Physics:Quantum mechanics measurements - Revision history

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	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
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	~~{{Documentation}}~~
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	===Examples===		===Examples===
	[[Image:Bloch sphere representation of optimal POVM and states for unambiguous quantum state discrimination.svg\|thumb\|right\|~~[[Wikipedia:~~Bloch sphere~~\|Bloch sphere]]~~ representation of states (in blue) and optimal POVM (in red) for unambiguous quantum state discrimination<ref>{{Cite journal\|last1=Peres\|first1=Asher\|author-link=W:Asher Peres\|last2=Terno\|first2=Daniel R.\|date=1998\|title=Optimal distinction between non-orthogonal quantum states\|journal=Journal of Physics A: Mathematical and General\|language=en\|volume=31\|issue=34\|pages=7105–7111\|doi=10.1088/0305-4470/31/34/013\|issn=0305-4470 \|arxiv=quant-ph/9804031\|bibcode=1998JPhA...31.7105P\|s2cid=18961213}}</ref>		[[Image:Bloch sphere representation of optimal POVM and states for unambiguous quantum state discrimination.svg\|thumb\|right\|Bloch sphere representation of states (in blue) and optimal POVM (in red) for unambiguous quantum state discrimination<ref>{{Cite journal\|last1=Peres\|first1=Asher\|author-link=W:Asher Peres\|last2=Terno\|first2=Daniel R.\|date=1998\|title=Optimal distinction between non-orthogonal quantum states\|journal=Journal of Physics A: Mathematical and General\|language=en\|volume=31\|issue=34\|pages=7105–7111\|doi=10.1088/0305-4470/31/34/013\|issn=0305-4470 \|arxiv=quant-ph/9804031\|bibcode=1998JPhA...31.7105P\|s2cid=18961213}}</ref>
	on the states <math>\|\psi\rangle=\|0\rangle</math> and <math>\|\varphi\rangle=(\|0\rangle+\|1\rangle)/\sqrt2</math>. Note that on the Bloch sphere orthogonal states are antiparallel.]]		on the states <math>\|\psi\rangle=\|0\rangle</math> and <math>\|\varphi\rangle=(\|0\rangle+\|1\rangle)/\sqrt2</math>. Note that on the Bloch sphere orthogonal states are antiparallel.]]
	The prototypical example of a finite-dimensional Hilbert space is a qubit, a quantum system whose Hilbert space is 2-dimensional. A pure state for a qubit can be written as a linear combination of two orthogonal basis states <math>\|0 \rangle </math> and <math>\|1 \rangle </math> with complex coefficients:		The prototypical example of a finite-dimensional Hilbert space is a qubit, a quantum system whose Hilbert space is 2-dimensional. A pure state for a qubit can be written as a linear combination of two orthogonal basis states <math>\|0 \rangle </math> and <math>\|1 \rangle </math> with complex coefficients:
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	==Interpretations of quantum mechanics==		==Interpretations of quantum mechanics==
	[[Image:Niels Bohr Albert Einstein4 by Ehrenfest cr.jpg\|thumb\|~~[[Wikipedia:~~Niels Bohr~~\|Niels Bohr]]~~ and Albert Einstein, pictured here at Paul Ehrenfest's home in Leiden (December 1925), had a long-running collegial dispute about what quantum mechanics implied for the nature of reality.]]		[[Image:Niels Bohr Albert Einstein4 by Ehrenfest cr.jpg\|thumb\|Niels Bohr and Albert Einstein, pictured here at Paul Ehrenfest's home in Leiden (December 1925), had a long-running collegial dispute about what quantum mechanics implied for the nature of reality.]]
