TITLE:
Monty Hall Problem and the Principle of Equal Probability in Measurement Theory
AUTHORS:
Shiro Ishikawa
KEYWORDS:
Linguistic Interpretation; Quantum and Classical Measurement Theory; Philosophy of Statistics; Fisher Maximum Likelihood Method; Bayes’ Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.7,
June
19,
2012
ABSTRACT: In this paper, we study the principle of equal probability (i.e., unless we have sufficient reason to regard one possible case as more probable than another, we treat them as equally probable) in measurement theory (i.e., the theory of quantum mechanical world view), which is characterized as the linguistic turn of quantum mechanics with the Copenhagen interpretation. This turn from physics to language does not only realize theremarkable extensionof quantum mechanicsbut alsoestablish the method of science. Our study will be executed in the easy example of the Monty Hall problem. Although our argument is simple, we believe that it is worth pointing out the fact that the principle of equal probability can be, for the first time, clarified in measurement theory (based on the dualism) and not the conventional statistics (based on Kolmogorov’s probability theory).