15. S. L. Weinberg, System/apparatus superposition and the Born rule

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Volume 21: Pages 78-83, 2008

System/apparatus superposition and the Born rule

S. L. Weinberg 1

1Department of Physics, Academy of Artscience and Physics, Box 1, 18 Langslow Street, Rochester, New York 14620-2928, USA

Born pioneered the time-independent matrix mechanics Born rule and the time-dependent wave mechanical formula for the expectation value of a variable V in terms of its associated Hermitian operator O, and wavefunction ψ(x,t). He formulated the probability density function |ψ|2. We set down this time-dependent wave mechanical equation but using σ(x,t)=(x,t)+                         (x,t)]/(C)½ as a normalized superposition of system and apparatus wavefunctions, respectively. We call it the Sigma-Born formula (SBF). The relevant quantity now is |σ|2, or actually σ*, and SBF is given an ensemble interpretation. Two effects are considered. Superpositions may, of course, decohere rapidly. Secondly, system/apparatus interaction may cause entanglement, but SBF can only be used for unentangled angular momentum.

Keywords: Superposition, Decoherence, Entanglement, Noncontextuality

Received: November 6, 2006; Accepted: April 23, 2008; Published Online: December 15, 2008