	Despite the consensus among scientists that quantum physics is in practice a successful theory, disagreements persist on a more philosophical level. Many debates in the area known as quantum foundations concern the role of measurement in quantum mechanics. Recurring questions include which interpretation of probability theory is best suited for the probabilities calculated from the Born rule; and whether the apparent randomness of quantum measurement outcomes is fundamental, or a consequence of a deeper deterministic process.<ref name="snapshot">{{Cite journal\| arxiv=1301.1069 \| title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics \| journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics \| volume=44 \| issue=3 \| pages=222–230 \| date=6 January 2013 \| last1=Schlosshauer \| first1=Maximilian \| last2=Kofler \| first2=Johannes \| last3=Zeilinger \| first3=Anton \| author-link3=Anton Zeilinger \| doi=10.1016/j.shpsb.2013.04.004 \| bibcode=2013SHPMP..44..222S \| s2cid=55537196 }}</ref><ref name="map">{{Cite book\|title=What is Quantum Information? \|last=Cabello \|first=Adán \|publisher=Cambridge University Press \|year=2017 \|isbn=978-1-107-14211-4 \|editor-last=Lombardi \|editor-first=Olimpia\|editor-link=W:Olimpia Lombardi \|pages=138–143 \|chapter=Interpretations of quantum theory: A map of madness \|arxiv=1509.04711 \|editor2-last=Fortin \|editor2-first=Sebastian \|editor3-last=Holik \|editor3-first=Federico \|editor4-last=López \|editor4-first=Cristian \|bibcode=2015arXiv150904711C \|doi=10.1017/9781316494233.009\|s2cid=118419619 }}</ref><ref>{{Cite journal\|last1=Schaffer\|first1=Kathryn\|last2=Barreto Lemos\|first2=Gabriela\|date=24 May 2019\|title=Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics\|journal=Foundations of Science\|volume=26 \|pages=7–26 \|language=en\|arxiv=1908.07936\|doi=10.1007/s10699-019-09608-5\|s2cid=182656563\|issn=1233-1821}}</ref> Worldviews that present answers to questions like these are known as "interpretations" of quantum mechanics; as the physicist N. David Mermin once quipped, "New interpretations appear every year. None ever disappear."<ref name="mermin2012">{{Cite journal\|last=Mermin\|first=N. David\|author-link=W:N. David Mermin \|date=1 July 2012\|title=Commentary: Quantum mechanics: Fixing the shifty split\|journal=Physics Today\|volume=65\|issue=7\|pages=8–10\|doi=10.1063/PT.3.1618\|issn=0031-9228\|bibcode=2012PhT....65g...8M\|doi-access=free}}</ref>		Despite the consensus among scientists that quantum physics is in practice a successful theory, disagreements persist on a more philosophical level. Many debates in the area known as quantum foundations concern the role of measurement in quantum mechanics. Recurring questions include which interpretation of probability theory is best suited for the probabilities calculated from the Born rule; and whether the apparent randomness of quantum measurement outcomes is fundamental, or a consequence of a deeper deterministic process.<ref name="snapshot">{{Cite journal\| arxiv=1301.1069 \| title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics \| journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics \| volume=44 \| issue=3 \| pages=222–230 \| date=6 January 2013 \| last1=Schlosshauer \| first1=Maximilian \| last2=Kofler \| first2=Johannes \| last3=Zeilinger \| first3=Anton \| author-link3=Anton Zeilinger \| doi=10.1016/j.shpsb.2013.04.004 \| bibcode=2013SHPMP..44..222S \| s2cid=55537196 }}</ref><ref name="map">{{Cite book\|title=What is Quantum Information? \|last=Cabello \|first=Adán \|publisher=Cambridge University Press \|year=2017 \|isbn=978-1-107-14211-4 \|editor-last=Lombardi \|editor-first=Olimpia\|editor-link=W:Olimpia Lombardi \|pages=138–143 \|chapter=Interpretations of quantum theory: A map of madness \|arxiv=1509.04711 \|editor2-last=Fortin \|editor2-first=Sebastian \|editor3-last=Holik \|editor3-first=Federico \|editor4-last=López \|editor4-first=Cristian \|bibcode=2015arXiv150904711C \|doi=10.1017/9781316494233.009\|s2cid=118419619 }}</ref><ref>{{Cite journal\|last1=Schaffer\|first1=Kathryn\|last2=Barreto Lemos\|first2=Gabriela\|date=24 May 2019\|title=Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics\|journal=Foundations of Science\|volume=26 \|pages=7–26 \|language=en\|arxiv=1908.07936\|doi=10.1007/s10699-019-09608-5\|s2cid=182656563\|issn=1233-1821}}</ref> Worldviews that present answers to questions like these are known as "interpretations" of quantum mechanics; as the physicist N. David Mermin once quipped, "New interpretations appear every year. None ever disappear."<ref name="mermin2012">{{Cite journal\|last=Mermin\|first=N. David\|author-link=W:N. David Mermin \|date=1 July 2012\|title=Commentary: Quantum mechanics: Fixing the shifty split\|journal=Physics Today\|volume=65\|issue=7\|pages=8–10\|doi=10.1063/PT.3.1618\|issn=0031-9228\|bibcode=2012PhT....65g...8M\|doi-access=free}}</ref>

