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{{Short description|Open problem concerning definite outcomes in quantum mechanics}}

{{Quantum book backlink|Conceptual and interpretations}}

'''Quantum measurement problem''' is the problem of explaining how definite measurement outcomes arise from the mathematical structure of [[Physics:Quantum mechanics|quantum mechanics]]. In ordinary quantum theory, the state of a system may evolve as a linear superposition of alternatives, while an actual experiment records one definite result. The problem is to explain how the formal quantum description is connected with the classical facts registered by measuring devices.

In the usual formulation, the wave function evolves deterministically according to the Schrödinger equation. A measurement, however, appears to produce a single result. This creates a tension between smooth quantum evolution and the apparently discontinuous selection of an outcome. The question is sometimes expressed as the question of whether, when, or how wave-function collapse occurs.

Steven Weinberg summarized the issue by asking why, if observers and measuring devices are also physical systems described by quantum theory, the theory predicts only probabilities for measurement outcomes rather than precise results.<ref name=Weinberg>{{cite book |title=The Oxford History of the Twentieth Century |first=Steven |last=Weinberg |chapter=The Great Reduction: Physics in the Twentieth Century |page=[https://archive.org/details/oxfordhistoryoft00howa/page/26 26] |chapter-url=https://books.google.com/books?id=WGvbAApi2roC&pg=PA22 |isbn=0-19-820428-0 |year=1998 |publisher=Oxford University Press |editor1=Michael Howard |name-list-style=amp |editor2=William Roger Louis |url-access=registration |url=https://archive.org/details/oxfordhistoryoft00howa/page/26 }}</ref><ref name=Weinberg2>{{cite journal |last=Weinberg |first=Steven |title=Einstein's Mistakes |journal=Physics Today |date=November 2005 |volume=58 |issue=11 |pages=31–35 |bibcode=2005PhT....58k..31W |doi=10.1063/1.2155755 |s2cid=120594692 |doi-access=free }}</ref> More broadly, the measurement problem asks how quantum reality gives rise to the classical world of definite experimental records.<ref name=Zurek>{{cite journal |last1=Zurek |first1=Wojciech Hubert |title=Decoherence, einselection, and the quantum origins of the classical |journal=Reviews of Modern Physics |date=22 May 2003 |volume=75 |issue=3 |pages=715–775 |arxiv=quant-ph/0105127 |bibcode=2003RvMP...75..715Z |doi=10.1103/RevModPhys.75.715 |s2cid=14759237 }}</ref>
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<div style="font-size:90%;">The measurement problem asks how a quantum superposition becomes a definite observed outcome.</div>
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== Basic issue ==

The measurement problem arises from the coexistence of two rules in standard quantum mechanics. First, the wave function evolves continuously and deterministically when no measurement is being made. Second, a measurement seems to return a definite result, with probabilities given by the quantum state.

If a quantum system is in a superposition of possible states, the Schrödinger equation alone does not obviously explain why only one result is observed. A detector does not record all possible outcomes at once. It records one pointer position, one click, one track, or one value. The measurement problem is the problem of explaining this transition from a superposition of possibilities to a definite classical outcome.

The issue is not simply that quantum mechanics is probabilistic. The deeper issue is why the mathematical description contains superpositions, while ordinary observations produce definite records.

== Schrödinger's cat ==

A common illustration is '''Schrödinger's cat'''. In the thought experiment, a cat is placed in a situation where its fate depends on a quantum event, such as the decay of an atom. If the atom decays, a mechanism kills the cat; if it does not decay, the cat remains alive.

Before observation, the atom may be described as a superposition of decayed and undecayed states. If the cat and the apparatus are treated as quantum systems, the total state appears to become a superposition involving both an alive cat and a dead cat. Yet an actual observation finds one definite outcome: the cat is alive or dead.

The point of the thought experiment is not the practical treatment of cats, but the conceptual problem of applying quantum superposition to large systems. It asks why macroscopic experience appears definite if the underlying quantum description allows superposed alternatives.

== Interpretations ==

Different interpretations of quantum mechanics give different answers to the measurement problem. They disagree about the meaning of the wave function, the status of collapse, the role of observers, and whether the theory describes reality directly or only the information available about experiments.

