The curious quantum statistics in the interval between measurements

Counterfactual Reasoning in Time-Symmetric Quantum Mechanics

“…It is apparent [7] that the ensembles selected by imposing the above selection criterion in the RW and the CFW are different conceptually and are usually also different numerically. They are different conceptually because the quantum system in the CFW is subject to an intermedi-ate measurement at time t and the quantum system in the RW is not.…”

“…In the context of TSQT, Aharonov, Vaidman and co-authors [2,3,4,5] have drawn a number of interesting conclusions based on counterfactual reasoning about different gedanken experiments. From the beginning [6,7], concerns have been expressed about the legitimacy of the counterfactual reasoning involved in some of the conclusions in TSQT [8,9,10,11,12,13,14,15,16,17]. Initially, there was a misunderstanding on the part of some authors (for example, [12]) that assertions about "elements of reality" on the basis of the counterfactual reasoning were being made in an ontological sense.…”

“…It has now been made clear that that is not the case and the counterfactual reasoning in TSQT has been defended [18,19,20,21,22]. Recently a new example reminiscent of the much-discussed 3-box example of time-symmetric counterfactual reasoning [1,2,4,6,7,8,14,15,16,17,19,20,23,24,25,26] has been proposed [27] and discussed [28].…”

“…If a|b = 0, the ensemble will be empty in the RW, although it will not be in the CFW provided a|c i = 0 and c i |b = 0. Whether or not the differences between the ensembles are significant has been the subject of discussion [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. For the purposes of the present work, it will be assumed that the differences between the ensembles are not significant.…”