	A central concern within quantum foundations is the "quantum measurement problem," though how this problem is delimited, and whether it should be counted as one question or multiple separate issues, are contested topics.<ref name="Barad">{{Cite book\|title=Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning\|last=Barad\|first=Karen\|publisher=Duke University Press\|year=2007\|isbn=978-0-8223-3917-5\|language=en\|oclc=1055296186\|author-link=W:Karen Barad}}</ref><ref>{{cite encyclopedia\|first1=Jeffrey \|last1=Bub \|author-link1=Jeffrey Bub \|first2=Itamar \|last2=Pitowsky \|title=Two dogmas about quantum mechanics \|arxiv=0712.4258 \|encyclopedia=Many Worlds? \|year=2010 \|pages=433–459 \|publisher=~~[[Wikipedia:Oxford University Press\|]]~~ \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref> Of primary interest is the seeming disparity between apparently distinct types of time evolution. Von Neumann declared that quantum mechanics contains "two fundamentally different types" of quantum-state change.<ref>{{cite book \|title=Mathematical Foundations of Quantum Mechanics. New Edition \|first=John \|last=von Neumann \|author-link=W:John von Neumann \|translator=Robert T. Beyer \|editor-first=Nicholas A. \|editor-last=Wheeler \|publisher=Princeton University Press \|date=2018 \|isbn=9-781-40088-992-1 \|oclc=1021172445}}</ref>{{rp\|§V.1}} First, there are those changes involving a measurement process, and second, there is unitary time evolution in the absence of measurement. The former is stochastic and discontinuous, writes von Neumann, and the latter deterministic and continuous. This dichotomy has set the tone for much later debate.<ref>{{Citation\|last=Wigner\|first=E. P.\|title=Philosophical Reflections and Syntheses\|chapter=Review of the Quantum-Mechanical Measurement Problem\|date=1995\|pages=225–244\|editor-last=Mehra\|editor-first=Jagdish\|publisher=Springer Berlin Heidelberg\|language=en\|doi=10.1007/978-3-642-78374-6_19\|isbn=978-3-540-63372-3\|author-link=W:Eugene Wigner\|editor-link=W:Jagdish Mehra}}</ref><ref name="stanford3">{{Cite book\|last=Faye\|first=Jan\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2019\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Copenhagen Interpretation of Quantum Mechanics\|author-link=W:Jan Faye\|chapter-url=https://plato.stanford.edu/entries/qm-copenhagen/}}</ref> Some interpretations of quantum mechanics find the reliance upon two different types of time evolution distasteful and regard the ambiguity of when to invoke one or the other as a deficiency of the way quantum theory was historically presented.<ref name="Bell-against-measurement">{{Cite journal\|last=Bell\|first=John\|author-link=W:John Stewart Bell \|date=1990\|title=Against 'measurement'\|journal=Physics World \|language=en\|volume=3\|issue=8\|pages=33–41\|doi=10.1088/2058-7058/3/8/26\|issn=2058-7058}}</ref> To bolster these interpretations, their proponents have worked to derive ways of regarding "measurement" as a secondary concept and deducing the seemingly stochastic effect of measurement processes as approximations to more fundamental deterministic dynamics. However, consensus has not been achieved among proponents of the correct way to implement this program, and in particular how to justify the use of the Born rule to calculate probabilities.<ref>{{cite encyclopedia\|first=Adrian \|last=Kent \|author-link=W:Adrian Kent \|title=One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation \|arxiv=0905.0624 \|encyclopedia=Many Worlds? \|year=2010 \|pages=307–354 \|publisher=Oxford University Press \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref><ref name="stanford1">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/qm-everett/\|title=Stanford Encyclopedia of Philosophy\|last=Barrett\|first=Jeffrey\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref> Other interpretations regard quantum states as statistical information about quantum systems, thus asserting that abrupt and discontinuous changes of quantum states are not problematic, simply reflecting updates of the available information.