Physics:Quantum Measurement problem

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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 (185 articles)

Index

Full contents

9. Quantum optics and experiments (5) ↑ Back to index
14. Plasma and fusion physics (8) ↑ Back to index
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.
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.

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. ↑ Template:Cite encyclopedia
  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. 

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