Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory
Ordinary quantum theory is a statistical theory without an underlying probability space. The Wiener-Siegel theory provides a probability space, defined in terms of the usual wave function and its ``stochastic coordinates``; i.e., projections of its components onto differentials of complex Wiener processes. The usual probabilities of quantum theory emerge as measures of subspaces defined by inequalities on stochastic coordinates. Since each point {alpha} of the probability space is assigned values (or arbitrarily small intervals) of all observables, the theory gives a pseudo-classical or ``hidden-variable`` view in which normally forbidden concepts are allowed. Joint probabilities for values of noncommuting variables are well-defined. This paper gives a brief description of the theory, including a new generalization to incorporate spin, and reports the first concrete calculation of a joint probability for noncommuting components of spin of a single particle. Bohm`s form of the Einstein-Podolsky-Rosen Gedankenexperiment is discussed along the lines of Carlen`s paper at this Congress. It would seem that the ``EPR Paradox`` is avoided, since to each {alpha} the theory assigns opposite values for spin components of two particles in a singlet state, along any axis. In accordance with Bell`s ideas, the price to pay for this attempt at greater theoretical detail is a disagreement with usual quantum predictions. The disagreement is computed and found to be large.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 220455
- Report Number(s):
- SLAC-PUB-7090; CONF-9411248-2; ON: DE96008057; TRN: 96:011303
- Resource Relation:
- Conference: Norbert Wiener centenary congress, East Lansing, MI (United States), 27 Nov - 3 Dec 1994; Other Information: PBD: Feb 1996
- Country of Publication:
- United States
- Language:
- English
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