=== Copenhagen-type views ===

Views grouped under the name '''Copenhagen interpretation''' are among the oldest approaches to quantum mechanics. They often emphasize the special role of measurement, classical descriptions of apparatus, and the practical connection between the theory and experimental outcomes. Surveys of physicists have found that Copenhagen-type attitudes remain influential, although there is no single universally agreed Copenhagen doctrine.<ref>{{cite journal |last1=Schlosshauer |first1=Maximilian |last2=Kofler |first2=Johannes |last3=Zeilinger |first3=Anton |title=A snapshot of foundational attitudes toward quantum mechanics |journal=Studies in History and Philosophy of Science Part B |date=August 2013 |volume=44 |issue=3 |pages=222–230 |arxiv=1301.1069 |bibcode=2013SHPMP..44..222S |doi=10.1016/j.shpsb.2013.04.004 |s2cid=55537196 }}</ref><ref>{{Cite journal |url=https://www.nature.com/news/experts-still-split-about-what-quantum-theory-means-1.12198 |doi=10.1038/nature.2013.12198 |title=Experts still split about what quantum theory means |journal=Nature |year=2013 |last1=Ball |first1=Philip |s2cid=124012568}}</ref>

N. David Mermin used the phrase "Shut up and calculate!" to describe a pragmatic attitude toward quantum foundations, though he later treated the phrase as too crude to capture the real issues.<ref>{{cite journal |journal=Physics Today |volume=42 |number=4 |year=1989 |page=9 |doi=10.1063/1.2810963 |first=N. David |last=Mermin |title=What's Wrong with this Pillow? |bibcode=1989PhT....42d...9D }}</ref><ref>{{cite journal |doi=10.1063/1.1768652 |title=Could Feynman have said this? |journal=Physics Today |volume=57 |issue=5 |pages=10–11 |year=2004 |last1=Mermin |first1=N. David |bibcode=2004PhT....57e..10M |doi-access=free }}</ref>

Historical studies have also argued that the so-called Copenhagen interpretation is not a single sharply defined doctrine, but a later reconstruction of diverse views associated with Niels Bohr, Werner Heisenberg, and others.<ref>{{Cite journal |last=Howard |first=Don |date=December 2004 |title=Who Invented the "Copenhagen Interpretation"? A Study in Mythology |url=https://www.journals.uchicago.edu/doi/10.1086/425941 |journal=Philosophy of Science |volume=71 |issue=5 |pages=669–682 |doi=10.1086/425941 |s2cid=9454552 }}</ref><ref>{{Cite journal |last=Camilleri |first=Kristian |date=May 2009 |title=Constructing the Myth of the Copenhagen Interpretation |url=http://www.mitpressjournals.org/doi/10.1162/posc.2009.17.1.26 |journal=Perspectives on Science |volume=17 |issue=1 |pages=26–57 |doi=10.1162/posc.2009.17.1.26 |s2cid=57559199 }}</ref>

Some Copenhagen-type and information-based approaches treat collapse not as a physical jump in the world, but as an update of information about a system after a measurement result is obtained.<ref>{{Cite journal |last=Englert |first=Berthold-Georg |date=2013-11-22 |title=On quantum theory |journal=The European Physical Journal D |volume=67 |issue=11 |pages=238 |arxiv=1308.5290 |doi=10.1140/epjd/e2013-40486-5 |bibcode=2013EPJD...67..238E |s2cid=119293245 }}</ref><ref name="Peierls">{{Cite journal |last=Peierls |first=Rudolf |date=1991 |title=In defence of "measurement" |journal=Physics World |volume=4 |issue=1 |pages=19–21 |doi=10.1088/2058-7058/4/1/19 }}</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>

=== Many-worlds interpretation ===

The '''many-worlds interpretation''' denies that wave-function collapse is a fundamental physical process. Instead, the universal wave function always evolves according to quantum dynamics. Measurement is treated as an ordinary quantum interaction that entangles the measured system, apparatus, environment, and observer.

On this view, all branches of the superposition persist, but observers within each branch experience a definite result. The measurement problem is transformed into the problem of explaining why observers experience probabilities and why the Born rule should be used to assign them. Everett's original relative-state idea was later developed by Bryce DeWitt and others, but the interpretation of probability in many-worlds remains debated.<ref>{{cite encyclopedia |first=Adrian |last=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=9780199560561 |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>

=== De Broglie–Bohm theory ===

The '''de Broglie–Bohm theory''' gives a different solution. It supplements the wave function with definite particle positions. The wave function guides the motion of particles, while the particles always have definite locations.

In this approach, measurement outcomes are definite because the configuration of particles is definite. Apparent collapse occurs when different parts of the wave function become effectively separated in configuration space. There is no fundamental collapse, but there is an effective collapse for observers inside a measurement situation.<ref>{{cite book |chapter-url=https://plato.stanford.edu/entries/qm-bohm/ |first=Goldstein |last=Sheldon |chapter=Bohmian Mechanics |title=Stanford Encyclopedia of Philosophy |year=2017 |publisher=Metaphysics Research Lab, Stanford University |editor-last=Zalta |editor-first=Edward N. }}</ref>

=== Objective-collapse models ===

'''Objective-collapse models''' modify the ordinary Schrödinger equation. They propose that collapse is a real physical process, not merely an update of information. These modifications are usually stochastic and nonlinear. For microscopic systems, the predictions remain extremely close to standard quantum mechanics, while for macroscopic systems collapse becomes significant.