<ref name="Peierls">{{Cite journal\|last=Peierls\|first=Rudolf\|author-link=W:Rudolf Peierls \|date=1991\|title=In defence of "measurement"\|journal=Physics World \|language=en\|volume=4\|issue=1\|pages=19–21\|doi=10.1088/2058-7058/4/1/19\|issn=2058-7058}}</ref><ref name="stanford2">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/\|title=Stanford Encyclopedia of Philosophy\|last=Healey\|first=Richard\|publisher=Metaphysics Research Lab, Stanford University\|year=2016\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> Of this line of thought, Bell asked, "''Whose'' information? Information about ''what''?"<ref name="Bell-against-measurement" /> Answers to these questions vary among proponents of the informationally-oriented interpretations.<ref name="map" /><ref name="stanford2" />		A central concern within quantum foundations is the "quantum measurement problem," though how this problem is delimited, and whether it should be counted as one question or multiple separate issues, are contested topics.<ref name="Barad">{{Cite book\|title=Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning\|last=Barad\|first=Karen\|publisher=Duke University Press\|year=2007\|isbn=978-0-8223-3917-5\|language=en\|oclc=1055296186\|author-link=W:Karen Barad}}</ref><ref>{{cite encyclopedia\|first1=Jeffrey \|last1=Bub \|author-link1=Jeffrey Bub \|first2=Itamar \|last2=Pitowsky \|title=Two dogmas about quantum mechanics \|arxiv=0712.4258 \|encyclopedia=Many Worlds? \|year=2010 \|pages=433–459 \|publisher= \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref> Of primary interest is the seeming disparity between apparently distinct types of time evolution. Von Neumann declared that quantum mechanics contains "two fundamentally different types" of quantum-state change.<ref>{{cite book \|title=Mathematical Foundations of Quantum Mechanics. New Edition \|first=John \|last=von Neumann \|author-link=W:John von Neumann \|translator=Robert T. Beyer \|editor-first=Nicholas A. \|editor-last=Wheeler \|publisher=Princeton University Press \|date=2018 \|isbn=9-781-40088-992-1 \|oclc=1021172445}}</ref>{{rp\|§V.1}} First, there are those changes involving a measurement process, and second, there is unitary time evolution in the absence of measurement. The former is stochastic and discontinuous, writes von Neumann, and the latter deterministic and continuous. This dichotomy has set the tone for much later debate.<ref>{{Citation\|last=Wigner\|first=E. P.\|title=Philosophical Reflections and Syntheses\|chapter=Review of the Quantum-Mechanical Measurement Problem\|date=1995\|pages=225–244\|editor-last=Mehra\|editor-first=Jagdish\|publisher=Springer Berlin Heidelberg\|language=en\|doi=10.1007/978-3-642-78374-6_19\|isbn=978-3-540-63372-3\|author-link=W:Eugene Wigner\|editor-link=W:Jagdish Mehra}}</ref><ref name="stanford3">{{Cite book\|last=Faye\|first=Jan\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2019\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Copenhagen Interpretation of Quantum Mechanics\|author-link=W:Jan Faye\|chapter-url=https://plato.stanford.edu/entries/qm-copenhagen/}}</ref> Some interpretations of quantum mechanics find the reliance upon two different types of time evolution distasteful and regard the ambiguity of when to invoke one or the other as a deficiency of the way quantum theory was historically presented.<ref name="Bell-against-measurement">{{Cite journal\|last=Bell\|first=John\|author-link=W:John Stewart Bell \|date=1990\|title=Against 'measurement'\|journal=Physics World \|language=en\|volume=3\|issue=8\|pages=33–41\|doi=10.1088/2058-7058/3/8/26\|issn=2058-7058}}</ref> To bolster these interpretations, their proponents have worked to derive ways of regarding "measurement" as a secondary concept and deducing the seemingly stochastic effect of measurement processes as approximations to more fundamental deterministic dynamics. However, consensus has not been achieved among proponents of the correct way to implement this program, and in particular how to justify the use of the Born rule to calculate probabilities.<ref>{{cite encyclopedia\|first=Adrian \|last=Kent \|author-link=W:Adrian Kent \|title=One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation \|arxiv=0905.0624 \|encyclopedia=Many Worlds? \|year=2010 \|pages=307–354 \|publisher=Oxford University Press \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref><ref name="stanford1">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/qm-everett/\|title=Stanford Encyclopedia of Philosophy\|last=Barrett\|first=Jeffrey\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref> Other interpretations regard quantum states as statistical information about quantum systems, thus asserting that abrupt and discontinuous changes of quantum states are not problematic, simply reflecting updates of the available information.