ON RETROACTIVE OCCURRENCE AND TWIN EVENTS IN QUANTUM-MECHANICS

Bohr's well-known claim that only a registered phenomenon is a true ph enomenon is further elaborated into occurrence in the past: If ideal o ccurrence of an event P ((1 - P)) is a state rho at a time t(i) makes another event Q ((1 - Q)) certain at a later time t(f), and, finally U is the evolution operator from ti to tf, then, it is proved that the final collapsed state Q(UrhoU+)Q/TrQU(rho)U(+), which comes about in i deal occurrence of Q at tf, equals the initial collapsed state U(PrhoP /TrP(rho)U+, which evolves from the state resulting from the ideal occ urrence of P in rho at t(i). Utilizing the latter state is called the retroactive apparent ideal occurrence (RAIO) of P in rho. A number of consequences, including the general notion of twin events (the case wh en t(f) = t(i), and U = 1) is derived. It is pointed out that RAIO is relevant in second-kind quantum measurement, in Wheeler's delayed-choi ce experiments ill second-kind (or conditional) quantum preparators.