Physics:Quantum Measurement collapse - Revision history

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	'''Measurement collapse''' ~~is a Book I topic~~ in ~~the Quantum Collection. In~~ quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome. Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation. In quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome.~~{{cite book }}~~ Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation.		'''Measurement collapse''' in quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome. Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation. In quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome. Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation. Here the coefficients c_i are probability amplitudes, given by
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	Here the coefficients <math>c_i</math> are [[probability ~~amplitude]]s~~, given by		Here the coefficients <math>c_i</math> are probability amplitudes, given by

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	Wave function collapse connects the probabilistic quantum description with definite measurement outcomes such as position, momentum, or spin.<ref name="Hall">{{Cite book \|last=Hall \|first=Brian C. \|title=Quantum Theory for Mathematicians \|publisher=Springer \|year=2013 \|isbn=978-1-4614-7115-8 \|page=68}}</ref> For an individual event, only one outcome is observed, even though the pre-measurement state may be a superposition of many possibilities.		Wave function collapse connects the probabilistic quantum description with definite measurement outcomes such as position, momentum, or spin.<ref name="Hall">{{Cite book \|last=Hall \|first=Brian C. \|title=Quantum Theory for Mathematicians \|publisher=Springer \|year=2013 \|isbn=978-1-4614-7115-8 \|page=68}}</ref> For an individual event, only one outcome is observed, even though the pre-measurement state may be a superposition of many possibilities.

	Examples include the [[double-slit experiment]], where each particle is detected at a definite location although many events build up an interference pattern, and the Stern–Gerlach experiment, where each atom is observed in one of the discrete spin channels.<ref name="Bach2013">{{cite journal \| last1=Bach \| first1=Roger \| last2=Pope \| first2=Damian \| last3=Liou \| first3=Sy-Hwang \| last4=Batelaan \| first4=Herman \| title=Controlled double-slit electron diffraction \| journal=New Journal of Physics \| volume=15 \| issue=3 \| year=2013 \| article-number=033018 \| doi=10.1088/1367-2630/15/3/033018 }}</ref>		Examples include the double-slit experiment, where each particle is detected at a definite location although many events build up an interference pattern, and the Stern–Gerlach experiment, where each atom is observed in one of the discrete spin channels.<ref name="Bach2013">{{cite journal \| last1=Bach \| first1=Roger \| last2=Pope \| first2=Damian \| last3=Liou \| first3=Sy-Hwang \| last4=Batelaan \| first4=Herman \| title=Controlled double-slit electron diffraction \| journal=New Journal of Physics \| volume=15 \| issue=3 \| year=2013 \| article-number=033018 \| doi=10.1088/1367-2630/15/3/033018 }}</ref>

	== The measurement problem ==		== The measurement problem ==

	The Schrödinger equation predicts a continuous evolution containing all possible outcomes in superposition, but an actual measurement yields only one definite result. This tension is known as the [[measurement problem]] of quantum mechanics.<ref name="Zurek2003">{{Cite journal \|last=Zurek \|first=Wojciech Hubert \|title=Decoherence, einselection, and the quantum origins of the classical \|journal=Reviews of Modern Physics \|volume=75 \|issue=3 \|pages=715–775 \|year=2003 \|doi=10.1103/RevModPhys.75.715}}</ref>		The Schrödinger equation predicts a continuous evolution containing all possible outcomes in superposition, but an actual measurement yields only one definite result. This tension is known as the measurement problem of quantum mechanics.<ref name="Zurek2003">{{Cite journal \|last=Zurek \|first=Wojciech Hubert \|title=Decoherence, einselection, and the quantum origins of the classical \|journal=Reviews of Modern Physics \|volume=75 \|issue=3 \|pages=715–775 \|year=2003 \|doi=10.1103/RevModPhys.75.715}}</ref>