<ref name="Peierls">{{Cite journal\|last=Peierls\|first=Rudolf\|author-link=W:Rudolf Peierls \|date=1991\|title=In defence of "measurement"\|journal=Physics World \|language=en\|volume=4\|issue=1\|pages=19–21\|doi=10.1088/2058-7058/4/1/19\|issn=2058-7058}}</ref><ref name="stanford2">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/\|title=Stanford Encyclopedia of Philosophy\|last=Healey\|first=Richard\|publisher=Metaphysics Research Lab, Stanford University\|year=2016\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> Of this line of thought, Bell asked, "''Whose'' information? Information about ''what''?"<ref name="Bell-against-measurement" /> Answers to these questions vary among proponents of the informationally-oriented interpretations.<ref name="map" /><ref name="stanford2" />
	==Look at==		==Look at==
	{{Div col\|colwidth=20em}}		{{Div col\|colwidth=20em}}

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	\|Photodiodes, homodyne detectors, superconducting qubits readout		\|Photodiodes, homodyne detectors, superconducting qubits readout
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	== Axiomatic formalism ==		== Axiomatic formalism ==
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	==See also==		==See also==
	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}
	~~{{quantum mechanics topics}}~~
	<noinclude>		<noinclude>
	{{Documentation}}		{{Documentation}}

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	===Examples===		===Examples===
	[[Image:Bloch sphere representation of optimal POVM and states for unambiguous quantum state discrimination.svg\|thumb\|right\|~~[[Wikipedia:~~Bloch sphere~~\|Bloch sphere]]~~ representation of states (in blue) and optimal POVM (in red) for unambiguous quantum state discrimination<ref>{{Cite journal\|last1=Peres\|first1=Asher\|author-link=W:Asher Peres\|last2=Terno\|first2=Daniel R.\|date=1998\|title=Optimal distinction between non-orthogonal quantum states\|journal=Journal of Physics A: Mathematical and General\|language=en\|volume=31\|issue=34\|pages=7105–7111\|doi=10.1088/0305-4470/31/34/013\|issn=0305-4470 \|arxiv=quant-ph/9804031\|bibcode=1998JPhA...31.7105P\|s2cid=18961213}}</ref>		[[Image:Bloch sphere representation of optimal POVM and states for unambiguous quantum state discrimination.svg\|thumb\|right\|Bloch sphere representation of states (in blue) and optimal POVM (in red) for unambiguous quantum state discrimination<ref>{{Cite journal\|last1=Peres\|first1=Asher\|author-link=W:Asher Peres\|last2=Terno\|first2=Daniel R.\|date=1998\|title=Optimal distinction between non-orthogonal quantum states\|journal=Journal of Physics A: Mathematical and General\|language=en\|volume=31\|issue=34\|pages=7105–7111\|doi=10.1088/0305-4470/31/34/013\|issn=0305-4470 \|arxiv=quant-ph/9804031\|bibcode=1998JPhA...31.7105P\|s2cid=18961213}}</ref>
	on the states <math>\|\psi\rangle=\|0\rangle</math> and <math>\|\varphi\rangle=(\|0\rangle+\|1\rangle)/\sqrt2</math>. Note that on the Bloch sphere orthogonal states are antiparallel.]]		on the states <math>\|\psi\rangle=\|0\rangle</math> and <math>\|\varphi\rangle=(\|0\rangle+\|1\rangle)/\sqrt2</math>. Note that on the Bloch sphere orthogonal states are antiparallel.]]
	The prototypical example of a finite-dimensional Hilbert space is a qubit, a quantum system whose Hilbert space is 2-dimensional. A pure state for a qubit can be written as a linear combination of two orthogonal basis states <math>\|0 \rangle </math> and <math>\|1 \rangle </math> with complex coefficients:		The prototypical example of a finite-dimensional Hilbert space is a qubit, a quantum system whose Hilbert space is 2-dimensional. A pure state for a qubit can be written as a linear combination of two orthogonal basis states <math>\|0 \rangle </math> and <math>\|1 \rangle </math> with complex coefficients:
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	==Interpretations of quantum mechanics==		==Interpretations of quantum mechanics==
	[[Image:Niels Bohr Albert Einstein4 by Ehrenfest cr.jpg\|thumb\|~~[[Wikipedia:~~Niels Bohr~~\|Niels Bohr]]~~ and Albert Einstein, pictured here at Paul Ehrenfest's home in Leiden (December 1925), had a long-running collegial dispute about what quantum mechanics implied for the nature of reality.]]		[[Image:Niels Bohr Albert Einstein4 by Ehrenfest cr.jpg\|thumb\|Niels Bohr and Albert Einstein, pictured here at Paul Ehrenfest's home in Leiden (December 1925), had a long-running collegial dispute about what quantum mechanics implied for the nature of reality.]]
