## Linguistic Interpretation of Quantum Mechanics S.ISHIKAWA

### Linguistic Interpretation of Quantum Mechanics

- Towards World-Description in Quantum Language -

by Shiro ISHIKAWA, 409 pages (B5)

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Inspired by the Copenhagen interpretation of quantum mechanics, the author introduces two axioms, one for measurement and the other for causality, to establish a new paradigm or world-description called "linguistic interpretation" or "quantum language".

The paradigm casts a new light on the wellknown problems in quantum mechanics including Heisenberg's uncertainty principle, EPR-paradox, Bell's inequality, Schrödinger's cat (Wigner's friend), Wheeler's delayed choice experiment, and double-slit experiment.

He shows that the paradigm works not only in quantum systems but also in classical systems, referring to regression analysis and Kalman filter in statistics and so on.

He emphasizes the paradigm is a natural consequence in the history of philosophy, and shows how the famous problems in philosophy are solved such as Leibniz=Clarke correspondence "What is space-time ?", Zeno's paradox , and the principle of equal probability.

He thus leads us to a conclusion that quantum language is a core concept of science.

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### Preface

Quantum Language A New Approach to World-Description

This is a note of my lecture for graduate students which has been given for about 15 years at the faculty of science and technology of Keio University.

The main theme of my lecture is "quantum language"(="measurement theory"), which was proposed by myself. Quantum language, inspired by the Copenhagen interpretation of quantum mechanics, is a powerful tool to describe classical systems as well as quantum systems.

In the present lecture, I will show its three aspects:

1 : the standard interpretation of quantum mechanics

(the authentic Copenhagen interpretation)

2 : the final goal of the dualistic idealism

(Descartes = Kant philosophy)

3 : theoretical statistics in the future

and conclude :

To do science is almost to describe phenomena in quantum language.

or

Quantum language is most fundamental in science.

This lecture note, an updated version for a course in 2015, may be regarded as a revised edition of the following two papers.

[28]: S. Ishikawa, Mathematical Foundations of Measurement Theory, Keio University Press Inc. 2006, (335 pages) .

[37]: S. Ishikawa, Measurement Theory in the Philosophy of Science, arXiv:1209.3483 [physics.hist-ph] 2012, (177 pages)

The terms "measurement theory" and "quantum language" used in this note mean the same in essence:

quantum language = measurement theory

Recently I use "quantum language" more frequently.

Shiro ISHIKAWA

### Contents

### about the author

Dr. Shiro Ishikawa, former associate professor at Keio University, graduated from Keio University in 1971. His research covers functional analysis, foundation of quantum mechanics, and philosophy of science.

For further information about quantum language, see also (url: http://www.math.keio.ac.jp/~ishikawa/indexe.html ).