Physics:Quantum measurement problem
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Quantum measurement problem is the problem of explaining how definite measurement outcomes arise from the mathematical structure of 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.[1][2] More broadly, the measurement problem asks how quantum reality gives rise to the classical world of definite experimental records.[3]
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.[4][5]
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.[6][7]
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.[8][9]
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.[10][11][12]
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.[13][14]
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.[15]
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.[16]
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.[17]
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.[18][19][20]
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.[3][21]
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.[22]
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
Table of contents (184 articles)
Index
Full contents
- Physics:Quantum basics
- Physics:Quantum Postulates
- Physics:Quantum Hilbert space
- Physics:Quantum Observables and operators
- Physics:Quantum mechanics
- Physics:Quantum mechanics measurements
- Physics:Quantum state
- Physics:Quantum system
- Physics:Quantum superposition
- Physics:Quantum probability
- Physics:Quantum Mathematical Foundations of Quantum Theory
- Physics:Quantum Interpretations of quantum mechanics
- Physics:Quantum Wave–particle duality
- Physics:Quantum Complementarity principle
- Physics:Quantum Uncertainty principle
- Physics:Quantum Measurement problem
- Physics:Quantum Bell's theorem
- Physics:Quantum Hidden variable theory
- Physics:Quantum nonlocality
- Physics:Quantum contextuality
- Physics:Quantum Darwinism
- Physics:Quantum A Spooky Action at a Distance
- Physics:Quantum A Walk Through the Universe
- Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together
- Physics:Quantum measurement problem
- Physics:Quantum Density matrix
- Physics:Quantum Exactly solvable quantum systems
- Physics:Quantum Formulas Collection
- Physics:Quantum A Matter Of Size
- Physics:Quantum Symmetry in quantum mechanics
- Physics:Quantum Angular momentum operator
- Physics:Quantum Runge–Lenz vector
- Physics:Quantum Approximation Methods
- Physics:Quantum Matter Elements and Particles
- Physics:Quantum Dirac equation
- Physics:Quantum Klein–Gordon equation
- Physics:Quantum pendulum
- Physics:Quantum configuration space
- Physics:Quantum Atomic structure and spectroscopy
- Physics:Quantum Hydrogen atom
- Physics:Quantum number
- Physics:Quantum Multi-electron atoms
- Physics:Quantum Fine structure
- Physics:Quantum Hyperfine structure
- Physics:Quantum Isotopic shift
- Physics:Quantum defect
- Physics:Quantum Zeeman effect
- Physics:Quantum Stark effect
- Physics:Quantum Spectral lines and series
- Physics:Quantum Selection rules
- Physics:Quantum Fermi's golden rule
- Physics:Quantum beats
- Physics:Quantum Wavefunction
- Physics:Quantum Superposition principle
- Physics:Quantum Eigenstates and eigenvalues
- Physics:Quantum Boundary conditions and quantization
- Physics:Quantum Standing waves and modes
- Physics:Quantum Normal modes and field quantization
- Physics:Number of independent spatial modes in a spherical volume
- Physics:Quantum Density of states
- Physics:Quantum carpet
- Physics:Quantum Time evolution
- Physics:Quantum Schrödinger equation
- Physics:Quantum Time-dependent Schrödinger equation
- Physics:Quantum Stationary states
- Physics:Quantum Perturbation theory
- Physics:Quantum Time-dependent perturbation theory
- Physics:Quantum Adiabatic theorem
- Physics:Quantum Scattering theory
- Physics:Quantum S-matrix
- Physics:Quantum tunnelling
- Physics:Quantum speed limit
- Physics:Quantum revival
- Physics:Quantum reflection
- Physics:Quantum oscillations
- Physics:Quantum jump
- Physics:Quantum boomerang effect
- Physics:Quantum chaos
- Physics:Quantum information theory
- Physics:Quantum Qubit