	To make predictions, orthodox quantum mechanics combines unitary evolution with the Born rule and the collapse postulate. Although this framework is extremely successful experimentally, the physical status of collapse remains debated.<ref name="Susskind">{{Cite book \|last1=Susskind \|first1=Leonard \|last2=Friedman \|first2=Art \|title=Quantum Mechanics: The Theoretical Minimum \|publisher=Basic Books \|year=2014 \|isbn=978-0-465-06290-4}}</ref>		To make predictions, orthodox quantum mechanics combines unitary evolution with the Born rule and the collapse postulate. Although this framework is extremely successful experimentally, the physical status of collapse remains debated.<ref name="Susskind">{{Cite book \|last1=Susskind \|first1=Leonard \|last2=Friedman \|first2=Art \|title=Quantum Mechanics: The Theoretical Minimum \|publisher=Basic Books \|year=2014 \|isbn=978-0-465-06290-4}}</ref>
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	* In the Copenhagen interpretation, collapse is taken as a fundamental part of measurement theory.		* In the Copenhagen interpretation, collapse is taken as a fundamental part of measurement theory.
	* In the [[many-worlds interpretation]], collapse does not occur; instead, all outcomes persist in different branches.		* In the many-worlds interpretation, collapse does not occur; instead, all outcomes persist in different branches.
	* In [[objective-collapse theory]], collapse is treated as a real physical process.		* In objective-collapse theory, collapse is treated as a real physical process.
	* In approaches based on [[quantum decoherence]], interaction with the environment explains why classical alternatives appear, though decoherence by itself does not select a single outcome.<ref name="Schlosshauer">{{cite journal \|last=Schlosshauer \|first=Maximilian \|title=Decoherence, the measurement problem, and interpretations of quantum mechanics \|journal=Reviews of Modern Physics \|volume=76 \|issue=4 \|pages=1267–1305 \|year=2005 \|doi=10.1103/RevModPhys.76.1267}}</ref>		* In approaches based on quantum decoherence, interaction with the environment explains why classical alternatives appear, though decoherence by itself does not select a single outcome.<ref name="Schlosshauer">{{cite journal \|last=Schlosshauer \|first=Maximilian \|title=Decoherence, the measurement problem, and interpretations of quantum mechanics \|journal=Reviews of Modern Physics \|volume=76 \|issue=4 \|pages=1267–1305 \|year=2005 \|doi=10.1103/RevModPhys.76.1267}}</ref>

	== History ==		== History ==

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	In [[quantum mechanics]], ~~'''~~wave function collapse~~'''~~, also called ~~'''~~reduction of the state vector~~'''~~, is the process by which a [[wave function~~]]—initially~~ in a [[quantum superposition]] of several ~~[[eigenstate]]s—reduces~~ to a single eigenstate when a measurement yields a definite outcome.~~<ref name="Grundlagen">~~{{cite book		'''Measurement collapse''' is a Book I topic in the Quantum Collection. In quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome. Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation. In quantum mechanics, wave function collapse, also called reduction of the state vector, is the process by which a wave function—initially in a quantum superposition of several eigenstates—reduces to a single eigenstate when a measurement yields a definite outcome.{{cite book }} Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the Schrödinger equation.
	~~\|author=J. von Neumann~~
	~~\|year=1955~~
	~~\|title=Mathematical Foundations of Quantum Mechanics~~
	~~\|publisher=Princeton University Press~~
	}}~~</ref>~~ Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the [[Schrödinger equation]].~~<ref name="Grundlagen" />~~
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	Wave function collapse connects the probabilistic quantum description with definite measurement outcomes such as position, momentum, or spin.<ref name="Hall">{{Cite book \|last=Hall \|first=Brian C. \|title=Quantum Theory for Mathematicians \|publisher=Springer \|year=2013 \|isbn=978-1-4614-7115-8 \|page=68}}</ref> For an individual event, only one outcome is observed, even though the pre-measurement state may be a superposition of many possibilities.		Wave function collapse connects the probabilistic quantum description with definite measurement outcomes such as position, momentum, or spin.<ref name="Hall">{{Cite book \|last=Hall \|first=Brian C. \|title=Quantum Theory for Mathematicians \|publisher=Springer \|year=2013 \|isbn=978-1-4614-7115-8 \|page=68}}</ref> For an individual event, only one outcome is observed, even though the pre-measurement state may be a superposition of many possibilities.

	Examples include the [[double-slit experiment]], where each particle is detected at a definite location although many events build up an interference pattern, and the [[Stern–Gerlach experiment]], where each atom is observed in one of the discrete spin channels.<ref name="Bach2013">{{cite journal \| last1=Bach \| first1=Roger \| last2=Pope \| first2=Damian \| last3=Liou \| first3=Sy-Hwang \| last4=Batelaan \| first4=Herman \| title=Controlled double-slit electron diffraction \| journal=New Journal of Physics \| volume=15 \| issue=3 \| year=2013 \| article-number=033018 \| doi=10.1088/1367-2630/15/3/033018 }}</ref>		Examples include the [[double-slit experiment]], where each particle is detected at a definite location although many events build up an interference pattern, and the Stern–Gerlach experiment, where each atom is observed in one of the discrete spin channels.<ref name="Bach2013">{{cite journal \| last1=Bach \| first1=Roger \| last2=Pope \| first2=Damian \| last3=Liou \| first3=Sy-Hwang \| last4=Batelaan \| first4=Herman \| title=Controlled double-slit electron diffraction \| journal=New Journal of Physics \| volume=15 \| issue=3 \| year=2013 \| article-number=033018 \| doi=10.1088/1367-2630/15/3/033018 }}</ref>

