Foundations of Physics

, Volume 16, Issue 4, pp 391–405 | Cite as

Quantum mechanics without probability amplitudes

  • William K. Wootters
Part III. Invited Papers Dedicated To John Archibald Wheeler


First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.


Quantum Mechanic Quantum State State Vector Density Matrice Special Measurement 
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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • William K. Wootters
    • 1
  1. 1.Department of Physics and AstronomyWilliams CollegeWilliamstown

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