Physics:Quantum Measurement problem

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Short description: Fundamental problem concerning the emergence of definite outcomes in quantum measurements

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Quantum Measurement problem is a central conceptual issue in quantum mechanics concerning how definite outcomes arise from probabilistic quantum states. While the wave function evolves deterministically according to the Schrödinger equation, measurements yield single, definite results rather than superpositions.[1][2]

This raises the fundamental question: how does a superposition of many possible outcomes reduce to a single observed reality?

Conceptual illustration of the quantum measurement problem: a superposed quantum state yielding a single classical outcome upon observation, often represented by Schrödinger’s cat.

Deterministic evolution vs measurement

In quantum theory, the state of a system is described by a wave function that evolves deterministically:

  • Continuous, unitary evolution governed by the Schrödinger equation
  • Linear superposition of multiple possible states

However, measurement introduces:

This mismatch between continuous evolution and discrete measurement outcomes defines the measurement problem.[3]

Schrödinger’s cat paradox

The measurement problem is famously illustrated by Schrödinger’s cat:

  • A quantum event (e.g., radioactive decay) determines the fate of a cat
  • Before observation, the system exists in a superposition
  • The cat is simultaneously “alive” and “dead” in the formalism

Yet observation always yields a definite state, raising the question:

→ How do probabilities become actual outcomes?

Major interpretations

Different interpretations of quantum mechanics provide distinct resolutions:

Copenhagen-type interpretations

The Copenhagen interpretation posits:

  • Measurement causes collapse of the wave function
  • The wave function encodes probabilistic knowledge

However, the mechanism of collapse remains undefined.[4]

Many-worlds interpretation

The many-worlds interpretation removes collapse entirely:

  • The universal wave function always evolves deterministically
  • Measurement creates branching worlds
  • All outcomes occur in separate branches

A key challenge is deriving the Born rule for probabilities.[5]

de Broglie–Bohm theory

The pilot-wave theory introduces hidden variables:

  • Particles have definite trajectories
  • The wave function guides motion
  • Apparent collapse emerges dynamically

No fundamental collapse occurs.[6]

Objective-collapse models

Objective-collapse theories modify quantum dynamics:

  • Collapse occurs spontaneously
  • Governed by stochastic nonlinear terms
  • Predict experimentally testable deviations

Example: GRW theory.[7]

Role of decoherence

Quantum decoherence provides a partial resolution:

  • Interaction with the environment suppresses interference
  • Quantum probabilities become classical probabilities
  • Explains emergence of classical behavior

However:

  • Decoherence does **not** produce actual collapse
  • It does not fully solve the measurement problem

It instead explains why classical outcomes appear stable.[8]

Conceptual significance

The measurement problem highlights a deep divide:

  • Quantum reality: superpositions and probabilities
  • Classical reality: definite outcomes

It remains one of the most important unresolved issues in the foundations of physics, closely linked to:

See also

Table of contents (138 articles)

Index

Full contents

1. Foundations (7)
  1. Physics:Quantum basics
  2. Physics:Quantum Postulates
  3. Physics:Quantum Hilbert space
  4. Physics:Quantum Observables and operators
  5. Physics:Quantum mechanics
  6. Physics:Quantum mechanics measurements
  7. Physics:Quantum Mathematical Foundations of Quantum Theory

2. Conceptual and interpretations (10)
  1. Physics:Quantum Interpretations of quantum mechanics
  2. Physics:Quantum Wave–particle duality
  3. Physics:Quantum Complementarity principle
  4. Physics:Quantum Uncertainty principle
  5. Physics:Quantum Measurement problem
  6. Physics:Quantum Bell's theorem
  7. Physics:Quantum Hidden variable theory
  8. Physics:Quantum A Spooky Action at a Distance
  9. Physics:Quantum A Walk Through the Universe
  10. Physics:Quantum The Secret of Cohesion and How Waves Hold Matter Together