	Despite the consensus among scientists that quantum physics is in practice a successful theory, disagreements persist on a more philosophical level. Many debates in the area known as quantum foundations concern the role of measurement in quantum mechanics. Recurring questions include which interpretation of probability theory is best suited for the probabilities calculated from the Born rule; and whether the apparent randomness of quantum measurement outcomes is fundamental, or a consequence of a deeper deterministic process.<ref name="snapshot">{{Cite journal\| arxiv=1301.1069 \| title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics \| journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics \| volume=44 \| issue=3 \| pages=222–230 \| date=6 January 2013 \| last1=Schlosshauer \| first1=Maximilian \| last2=Kofler \| first2=Johannes \| last3=Zeilinger \| first3=Anton \| author-link3=Anton Zeilinger \| doi=10.1016/j.shpsb.2013.04.004 \| bibcode=2013SHPMP..44..222S \| s2cid=55537196 }}</ref><ref name="map">{{Cite book\|title=What is Quantum Information? \|last=Cabello \|first=Adán \|publisher=Cambridge University Press \|year=2017 \|isbn=978-1-107-14211-4 \|editor-last=Lombardi \|editor-first=Olimpia\|editor-link=W:Olimpia Lombardi \|pages=138–143 \|chapter=Interpretations of quantum theory: A map of madness \|arxiv=1509.04711 \|editor2-last=Fortin \|editor2-first=Sebastian \|editor3-last=Holik \|editor3-first=Federico \|editor4-last=López \|editor4-first=Cristian \|bibcode=2015arXiv150904711C \|doi=10.1017/9781316494233.009\|s2cid=118419619 }}</ref><ref>{{Cite journal\|last1=Schaffer\|first1=Kathryn\|last2=Barreto Lemos\|first2=Gabriela\|date=24 May 2019\|title=Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics\|journal=Foundations of Science\|volume=26 \|pages=7–26 \|language=en\|arxiv=1908.07936\|doi=10.1007/s10699-019-09608-5\|s2cid=182656563\|issn=1233-1821}}</ref> Worldviews that present answers to questions like these are known as "interpretations" of quantum mechanics; as the physicist N. David Mermin once quipped, "New interpretations appear every year. None ever disappear."<ref name="mermin2012">{{Cite journal\|last=Mermin\|first=N. David\|author-link=W:N. David Mermin \|date=1 July 2012\|title=Commentary: Quantum mechanics: Fixing the shifty split\|journal=Physics Today\|volume=65\|issue=7\|pages=8–10\|doi=10.1063/PT.3.1618\|issn=0031-9228\|bibcode=2012PhT....65g...8M\|doi-access=free}}</ref>		Despite the consensus among scientists that quantum physics is in practice a successful theory, disagreements persist on a more philosophical level. Many debates in the area known as quantum foundations concern the role of measurement in quantum mechanics. Recurring questions include which interpretation of probability theory is best suited for the probabilities calculated from the Born rule; and whether the apparent randomness of quantum measurement outcomes is fundamental, or a consequence of a deeper deterministic process.<ref name="snapshot">{{Cite journal\| arxiv=1301.1069 \| title=A Snapshot of Foundational Attitudes Toward Quantum Mechanics \| journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics \| volume=44 \| issue=3 \| pages=222–230 \| date=6 January 2013 \| last1=Schlosshauer \| first1=Maximilian \| last2=Kofler \| first2=Johannes \| last3=Zeilinger \| first3=Anton \| author-link3=Anton Zeilinger \| doi=10.1016/j.shpsb.2013.04.004 \| bibcode=2013SHPMP..44..222S \| s2cid=55537196 }}</ref><ref name="map">{{Cite book\|title=What is Quantum Information? \|last=Cabello \|first=Adán \|publisher=Cambridge University Press \|year=2017 \|isbn=978-1-107-14211-4 \|editor-last=Lombardi \|editor-first=Olimpia\|editor-link=W:Olimpia Lombardi \|pages=138–143 \|chapter=Interpretations of quantum theory: A map of madness \|arxiv=1509.04711 \|editor2-last=Fortin \|editor2-first=Sebastian \|editor3-last=Holik \|editor3-first=Federico \|editor4-last=López \|editor4-first=Cristian \|bibcode=2015arXiv150904711C \|doi=10.1017/9781316494233.009\|s2cid=118419619 }}</ref><ref>{{Cite journal\|last1=Schaffer\|first1=Kathryn\|last2=Barreto Lemos\|first2=Gabriela\|date=24 May 2019\|title=Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics\|journal=Foundations of Science\|volume=26 \|pages=7–26 \|language=en\|arxiv=1908.07936\|doi=10.1007/s10699-019-09608-5\|s2cid=182656563\|issn=1233-1821}}</ref> Worldviews that present answers to questions like these are known as "interpretations" of quantum mechanics; as the physicist N. David Mermin once quipped, "New interpretations appear every year. None ever disappear."<ref name="mermin2012">{{Cite journal\|last=Mermin\|first=N. David\|author-link=W:N. David Mermin \|date=1 July 2012\|title=Commentary: Quantum mechanics: Fixing the shifty split\|journal=Physics Today\|volume=65\|issue=7\|pages=8–10\|doi=10.1063/PT.3.1618\|issn=0031-9228\|bibcode=2012PhT....65g...8M\|doi-access=free}}</ref>

