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Breakdown of Bell's theorem for certain objective local parameter spaces.

Karl Hess1, Walter Philipp

  • 1Beckman Institute, Department of Electrical Engineering, University of Illinois, Urbana, IL 61801, USA. k-hess@uiuc.edu

Proceedings of the National Academy of Sciences of the United States of America
|January 24, 2004
PubMed
Summary

Bell

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Area of Science:

  • Quantum mechanics
  • Probability theory

Background:

  • Bell's inequalities are crucial for understanding quantum mechanics.
  • Existing proofs rely on specific algebraic manipulations.

Purpose of the Study:

  • To rigorously examine the mathematical validity of proofs for Bell's inequalities.
  • To identify limitations in applying Kolmogorov's axioms to these proofs.

Main Methods:

  • Analysis of algebraic manipulations within Bell's inequality proofs.
  • Application of Kolmogorov's axioms for probability theory.
  • Investigation of objective local parameter spaces.

Main Results:

  • Known proofs of Bell's inequalities employ invalid algebraic steps under Kolmogorov's axioms.
  • Justification is possible for a subset of objective local parameter spaces.
  • An extended parameter space, including instrument parameters with time and setting dependencies, cannot be justified.

Conclusions:

  • The mathematical foundation of some Bell's inequality proofs requires revision.
  • The scope of applicability for objective local theories is narrower than previously assumed.
  • Instrument parameter correlations pose a challenge for objective local realism.

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