Such models are important because they can make experimentally testable predictions that differ from standard quantum mechanics.<ref>{{cite journal |author=Angelo Bassi |author2=Kinjalk Lochan |author3=Seema Satin |author4=Tejinder P. Singh |author5=Hendrik Ulbricht |title=Models of wave-function collapse, underlying theories, and experimental tests |journal=Reviews of Modern Physics |year=2013 |volume=85 |issue=2 |pages=471–527 |arxiv=1204.4325 |bibcode=2013RvMP...85..471B |doi=10.1103/RevModPhys.85.471 |s2cid=119261020 }}</ref>

The Ghirardi–Rimini–Weber theory is a well-known collapse model. It proposes that particles have a small probability of undergoing spontaneous localization. For a single microscopic particle such a collapse is extremely rare, but in a macroscopic measurement apparatus containing many particles, the probability of an effective collapse becomes large.<ref>Bell, J. S. (2004). "Are there quantum jumps?". ''Speakable and Unspeakable in Quantum Mechanics'': 201–212.</ref>

== Role of decoherence ==

'''Quantum decoherence''' explains how interaction with the environment suppresses interference between different branches of a quantum state. It helps explain why macroscopic systems appear classical and why certain stable states become preferred through their interaction with the environment.<ref>{{cite journal |last1=Joos |first1=E. |last2=Zeh |first2=H. D. |title=The emergence of classical properties through interaction with the environment |journal=Zeitschrift für Physik B |date=June 1985 |volume=59 |issue=2 |pages=223–243 |doi=10.1007/BF01725541 |bibcode=1985ZPhyB..59..223J |s2cid=123425824 }}</ref><ref name=Zeh>{{cite book |title=Decoherence and the Appearance of a Classical World in Quantum Theory |pages=7 |chapter=Chapter 2: Basic Concepts and Their Interpretation |isbn=3-540-00390-8 |publisher=Springer-Verlag |year=2003 |edition=2nd |editor=E. Joos |author=H. D. Zeh |url=https://books.google.com/books?id=6eTHcxeNxdUC |arxiv=quant-ph/9506020 |bibcode=2003dacw.conf....7Z }}</ref><ref>{{cite journal |last1=Jaeger |first1=Gregg |title=What in the (quantum) world is macroscopic? |journal=American Journal of Physics |date=September 2014 |volume=82 |issue=9 |pages=896–905 |doi=10.1119/1.4878358 |bibcode=2014AmJPh..82..896J }}</ref>

Decoherence is now central to many discussions of the measurement problem. It shows how quantum interference becomes practically inaccessible for macroscopic systems, and how classical-looking probabilities can emerge from quantum dynamics.<ref name=Zurek/><ref name=Schlosshauer>{{cite journal |author=Maximilian Schlosshauer |title=Decoherence, the measurement problem, and interpretations of quantum mechanics |journal=Reviews of Modern Physics |volume=76 |year=2005 |pages=1267–1305 |doi=10.1103/RevModPhys.76.1267 |arxiv=quant-ph/0312059 |bibcode=2004RvMP...76.1267S |issue=4 |s2cid=7295619 }}</ref>

However, decoherence by itself does not necessarily solve the entire measurement problem. It explains why interference between alternatives becomes negligible, but it does not by itself select one actual outcome from the alternatives. For this reason, decoherence is often regarded as an essential part of the modern explanation of classicality, but not a complete interpretation of quantum mechanics.<ref name=Schlosshauer2>{{cite journal |author=Maximilian Schlosshauer |title=Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics |journal=Annals of Physics |volume=321 |issue=1 |date=January 2006 |pages=112–149 |doi=10.1016/j.aop.2005.10.004 |arxiv=quant-ph/0506199 |bibcode=2006AnPhy.321..112S |s2cid=55561902 }}</ref>

== Why it remains unsolved ==

The measurement problem remains open because the standard quantum formalism is highly successful but conceptually ambiguous. It gives extremely accurate probabilities for experimental outcomes, yet it does not by itself settle what the wave function represents, whether collapse is real, whether all outcomes occur in different branches, or whether hidden variables or modified dynamics are needed.

The problem therefore lies at the boundary between physics, mathematics, and philosophy of science. It is connected to quantum information, decoherence, macroscopic superpositions, the Born rule, the quantum-classical transition, and the interpretation of probability.

== See also ==

{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}

=References=

{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Measurement problem|1}}

Physics:Quantum measurement problem - Revision history

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