Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalized Valuations

@article{Isham1998ToposPO,
  title={Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalized Valuations},
  author={C. J. Isham and Jeremy Butterfield},
  journal={International Journal of Theoretical Physics},
  year={1998},
  volume={37},
  pages={2669-2733}
}
AbstractAny attempt to construct a realistinterpretation of quantum theory founders on theKochen–Specker theorem, which asserts theimpossibility of assigning values to quantum quantitiesin a way that preserves functional relations between them. We constructa new type of valuation which is defined on alloperators, and which respects an appropriate version ofthe functional composition principle. The truth-values assigned to propositions are (i) contextual and(ii) multivalued, where the space of… 

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References

SHOWING 1-10 OF 21 REFERENCES

A Topos Perspective on the Kochen-Specker Theorem II. Conceptual Aspects and Classical Analogues

In a previous paper, we proposed assigning asthe value of a physical quantity in quantum theory acertain kind of set (a sieve) of quantities that arefunctions of the given quantity. The motivation

Topos theory and consistent histories: The internal logic of the set of all consistent sets

A major problem in the consistent-histories approach to quantum theory is contending with the potentially large number of consistent sets of history propositions. One possibility is to find a scheme

Independently Motivating the Kochen—Dieks Modal Interpretation of Quantum Mechanics

  • Rob Clifton
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1995
The distinguishing feature of ‘modal’ interpretations of quantum mechanics is their abandonment of the orthodox eigenstate–eigenvalue rule, which says that an observable possesses a definite value if

Sheaves in geometry and logic: a first introduction to topos theory

This text presents topos theory as it has developed from the study of sheaves. Sheaves arose in geometry as coefficients for cohomology and as descriptions of the functions appropriate to various

The Modal Interpretation of Quantum Mechanics

Preface D. Dieks, P.E. Vermaas. Introduction D. Dieks, P.E. Vermaas. Lorentz-Invariance in Modal Interpretations M. Dickson, R. Clifton. Locality and Lorentz-Covariance in the Modal Interpretation of

Operational Quantum Physics

Quantum physics is certainly one of the greatest scientific achievements of the 20th century. Nevertheless, there has always been a gap between the formalistics approach of quantum theory and its

The Logic of Quantum Mechanics

One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical

Quantum Mechanics: An Empiricist View

Part 1 Determinism and inderterminism in classical perspective: determinism indeterminism and probability. Part 2 How the phenomena demand quantum theory: the empirical basis of quantum theory new

Physical motivation of the modal interpretation of quantum mechanics