- Physics:Quantum Entanglement
- Physics:Quantum Gates and circuits
- Physics:Quantum Computing Algorithms in the NISQ Era
- Physics:Quantum Noisy Qubits
- Physics:Quantum random access code
- Physics:Quantum pseudo-telepathy
- Physics:Quantum network
- Physics:Quantum money
- Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
- Physics:Quantum optics beam splitter experiments
- Physics:Quantum Ultra fast lasers
- Physics:Quantum Experimental quantum physics
- Physics:Quantum optics Template:Quantum optics operators
- Physics:Quantum field theory (QFT) basics
- Physics:Quantum field theory (QFT) core
- Physics:Quantum Fields and Particles
- Physics:Quantum Second quantization
- Physics:Quantum Harmonic Oscillator field modes
- Physics:Quantum Creation and annihilation operators
- Physics:Quantum vacuum fluctuations
- Physics:Quantum Propagators in quantum field theory
- Physics:Quantum Feynman diagrams
- Physics:Quantum Path integral formulation
- Physics:Quantum Renormalization in field theory
- Physics:Quantum Renormalization group
- Physics:Quantum Field Theory Gauge symmetry
- Physics:Quantum Non-Abelian gauge theory
- Physics:Quantum Electrodynamics (QED)
- Physics:Quantum chromodynamics (QCD)
- Physics:Quantum Electroweak theory
- Physics:Quantum Standard Model
- Physics:Quantum triviality
- Physics:Quantum confinement problem
- Physics:Quantum Statistical mechanics
- Physics:Quantum Partition function
- Physics:Quantum Distribution functions
- Physics:Quantum Liouville equation
- Physics:Quantum Kinetic theory
- Physics:Quantum Boltzmann equation
- Physics:Quantum BBGKY hierarchy
- Physics:Quantum Relaxation and thermalization
- Physics:Quantum Thermodynamics
- Physics:Quantum Band structure
- Physics:Quantum Fermi surfaces
- Physics:Quantum Semiconductor physics
- Physics:Quantum Phonons
- Physics:Quantum Electron-phonon interaction
- Physics:Quantum Superconductivity
- Physics:Quantum Topological phases of matter
- Physics:Quantum well
- Physics:Quantum spin liquid
- Physics:Quantum spin Hall effect
- Physics:Quantum phase transition
- Physics:Quantum critical point
- Physics:Quantum dot
- Physics:Quantum Fusion reactions and Lawson criterion
- Physics:Quantum Plasma (fusion context)
- Physics:Quantum Magnetic confinement fusion
- Physics:Quantum Inertial confinement fusion
- Physics:Quantum Plasma instabilities and turbulence
- Physics:Quantum Tokamak core plasma
- Physics:Quantum Tokamak edge physics and recycling asymmetries
- Physics:Quantum Stellarator
- Physics:Quantum mechanics/Timeline
- Physics:Quantum mechanics/Timeline/Pre-quantum era
- Physics:Quantum mechanics/Timeline/Old quantum theory
- Physics:Quantum mechanics/Timeline/Modern quantum mechanics
- Physics:Quantum mechanics/Timeline/Quantum field theory era
- Physics:Quantum mechanics/Timeline/Quantum information era
- Physics:Quantum mechanics/Timeline/Quantum technology era
- Physics:Quantum mechanics/Timeline/Quiz
- Physics:Quantum topology
- Physics:Quantum battery
- Physics:Quantum Supersymmetry
- Physics:Quantum Black hole thermodynamics
- Physics:Quantum Holographic principle
- Physics:Quantum gravity
- Physics:Quantum De Sitter invariant special relativity
- Physics:Quantum Doubly special relativity
- Physics:Quantum arithmetic geometry
- Physics:Quantum unsolved problems
- Physics:Quantum Yang-Mills mass gap
- Physics:Quantum gravity problem
- Physics:Quantum black hole information paradox
- Physics:Quantum dark matter problem
- Physics:Quantum neutrino mass problem
- Physics:Quantum matter-antimatter asymmetry problem
References
- ↑ Weinberg, Steven (1998). "The Great Reduction: Physics in the Twentieth Century". The Oxford History of the Twentieth Century. Oxford University Press. p. 26. ISBN 0-19-820428-0. https://books.google.com/books?id=WGvbAApi2roC&pg=PA22.
- ↑ Weinberg, Steven (November 2005). "Einstein's Mistakes". Physics Today 58 (11): 31–35. doi:10.1063/1.2155755. Bibcode: 2005PhT....58k..31W.
- ↑ 3.0 3.1 Zurek, Wojciech Hubert (22 May 2003). "Decoherence, einselection, and the quantum origins of the classical". Reviews of Modern Physics 75 (3): 715–775. doi:10.1103/RevModPhys.75.715. Bibcode: 2003RvMP...75..715Z.