3. Mathematical structure and systems (11)
  1. Physics:Quantum Density matrix
  2. Physics:Quantum Exactly solvable quantum systems
  3. Physics:Quantum Formulas Collection
  4. Physics:Quantum A Matter Of Size
  5. Physics:Quantum Symmetry in quantum mechanics
  6. Physics:Quantum Angular momentum operator
  7. Physics:Quantum Runge–Lenz vector
  8. Physics:Quantum Approximation Methods
  9. Physics:Quantum Matter Elements and Particles
  10. Physics:Quantum Dirac equation
  11. Physics:Quantum Klein–Gordon equation

4. Atomic and spectroscopy (11)
    Quantum atomic structure and spectroscopy: orbitals, energy levels, and emission and absorption spectra.
  1. Physics:Quantum Atomic structure and spectroscopy
  2. Physics:Quantum Hydrogen atom
  3. Physics:Quantum Multi-electron atoms
  4. Physics:Quantum Fine structure
  5. Physics:Quantum Hyperfine structure
  6. Physics:Quantum Isotopic shift
  7. Physics:Quantum Zeeman effect
  8. Physics:Quantum Stark effect
  9. Physics:Quantum Spectral lines and series
  10. Physics:Quantum Selection rules
  11. Physics:Quantum Fermi's golden rule

5. Wavefunctions and modes (8)
    A quantum wavefunction showing probability amplitude in space; the square of its magnitude gives the probability density.
  1. Physics:Quantum Wavefunction
  2. Physics:Quantum Superposition principle
  3. Physics:Quantum Eigenstates and eigenvalues
  4. Physics:Quantum Boundary conditions and quantization
  5. Physics:Quantum Standing waves and modes
  6. Physics:Quantum Normal modes and field quantization
  7. Physics:Number of independent spatial modes in a spherical volume
  8. Physics:Quantum Density of states

6. Quantum dynamics and evolution (9)
  1. Physics:Quantum Time evolution
  2. Physics:Quantum Schrödinger equation
  3. Physics:Quantum Time-dependent Schrödinger equation
  4. Physics:Quantum Stationary states
  5. Physics:Quantum Perturbation theory
  6. Physics:Quantum Time-dependent perturbation theory
  7. Physics:Quantum Adiabatic theorem
  8. Physics:Quantum Scattering theory
  9. Physics:Quantum S-matrix

7. Measurement and information (6)
  1. Physics:Quantum Measurement theory
  2. Physics:Quantum Measurement operators
  3. Physics:Quantum Projective measurement
  4. Physics:Quantum POVM
  5. Physics:Quantum Weak measurement
  6. Physics:Quantum Measurement collapse

8. Quantum information and computing (6)
  1. Physics:Quantum information theory
  2. Physics:Quantum Qubit
  3. Physics:Quantum Entanglement
  4. Physics:Quantum Gates and circuits
  5. Physics:Quantum Computing Algorithms in the NISQ Era
  6. Physics:Quantum Noisy Qubits

9. Quantum optics and experiments (4)
    Experimental quantum physics: qubits, dilution refrigerators, quantum communication, and laboratory systems.
  1. Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy
  2. Physics:Quantum optics beam splitter experiments
  3. Physics:Quantum Ultra fast lasers
  4. Physics:Quantum Experimental quantum physics
    5. Template:Quantum optics operators

10. Open quantum systems (7)
  1. Physics:Quantum Open systems
  2. Physics:Quantum Master equation
  3. Physics:Quantum Lindblad equation
  4. Physics:Quantum Decoherence
  5. Physics:Quantum Markovian dynamics
  6. Physics:Quantum Non-Markovian dynamics
  7. Physics:Quantum Trajectories

11. Quantum field theory (18)
    Structural dependency map of quantum field theory.
  1. Physics:Quantum field theory (QFT) basics
  2. Physics:Quantum field theory (QFT) core
  3. Physics:Quantum Fields and Particles
  4. Physics:Quantum Second quantization
  5. Physics:Quantum Harmonic Oscillator field modes
  6. Physics:Quantum Creation and annihilation operators
  7. Physics:Quantum vacuum fluctuations
  8. Physics:Quantum Propagators in quantum field theory
  9. Physics:Quantum Feynman diagrams
  10. Physics:Quantum Path integral formulation
  11. Physics:Quantum Renormalization in field theory
  12. Physics:Quantum Renormalization group
  13. Physics:Quantum Field Theory Gauge symmetry
  14. Physics:Quantum Non-Abelian gauge theory
  15. Physics:Quantum Electrodynamics (QED)
  16. Physics:Quantum chromodynamics (QCD)
  17. Physics:Quantum Electroweak theory
  18. Physics:Quantum Standard Model

