Abstract of Chap. 2
Quantum language (= measurement theory ) is formulated as follows.
\[
\underset{\mbox{ (=quantum language)}}{\fbox{pure measurement theory (A)}}
:=
\underbrace{
\underset{\mbox{ (\(\S\)2.7)}}{
\overset{
[\mbox{ (pure) Axiom 1}]
}{\fbox{pure measurement}}
}
+
\underset{\mbox{ ( \(\S \)10.3)}}{
\overset{
[{\mbox{ Axiom 2}}]
}{\fbox{Causality}}
}
}_{\mbox{ a kind of incantation (a priori judgment)}}
+
\underbrace{
\underset{\mbox{
(\(\S\)3.1)
}}
{
\overset{
{}}{\fbox{Linguistic interpretation}}
}
}_{\mbox{ the manual on how to use spells}}
\]
That is, "measurement" and "causality" are closely related in quantum language:
It should be compared to Newtonian mechanics:
\begin{align}
\underset{\mbox{ (physics)}}{\fbox{Newtonian mechanics}}
=
\overset{\mbox{ }}{\fbox{Nothing}}
+
\overset{\mbox{ (Newtonian equation)}}{\fbox{Causality}}
\end{align}
Measurement theory asserts that
| (A): | Describe every phenomenon modeled on Axioms 1 and 2 (by a hint of the linguistic interpretation)!
|
In this chapter 2, we introduce Axiom 1 (measurement). Axiom 2 concerning causality will be explained in Chapter 10.
Some may have a question that
Why does Newtonian mechanics have "measurement"?
This will be answered throughout this book.
However, I add a brief answer below:
Recall Einstein's words:
The moon is there whether one looks at it or not.
which implies that
physics exists without measurement.
That is,
Newton as well as Einstein found out the essence:
"measurement" is not the concept in physics
The
The Hilbert space formulation of quantum mechanics is due to von Neumann (1903-1957).
I cannot emphasize too much the importance of his work.
We think that
von Neumann's quantum mechanics
$\doteqdot$
quantu mechanics
The above "$\doteqdot$"
cannot be replaced by
"$=$"
since von Neumann believed in that quantum mechanis is physics.
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:
$$
\left\{\begin{array}{ll}
\mbox{ ⑦ :the standard interpretation of quantum mechanics}
\\
\mbox{
$\qquad$
(i.e., the true colors of the Copenhagen interpretation)
}
\\
\\
\mbox{ ⑧ :
the final goal of the dualistic idealism (Descartes=Kant philosophy)
}
\\
\\
\mbox{ ⑨ :
theoretical statistics of the future
}
\end{array}\right.
$$
