System/apparatus superposition and the Born rule

摘要

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) =[ψ(x,t) + φ(x,t)]/ ~C~(1/2)as a normalized superposition of system and aparatus wavefunctions, respectively. We call it the Sigma-Born formula (SBF). The relevant quantity now is or actually *σOσ, and SB~F is given an ensemble interpretation. Two efects 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.