	== The measurement problem ==		== The measurement problem ==
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	The Schrödinger equation predicts a continuous evolution containing all possible outcomes in superposition, but an actual measurement yields only one definite result. This tension is known as the [[measurement problem]] of quantum mechanics.<ref name="Zurek2003">{{Cite journal \|last=Zurek \|first=Wojciech Hubert \|title=Decoherence, einselection, and the quantum origins of the classical \|journal=Reviews of Modern Physics \|volume=75 \|issue=3 \|pages=715–775 \|year=2003 \|doi=10.1103/RevModPhys.75.715}}</ref>		The Schrödinger equation predicts a continuous evolution containing all possible outcomes in superposition, but an actual measurement yields only one definite result. This tension is known as the [[measurement problem]] of quantum mechanics.<ref name="Zurek2003">{{Cite journal \|last=Zurek \|first=Wojciech Hubert \|title=Decoherence, einselection, and the quantum origins of the classical \|journal=Reviews of Modern Physics \|volume=75 \|issue=3 \|pages=715–775 \|year=2003 \|doi=10.1103/RevModPhys.75.715}}</ref>

	To make predictions, orthodox quantum mechanics combines unitary evolution with the [[Born rule]] and the collapse postulate. Although this framework is extremely successful experimentally, the physical status of collapse remains debated.<ref name="Susskind">{{Cite book \|last1=Susskind \|first1=Leonard \|last2=Friedman \|first2=Art \|title=Quantum Mechanics: The Theoretical Minimum \|publisher=Basic Books \|year=2014 \|isbn=978-0-465-06290-4}}</ref>		To make predictions, orthodox quantum mechanics combines unitary evolution with the Born rule and the collapse postulate. Although this framework is extremely successful experimentally, the physical status of collapse remains debated.<ref name="Susskind">{{Cite book \|last1=Susskind \|first1=Leonard \|last2=Friedman \|first2=Art \|title=Quantum Mechanics: The Theoretical Minimum \|publisher=Basic Books \|year=2014 \|isbn=978-0-465-06290-4}}</ref>

	== Interpretations ==		== Interpretations ==
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	Different interpretations of quantum mechanics treat collapse in different ways.		Different interpretations of quantum mechanics treat collapse in different ways.

	* In the [[Copenhagen interpretation]], collapse is taken as a fundamental part of measurement theory.		* In the Copenhagen interpretation, collapse is taken as a fundamental part of measurement theory.
	* In the [[many-worlds interpretation]], collapse does not occur; instead, all outcomes persist in different branches.		* In the [[many-worlds interpretation]], collapse does not occur; instead, all outcomes persist in different branches.
	* In [[objective-collapse theory]], collapse is treated as a real physical process.		* In [[objective-collapse theory]], collapse is treated as a real physical process.
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	== History ==		== History ==

	The idea of wave function reduction appeared early in the development of quantum mechanics. [[Werner Heisenberg]] used it in 1927 in discussing quantum measurement, and [[John von Neumann]] gave it a systematic mathematical formulation in 1932.<ref name="Kiefer">{{Cite book \|last=Kiefer \|first=Claus \|chapter=On the Interpretation of Quantum Theory — from Copenhagen to the Present Day \|title=Time, Quantum and Information \|publisher=Springer \|year=2003 \|pages=291–299 \|doi=10.1007/978-3-662-10557-3_19}}</ref>		The idea of wave function reduction appeared early in the development of quantum mechanics. Werner Heisenberg used it in 1927 in discussing quantum measurement, and John von Neumann gave it a systematic mathematical formulation in 1932.<ref name="Kiefer">{{Cite book \|last=Kiefer \|first=Claus \|chapter=On the Interpretation of Quantum Theory — from Copenhagen to the Present Day \|title=Time, Quantum and Information \|publisher=Springer \|year=2003 \|pages=291–299 \|doi=10.1007/978-3-662-10557-3_19}}</ref>

	=See also=		=See also=

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			{{Short description\|Quantum Collection topic on Quantum Measurement collapse}}

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	In [[quantum mechanics]], '''wave function collapse''', also called '''reduction of the state vector''', is the process by which a [[wave function]]—initially in a [[quantum superposition]] of several [[eigenstate]]s—reduces to a single eigenstate when a measurement yields a definite outcome.<ref name="Grundlagen">{{cite book		In [[quantum mechanics]], '''wave function collapse''', also called '''reduction of the state vector''', is the process by which a [[wave function]]—initially in a [[quantum superposition]] of several [[eigenstate]]s—reduces to a single eigenstate when a measurement yields a definite outcome.<ref name="Grundlagen">{{cite book
	\|author=J. von Neumann		\|author=J. von Neumann
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	\|publisher=Princeton University Press		\|publisher=Princeton University Press
	}}</ref> Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the [[Schrödinger equation]].<ref name="Grundlagen" />		}}</ref> Collapse is one of the two ways quantum systems are commonly described as evolving in time; the other is the continuous deterministic evolution governed by the [[Schrödinger equation]].<ref name="Grundlagen" />
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			[[File:Wave-Collapse.png\|thumb\|280px\|Quantum Measurement collapse.]]
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	[[File:Wave-Collapse.png\|thumb\|400px\|right\|Visualization of quantum measurement regimes: POVM allows non-orthogonal outcomes, weak measurement minimally perturbs the state, and projective measurement collapses the state onto an eigenbasis.]]		</div>

	== Mathematical description ==		== Mathematical description ==

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