- ↑ Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (August 2013). "A snapshot of foundational attitudes toward quantum mechanics". Studies in History and Philosophy of Science Part B 44 (3): 222–230. doi:10.1016/j.shpsb.2013.04.004. Bibcode: 2013SHPMP..44..222S.
- ↑ Ball, Philip (2013). "Experts still split about what quantum theory means". Nature. doi:10.1038/nature.2013.12198. https://www.nature.com/news/experts-still-split-about-what-quantum-theory-means-1.12198.
- ↑ Mermin, N. David (1989). "What's Wrong with this Pillow?". Physics Today 42 (4): 9. doi:10.1063/1.2810963. Bibcode: 1989PhT....42d...9D.
- ↑ Mermin, N. David (2004). "Could Feynman have said this?". Physics Today 57 (5): 10–11. doi:10.1063/1.1768652. Bibcode: 2004PhT....57e..10M.
- ↑ Howard, Don (December 2004). "Who Invented the "Copenhagen Interpretation"? A Study in Mythology". Philosophy of Science 71 (5): 669–682. doi:10.1086/425941. https://www.journals.uchicago.edu/doi/10.1086/425941.
- ↑ Camilleri, Kristian (May 2009). "Constructing the Myth of the Copenhagen Interpretation". Perspectives on Science 17 (1): 26–57. doi:10.1162/posc.2009.17.1.26. http://www.mitpressjournals.org/doi/10.1162/posc.2009.17.1.26.
- ↑ Englert, Berthold-Georg (2013-11-22). "On quantum theory". The European Physical Journal D 67 (11): 238. doi:10.1140/epjd/e2013-40486-5. Bibcode: 2013EPJD...67..238E.
- ↑ Peierls, Rudolf (1991). "In defence of "measurement"". Physics World 4 (1): 19–21. doi:10.1088/2058-7058/4/1/19.
- ↑ Healey, Richard (2016). "Quantum-Bayesian and Pragmatist Views of Quantum Theory". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/quantum-bayesian/.
- ↑ Kent, Adrian (2010). "One world versus many: the inadequacy of Everettian accounts of evolution, probability, and scientific confirmation". Many Worlds?. Oxford University Press. pp. 307–354. ISBN 9780199560561. OCLC 696602007.
- ↑ Barrett, Jeffrey (2018). "Everett's Relative-State Formulation of Quantum Mechanics". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/qm-everett/.
- ↑ Sheldon, Goldstein (2017). "Bohmian Mechanics". in Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University. https://plato.stanford.edu/entries/qm-bohm/.
- ↑ Angelo Bassi; Kinjalk Lochan; Seema Satin; Tejinder P. Singh; Hendrik Ulbricht (2013). "Models of wave-function collapse, underlying theories, and experimental tests". Reviews of Modern Physics 85 (2): 471–527. doi:10.1103/RevModPhys.85.471. Bibcode: 2013RvMP...85..471B.
- ↑ Bell, J. S. (2004). "Are there quantum jumps?". Speakable and Unspeakable in Quantum Mechanics: 201–212.
- ↑ Joos, E.; Zeh, H. D. (June 1985). "The emergence of classical properties through interaction with the environment". Zeitschrift für Physik B 59 (2): 223–243. doi:10.1007/BF01725541. Bibcode: 1985ZPhyB..59..223J.
- ↑ H. D. Zeh (2003). "Chapter 2: Basic Concepts and Their Interpretation". in E. Joos. Decoherence and the Appearance of a Classical World in Quantum Theory (2nd ed.). Springer-Verlag. pp. 7. ISBN 3-540-00390-8. Bibcode: 2003dacw.conf....7Z. https://books.google.com/books?id=6eTHcxeNxdUC.
- ↑ Jaeger, Gregg (September 2014). "What in the (quantum) world is macroscopic?". American Journal of Physics 82 (9): 896–905. doi:10.1119/1.4878358. Bibcode: 2014AmJPh..82..896J.
- ↑ Maximilian Schlosshauer (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics". Reviews of Modern Physics 76 (4): 1267–1305. doi:10.1103/RevModPhys.76.1267. Bibcode: 2004RvMP...76.1267S.
- ↑ Maximilian Schlosshauer (January 2006). "Experimental motivation and empirical consistency in minimal no-collapse quantum mechanics". Annals of Physics 321 (1): 112–149. doi:10.1016/j.aop.2005.10.004. Bibcode: 2006AnPhy.321..112S.
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