International Journal of Theoretical Physics

, Volume 36, Issue 1, pp 167–176 | Cite as

Pure quantum states are fundamental, mixtures (composite states) are mathematical constructions: An argument using algorithmic information theory

  • Vladik Kreinovich
  • Luc Longpré
Article

Abstract

From the philosophical viewpoint, two interpretations of the quantum measurement process are possible: According to the first interpretation, when we measure an observable, the measured system moves into one of the eigenstates of this observable (“the wave function collapses”); in other words, the universe “branches” by itself, due to the very measurement procedure, even if we do not use the result of the measurement. According to the second interpretation, the system simply moves into amixture of eigenstates, and the actual “branching” occurs only when anobserver reads the measurement results. According to the first interpretation, a mixture is a purely mathematical construction, and in the real physical world, a mixture actually means that the system is in one of the “component” states. In this paper, we analyze this difference from the viewpoint ofalgorithmic information theory; as a result of this analysis, we argue that onlypure quantum states are fundamental, while mixtures are simply useful mathematical constructions.

Keywords

Probability Measure Mathematical Term Composite State Kolmogorov Complexity Pure Quantum State 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benioff, P. A. (1976). Models of Zermelo Frankel set theory as carriers for the mathematics of physics. I, II,Journal of Mathematical Physics,17(5), 618–628, 629–640.MATHMathSciNetCrossRefADSGoogle Scholar
  2. Gács, P. (1980). Exact expressions for some randomness tests,Zeitschrift für Mathematische Logik und Grundlagen der Mathematik,26, 385–394.MATHGoogle Scholar
  3. Kreinovich, V., and Longpré, L. (1995). Random elements, composite measures, and quantum mechanics, 1995 Structures Conference Research Abstracts, June 1995, Abstract no. 95-28.Google Scholar
  4. Kreinovich, V., and Longpré, L. (1996). On the unreasonable effectiveness of symmetries in physics,International Journal of Theoretical Physics,35, 1549–1555.MATHMathSciNetCrossRefGoogle Scholar
  5. Levin, L. A. (1976). Uniform tests of randomness,Soviet Mathematics Doklady,17, 601–605.MATHGoogle Scholar
  6. Li, M., and Vitányi, P. (1993).An Introduction to Kolmogorov Complexity and Its Applications, Springer-Verlag, New York.Google Scholar
  7. Martin-Löf, P. (1966). The definition of random sequences,Information and Control,9, 602–619.MathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • Vladik Kreinovich
    • 1
  • Luc Longpré
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl Paso

Personalised recommendations