Shih}}</ref><ref>{{Cite book \|url=https://alterlab.org/publications/Alter_Yamamoto_Wiley-Interscience_2001.pdf \|title=Quantum Measurement of a Single System \|date=2001 \|publisher=Wiley-Interscience \|doi=10.1002/9783527617128 \|author=Orly Alter and Yoshihisa Yamamoto \|isbn=978-0-471-28308-9 \|access-date=2021-12-04 \|archive-date=2021-12-04 \|archive-url=https://web.archive.org/web/20211204211255/https://alterlab.org/publications/Alter_Yamamoto_Wiley-Interscience_2001.pdf }}</ref>		The idea is implicit in John von Neumann's early work ''Mathematical Foundations of Quantum Mechanics'', and in particular the rule sometimes called the ''reduction postulate''.<ref name="vonNeumann">{{cite book \|title=Mathematische Grundlagen der Quantenmechanik \|publisher=Springer \|year=1932 \|isbn=978-3-540-59207-5 \|page=Chapter V.2 \|no-pp=true \|last1=von Neumann \|first1=J.}} See also {{cite book \|title=Mathematical Foundations of Quantum Mechanics \|url=https://archive.org/details/mathematicalfoun0613vonn \|url-access=registration \|publisher=Princeton University Press \|year=1955 \|isbn=978-0-691-02893-4 \|page=[https://archive.org/details/mathematicalfoun0613vonn/page/366 366] \|last1=von Neumann \|first1=J.}}); {{cite book \|url=https://books.google.com/books?id=Bo7jujlMqL8C&pg=PA80 \|title=Quantum Measurements and Decoherence \|publisher=Springer \|year=2000 \|isbn=978-0-7923-6227-2 \|page=§4.1.1, pp. 315 ff \|no-pp=yes \|last1=Menskey \|first1=M. B.}}; {{cite book \|url=https://books.google.com/books?id=mmhJ37o8fdwC&pg=PA315 \|title=Quantum Measurements and New Concepts for Experiments with Trapped Ions \|last2=Balzer \|first2=C. \|publisher=Academic Press \|year=2003 \|isbn=978-0-12-003849-7 \|series=Advances in Atomic, Molecular, and Optical Physics \|volume=49 \|page=315 \|last1=Wunderlich \|first1=C. \|editor1-last=Bederson \|editor1-first=B. \|editor2-last=Walther \|editor2-first=H.}}</ref> It was later shown that the quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system.<ref>{{Cite journal \|date=April 1997 \|title=Quantum Zeno Effect and the Impossibility of Determining the Quantum State of a Single System \|journal=Phys. Rev. A \|volume=55 \|issue=5 \|pages=R2499–R2502 \|bibcode=1997PhRvA..55.2499A \|doi=10.1103/PhysRevA.55.R2499 \|author=Orly Alter and Yoshihisa Yamamoto}}</ref><ref>{{Cite book \|chapter-url=http://www.alterlab.org/publications/Alter_Yamamoto_Quantum_Interferometry_1996.pdf \|title=Quantum Interferometry \|date=October 1996 \|publisher=Wiley-VCH \|pages=539–544 \|chapter=The quantum Zeno effect of a single system is equivalent to the indetermination of the quantum state of a single system \|author=Orly Alter and Yoshihisa Yamamoto \|editor=F. De Martini, G. Denardo and Y. Shih}}</ref><ref>{{Cite book \|url=https://alterlab.org/publications/Alter_Yamamoto_Wiley-Interscience_2001.pdf \|title=Quantum Measurement of a Single System \|date=2001 \|publisher=Wiley-Interscience \|doi=10.1002/9783527617128 \|author=Orly Alter and Yoshihisa Yamamoto \|isbn=978-0-471-28308-9 \|access-date=2021-12-04 \|archive-date=2021-12-04 \|archive-url=https://web.archive.org/web/20211204211255/https://alterlab.org/publications/Alter_Yamamoto_Wiley-Interscience_2001.pdf }}</ref>

	==History==		==History==
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	== External links ==		== External links ==
	* [http://www.lysator.liu.se/~jc/zeno.qcl.html Zeno.qcl] A computer program written in ~~[[Quantum programming#Quantum programming languages\|~~QCL]] which demonstrates the Quantum Zeno effect		* [http://www.lysator.liu.se/~jc/zeno.qcl.html Zeno.qcl] A computer program written in QCL which demonstrates the Quantum Zeno effect
	* {{cite web\|title=How the quantum Zeno effect impacts Schrodinger's cat\|url=https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html\|website=phys.org\|access-date=18 June 2017\|url-status=live\|archive-url=https://web.archive.org/web/20170617153012/https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html\|archive-date=17 June 2017}}		* {{cite web\|title=How the quantum Zeno effect impacts Schrodinger's cat\|url=https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html\|website=phys.org\|access-date=18 June 2017\|url-status=live\|archive-url=https://web.archive.org/web/20170617153012/https://phys.org/news/2017-06-quantum-zeno-effect-impacts-schroedinger.html\|archive-date=17 June 2017}}

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	* [[Zeno's paradoxes]]		* [[Zeno's paradoxes]]
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			== See also ==
			{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

	==References==		==References==
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	[[Category:Quantum mechanical entropy]]		[[Category:Quantum mechanical entropy]]

	{{Sourceattribution\|Quantum Zeno effect}}		{{Author\|Harold Foppele}}

			{{Sourceattribution\|Physics:Quantum Zeno effect\|1}}

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	{{Quantum book backlink\|Measurement and information}}		{{Quantum book backlink\|Measurement and information}}
	~~[[File~~:~~Quantum Zeno effect animation~~.gif\|thumb\|400px\|With the increasing number of measurements the wave function tends to stay in its initial form. In the animation, a free time evolution of a wave function, depicted on the left, is in the central part interrupted by occasional position measurements that localize the wave function in one of nine sectors. On the right, a series of very frequent measurements leads to the quantum Zeno effect.]]
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	In [[Physics:Quantum mechanics\|quantum mechanics]], frequent measurements cause the '''quantum Zeno effect''', a reduction in transitions away from the system's initial state, slowing a system's [[Time evolution\|time evolution]].<ref name=Facchi-2008/>{{rp\|5}}		In [[Physics:Quantum mechanics\|quantum mechanics]], frequent measurements cause the '''quantum Zeno effect''', a reduction in transitions away from the system's initial state, slowing a system's [[Time evolution\|time evolution]].<ref name=Facchi-2008/>{{rp\|5}}

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			[[File:Quantum Zeno effect animation.gif\|thumb\|280px\|Quantum Zeno effect.]]
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	==Description==		==Description==

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