	A central concern within quantum foundations is the "quantum measurement problem," though how this problem is delimited, and whether it should be counted as one question or multiple separate issues, are contested topics.<ref name="Barad">{{Cite book\|title=Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning\|last=Barad\|first=Karen\|publisher=Duke University Press\|year=2007\|isbn=978-0-8223-3917-5\|language=en\|oclc=1055296186\|author-link=W:Karen Barad}}</ref><ref>{{cite encyclopedia\|first1=Jeffrey \|last1=Bub \|author-link1=Jeffrey Bub \|first2=Itamar \|last2=Pitowsky \|title=Two dogmas about quantum mechanics \|arxiv=0712.4258 \|encyclopedia=Many Worlds? \|year=2010 \|pages=433–459 \|publisher=~~[[Wikipedia:Oxford University Press\|]]~~ \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref> Of primary interest is the seeming disparity between apparently distinct types of time evolution. Von Neumann declared that quantum mechanics contains "two fundamentally different types" of quantum-state change.<ref>{{cite book \|title=Mathematical Foundations of Quantum Mechanics. New Edition \|first=John \|last=von Neumann \|author-link=W:John von Neumann \|translator=Robert T. Beyer \|editor-first=Nicholas A. \|editor-last=Wheeler \|publisher=Princeton University Press \|date=2018 \|isbn=9-781-40088-992-1 \|oclc=1021172445}}</ref>{{rp\|§V.1}} First, there are those changes involving a measurement process, and second, there is unitary time evolution in the absence of measurement. The former is stochastic and discontinuous, writes von Neumann, and the latter deterministic and continuous. This dichotomy has set the tone for much later debate.<ref>{{Citation\|last=Wigner\|first=E. P.\|title=Philosophical Reflections and Syntheses\|chapter=Review of the Quantum-Mechanical Measurement Problem\|date=1995\|pages=225–244\|editor-last=Mehra\|editor-first=Jagdish\|publisher=Springer Berlin Heidelberg\|language=en\|doi=10.1007/978-3-642-78374-6_19\|isbn=978-3-540-63372-3\|author-link=W:Eugene Wigner\|editor-link=W:Jagdish Mehra}}</ref><ref name="stanford3">{{Cite book\|last=Faye\|first=Jan\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2019\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Copenhagen Interpretation of Quantum Mechanics\|author-link=W:Jan Faye\|chapter-url=https://plato.stanford.edu/entries/qm-copenhagen/}}</ref> Some interpretations of quantum mechanics find the reliance upon two different types of time evolution distasteful and regard the ambiguity of when to invoke one or the other as a deficiency of the way quantum theory was historically presented.<ref name="Bell-against-measurement">{{Cite journal\|last=Bell\|first=John\|author-link=W:John Stewart Bell \|date=1990\|title=Against 'measurement'\|journal=Physics World \|language=en\|volume=3\|issue=8\|pages=33–41\|doi=10.1088/2058-7058/3/8/26\|issn=2058-7058}}</ref> To bolster these interpretations, their proponents have worked to derive ways of regarding "measurement" as a secondary concept and deducing the seemingly stochastic effect of measurement processes as approximations to more fundamental deterministic dynamics. However, consensus has not been achieved among proponents of the correct way to implement this program, and in particular how to justify the use of the Born rule to calculate probabilities.<ref>{{cite encyclopedia\|first=Adrian \|last=Kent \|author-link=W:Adrian Kent \|title=One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation \|arxiv=0905.0624 \|encyclopedia=Many Worlds? \|year=2010 \|pages=307–354 \|publisher=Oxford University Press \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref><ref name="stanford1">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/qm-everett/\|title=Stanford Encyclopedia of Philosophy\|last=Barrett\|first=Jeffrey\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref> Other interpretations regard quantum states as statistical information about quantum systems, thus asserting that abrupt and discontinuous changes of quantum states are not problematic, simply reflecting updates of the available information.<ref name="Peierls">{{Cite journal\|last=Peierls\|first=Rudolf\|author-link=W:Rudolf Peierls \|date=1991\|title=In defence of "measurement"\|journal=Physics World \|language=en\|volume=4\|issue=1\|pages=19–21\|doi=10.1088/2058-7058/4/1/19\|issn=2058-7058}}</ref><ref name="stanford2">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/\|title=Stanford Encyclopedia of Philosophy\|last=Healey\|first=Richard\|publisher=Metaphysics Research Lab, Stanford University\|year=2016\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> Of this line of thought, Bell asked, "''Whose'' information? Information about ''what''?"<ref name="Bell-against-measurement" /> Answers to these questions vary among proponents of the informationally-oriented interpretations.<ref name="map" /><ref name="stanford2" />		A central concern within quantum foundations is the "quantum measurement problem," though how this problem is delimited, and whether it should be counted as one question or multiple separate issues, are contested topics.