12. Statistical mechanics and kinetic theory (10)
  1. Physics:Quantum Statistical mechanics
  2. Physics:Quantum Partition function
  3. Physics:Quantum Distribution functions
  4. Physics:Quantum Liouville equation
  5. Physics:Quantum Kinetic theory
  6. Physics:Quantum Boltzmann equation
  7. Physics:Quantum BBGKY hierarchy
  8. Physics:Quantum Transport theory
  9. Physics:Quantum Relaxation and thermalization
  10. Physics:Quantum Thermodynamics

13. Condensed matter and solid-state physics (7)
  1. Physics:Quantum Band structure
  2. Physics:Quantum Fermi surfaces
  3. Physics:Quantum Semiconductor physics
  4. Physics:Quantum Phonons
  5. Physics:Quantum Electron-phonon interaction
  6. Physics:Quantum Superconductivity
  7. Physics:Quantum Topological phases of matter

14. Plasma and fusion physics (9)
    Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
  1. Physics:Quantum Plasma (fusion context)
  2. Physics:Quantum Fusion reactions and Lawson criterion
  3. Physics:Quantum Magnetic confinement fusion
  4. Physics:Quantum Inertial confinement fusion
  5. Physics:Quantum Plasma instabilities and turbulence
  6. Physics:Quantum Tokamak
  7. Physics:Quantum Tokamak core plasma
  8. Physics:Quantum Tokamak edge physics and recycling asymmetries
  9. Physics:Quantum Stellarator

15. Timeline (8)
  1. Physics:Quantum mechanics/Timeline
  2. Physics:Quantum mechanics/Timeline/Pre-quantum era
  3. Physics:Quantum mechanics/Timeline/Old quantum theory
  4. Physics:Quantum mechanics/Timeline/Modern quantum mechanics
  5. Physics:Quantum mechanics/Timeline/Quantum field theory era
  6. Physics:Quantum mechanics/Timeline/Quantum information era
  7. Physics:Quantum mechanics/Timeline/Quantum technology era
  8. Physics:Quantum mechanics/Timeline/Quiz/

16. Advanced and frontier topics (6)
  1. Physics:Quantum Supersymmetry
  2. Physics:Quantum Black hole thermodynamics
  3. Physics:Quantum Holographic principle
  4. Physics:Quantum gravity
  5. Physics:Quantum De Sitter invariant special relativity
  6. Physics:Quantum Doubly special relativity

References

  1. ↑ Weinberg, Steven (1998). The Oxford History of the Twentieth Century. Oxford University Press. ISBN 0-19-820428-0. 
  2. ↑ Zurek, Wojciech H. (2003). "Decoherence, einselection, and the quantum origins of the classical". Reviews of Modern Physics 75 (3): 715–775. doi:10.1103/RevModPhys.75.715. 
  3. ↑ Weinberg, Steven (2005). "Einstein's Mistakes". Physics Today 58 (11): 31–35. doi:10.1063/1.2155755. 
  4. ↑ Schlosshauer, Maximilian; Kofler, Johannes; Zeilinger, Anton (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. 
  5. ↑ Kent, Adrian (2010). "One world versus many". One world versus many. Oxford University Press. 
  6. ↑ Goldstein, Sheldon (2017). Bohmian Mechanics. Stanford Encyclopedia of Philosophy. 
  7. ↑ Bassi, Angelo; Lochan, Kinjalk; Satin, Seema; Singh, Tejinder P.; Ulbricht, Hendrik (2013). "Models of wave-function collapse". Reviews of Modern Physics 85 (2): 471–527. doi:10.1103/RevModPhys.85.471. 
  8. ↑ Schlosshauer, Maximilian (2005). "Decoherence, the measurement problem, and interpretations of quantum mechanics". Reviews of Modern Physics 76: 1267–1305. doi:10.1103/RevModPhys.76.1267. 

[[author|Harold Foppele}}



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