Abstract of Chapter 9

Quantum language (= measurement theory ) is classified as follows.

$(\sharp):$ $ \underset{(=\mbox{ quantum language})}{\mbox{measurement theory}} \left\{\begin{array}{ll} \underset{\mbox{($\sharp_1$)}}{ \mbox{pure type}} \left\{\begin{array}{ll} \!\! \mbox{classical system} : \mbox{ Fisher statistics} \\ \!\! \mbox{ quantum system} : \mbox{ usual quantum mechanics } \\ \end{array}\right. \\ \\ \underset{\mbox{($\sharp_2$)}} {\mbox{mixed type}} \left\{\begin{array}{ll} \!\! \mbox{ classical system} : \mbox{including Bayesian statistics, }\\ \qquad \qquad \qquad \qquad \mbox{Kalman filter} \\ \!\! \mbox{ quantum system} : \mbox{ quantum decoherence } \\ \end{array}\right. \end{array}\right. $

In this chapter, we study mixed measurement theory, which includes Bayesian statistics.



Again recall that, as mentioned in $\S$1.1, the main purpose of this book is to assert the following figure 1.1:

Fig.1.1: the location of "quantum language" in the world-views
This(particularly, ⑦--⑨) implies that quantum language has the following three aspects: $$ \left\{\begin{array}{ll} \mbox{ ⑦ :the standard interpretation of quantum mechanics} \\ \mbox{ $\qquad$ (i.e., the true colors of the Copenhagen interpretation) } \\ \\ \mbox{ ⑧ : the final goal of the dualistic idealism (Descartes=Kant philosophy) } \\ \\ \mbox{ ⑨ : theoretical statistics of the future } \end{array}\right. $$