<ref name="Barad">{{Cite book\|title=Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning\|last=Barad\|first=Karen\|publisher=Duke University Press\|year=2007\|isbn=978-0-8223-3917-5\|language=en\|oclc=1055296186\|author-link=W:Karen Barad}}</ref><ref>{{cite encyclopedia\|first1=Jeffrey \|last1=Bub \|author-link1=Jeffrey Bub \|first2=Itamar \|last2=Pitowsky \|title=Two dogmas about quantum mechanics \|arxiv=0712.4258 \|encyclopedia=Many Worlds? \|year=2010 \|pages=433–459 \|publisher= \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref> Of primary interest is the seeming disparity between apparently distinct types of time evolution. Von Neumann declared that quantum mechanics contains "two fundamentally different types" of quantum-state change.<ref>{{cite book \|title=Mathematical Foundations of Quantum Mechanics. New Edition \|first=John \|last=von Neumann \|author-link=W:John von Neumann \|translator=Robert T. Beyer \|editor-first=Nicholas A. \|editor-last=Wheeler \|publisher=Princeton University Press \|date=2018 \|isbn=9-781-40088-992-1 \|oclc=1021172445}}</ref>{{rp\|§V.1}} First, there are those changes involving a measurement process, and second, there is unitary time evolution in the absence of measurement. The former is stochastic and discontinuous, writes von Neumann, and the latter deterministic and continuous. This dichotomy has set the tone for much later debate.<ref>{{Citation\|last=Wigner\|first=E. P.\|title=Philosophical Reflections and Syntheses\|chapter=Review of the Quantum-Mechanical Measurement Problem\|date=1995\|pages=225–244\|editor-last=Mehra\|editor-first=Jagdish\|publisher=Springer Berlin Heidelberg\|language=en\|doi=10.1007/978-3-642-78374-6_19\|isbn=978-3-540-63372-3\|author-link=W:Eugene Wigner\|editor-link=W:Jagdish Mehra}}</ref><ref name="stanford3">{{Cite book\|last=Faye\|first=Jan\|title=Stanford Encyclopedia of Philosophy\|publisher=Metaphysics Research Lab, Stanford University\|year=2019\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Copenhagen Interpretation of Quantum Mechanics\|author-link=W:Jan Faye\|chapter-url=https://plato.stanford.edu/entries/qm-copenhagen/}}</ref> Some interpretations of quantum mechanics find the reliance upon two different types of time evolution distasteful and regard the ambiguity of when to invoke one or the other as a deficiency of the way quantum theory was historically presented.<ref name="Bell-against-measurement">{{Cite journal\|last=Bell\|first=John\|author-link=W:John Stewart Bell \|date=1990\|title=Against 'measurement'\|journal=Physics World \|language=en\|volume=3\|issue=8\|pages=33–41\|doi=10.1088/2058-7058/3/8/26\|issn=2058-7058}}</ref> To bolster these interpretations, their proponents have worked to derive ways of regarding "measurement" as a secondary concept and deducing the seemingly stochastic effect of measurement processes as approximations to more fundamental deterministic dynamics. However, consensus has not been achieved among proponents of the correct way to implement this program, and in particular how to justify the use of the Born rule to calculate probabilities.<ref>{{cite encyclopedia\|first=Adrian \|last=Kent \|author-link=W:Adrian Kent \|title=One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation \|arxiv=0905.0624 \|encyclopedia=Many Worlds? \|year=2010 \|pages=307–354 \|publisher=Oxford University Press \|isbn=978-0-19-956056-1 \|oclc=696602007}}</ref><ref name="stanford1">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/qm-everett/\|title=Stanford Encyclopedia of Philosophy\|last=Barrett\|first=Jeffrey\|publisher=Metaphysics Research Lab, Stanford University\|year=2018\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Everett's Relative-State Formulation of Quantum Mechanics}}</ref> Other interpretations regard quantum states as statistical information about quantum systems, thus asserting that abrupt and discontinuous changes of quantum states are not problematic, simply reflecting updates of the available information.<ref name="Peierls">{{Cite journal\|last=Peierls\|first=Rudolf\|author-link=W:Rudolf Peierls \|date=1991\|title=In defence of "measurement"\|journal=Physics World \|language=en\|volume=4\|issue=1\|pages=19–21\|doi=10.1088/2058-7058/4/1/19\|issn=2058-7058}}</ref><ref name="stanford2">{{Cite book\|chapter-url=https://plato.stanford.edu/entries/quantum-bayesian/\|title=Stanford Encyclopedia of Philosophy\|last=Healey\|first=Richard\|publisher=Metaphysics Research Lab, Stanford University\|year=2016\|editor-last=Zalta\|editor-first=Edward N.\|chapter=Quantum-Bayesian and Pragmatist Views of Quantum Theory}}</ref> Of this line of thought, Bell asked, "''Whose'' information? Information about ''what''?"<ref name="Bell-against-measurement" /> Answers to these questions vary among proponents of the informationally-oriented interpretations.<ref name="map" /><ref name="stanford2" />
	==Look at==		==Look at==
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