Math 2.0

Quantum theory Foundations and measurement Problem

EPR paradox

Builds on Quantum entanglementObservable

Problem

Two particles are prepared in an entangled state and then separated. For this state, measuring the position of the first particle predicts with certainty the position of the second one. The same holds for momentum. Assume locality: a measurement on the first particle does not change the physical situation of the distant second particle. Assume the reality criterion: if the value of a quantity can be predicted with certainty without disturbing a system, the quantity has a definite value. Then both the position and the momentum of the second particle have definite values. Quantum mechanics assigns no state with definite values of both, since these observables do not commute. The question is whether quantum mechanics is therefore an incomplete description of physical reality.

Remarks

Einstein, Podolsky and Rosen concluded that the quantum description is incomplete, which suggests a theory with additional variables. Bohr replied in the same year that the reality criterion is ambiguous when the choice of measurement is part of the experimental arrangement. Bohm reformulated the argument with two spin-12\tfrac{1}{2} particles in the singlet state, where spin components along any axis are perfectly anticorrelated. Bell's theorem later showed that local hidden-variable theories cannot reproduce all quantum predictions for this state. Experiments find violations of Bell inequalities, as quantum mechanics predicts.

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To understand this page from the ground up, read these 3 pages in order. The foundations come first.

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Observable, concept, no evidence levelObservableconceptQuantum entanglement, concept, no evidence levelQuantum entanglementconceptEPR paradox, problem, no evidence levelEPR paradoxproblem
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Observable concept
  2. Quantum entanglement concept
  3. EPR paradox problem

Further reading

  1. Web https://en.wikipedia.org/wiki/Einstein%E2%80%93Podolsky%E2%80%93Rosen_paradox
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AboutQuantum entanglement, Hidden-variable theory
UsesQuantum entanglement, Observable
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Changed3 November 2026

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