Almost all my outcomes are written in the following preprint (the lecture note of the master course in Dept of Math. Keio university).
Shiro Ishikawa, "Linguistic Interpretation of Quantum Mechanics : Quantum language [ver.2]"
KSTS/RR-16/001 (2016, Research Report in Keio Math)

The following web-version is extracted from the above preprint. Proofs and detailed calculations are omitted. But many figures are added.




CONTENTS
:PDF + HTML

0.0 Home page
0.1: Preface
1.0: 1.0:Feynman's question
1.1:Quantum language
1.2(1):Axioms 1 and 2 (measurement and causality ) and interpretation:
1.2(2):Linguistic interpretation
1.2(3):Summary
1.3:Example (Hot or Cold?)
2.0: Axiom 1( measurement ); Abstract
2.1: Basic structure $[{\mathcal A} \subseteq$ $ \overline{\mathcal A} \subseteq B(H)]$( General Theory)
2.2: Quantum basic structure $[{\mathcal C}(H) \subseteq$ $ B(H) \subseteq B(H)]$
2.3: Classical basic structure $[C_0(\Omega ) \subseteq$ $ L^\infty ( \Omega, \nu ) \subseteq B(H)]$
2.4: State and observable
2.5: Examples of observables
2.6: System quantity
2.7: Axiom 1 ; No science without measurements
2.8: Classicalexamples ( urn problem, etc.)
2.9: Stern=Gerlach experiment
2.10: de Broglie paradox
3.0: Linguistic interpretation; Abstract
3.1: The linguistic interpretation
3.2: Tensor operator algebra
3.3.1: Only one observable
3.3.2: state doesnot move
3.3.3: Only one state
4.0: Linguistic interpretation; quantum systems
4.1: Kolmogorov extension theorem
4.2: The law of large numbers
4.3.1: Why is Heisenberg's uncertainty principle famous?
4.3.2: Mathematical formulation of Heisenberg's uncertainty principle
4.3.3: except approximately simultaneous measurement
4.4: EPR-paradox
4.5: Bell's inequalirty
5.0: Fisher statistics (abstract)
5.1: Urn problem
5.2: Fisher's maximum likrlihoof method
5.3: Examples of Fisher's maximum likrlihoof method
5.4: Moment method
5.5: Monty Hall problem: High school student puzzle
5.6: Two envelope problem: High school student puzzle
6.0: Confidence interval and statistical hypothesis testing ( Abstract )
6.1: Review: classical quantum language
6.2: The reverse relation between confidence interval and statistical hypothesis
6.3(1): Population mean (Confidence interval and statistical hypothesis testing)
6.3(2): Population mean (Confidence interval and statistical hypothesis testing)
6.4(1): Population variance (Confidence interval and statistical hypothesis testing)
6.4(2): Population variance (Confidence interval and statistical hypothesis testing)
6.5: Difference of population means (Confidence interval and statistical hypothesis
6.6: Student $t$-distribution of population mean
7.0: ANOVA(Analysis of variance) ( Abstract )
7.1: Zero way ANOVA (= Student $t$-distribution )
7.2: The one way ANOVA
7.3(1): The two way ANOVA
7.3(2): The two way ANOVA
7.4: Supplement (Gauss integral )
8.0: Practical logic - Do you believe in syllogism?
8.1: Marginal observable and quasi-product observable
8.2: Properties of quasi-product observables
8.3: The definition of "implication "
8.4: Cogito-- I think, therefore I am
8.5: Combined observable -- Only one measurement is permitted
8.6: Syllogism-- Does Socrates die?
8.7: Syllogism does not hold in quantum systems
9.0: Mixed measurement theory ($\supset$Bayesian statistics)
9.1: Mixed measurement theory ( Bayesian statistics )
9.2: Simple examples in mixed measurements
9.3: St. Petersburg two envelope problem
9.4: Bayesian statistics is to use Bayes theorem
9.5: Two envelope problem (Bayes' method)
9.6:Monty Hall problem ( Bayesian approach )
9.7:Monty Hall problem ( The principle of equal weight )
9.8: Averaging information ( Entropy )
9.9: Fisher statistics: Monty Hall problem [three prisoners problem]
9.10:Bayesian statistics: Monty Hall problem [three prisoners problem]
9.11: Equal probability}: Monty Hall problem [three prisoners problem]
9.12: Bertrand's paradox( "randomness" depends on how you look at)
10.0: Causality (Abstract)
10.1: The most important unsolved problem---what is causality?
10.2: Causality---Mathematical preparation
10.2.2: Simple example---Finite causal operator is represented bymatrix
10.3:Axiom 2---Smoke is not located on the place which does not have fire
10.4: Kinetic equation (in classical mechanics and quantum mechanics)
10.5: Exercise:Solve Schrödinger equation by variable separation method
10.6:Random walk and quantum decoherence
10.7: Leibniz=Clarke Correspondence: What is space-time?
11.0: Measurement and causality (Abstract)
11.1: The Heisenberg picture and the Schrödinger picture
11.2: Wave function collapse ( = Projection postulate )
11.3:de Broglie's paradox(non-locality=faster-than-light)
11.4: Quantum Zeno effect
11.5: Schrödinger's cat, Wigner's friend and Laplace's demon
11.6: Wheeler's Delayed choice experiment: "Particle or wave?" is a foolish question
12.0: Realized causal observable in general theory
12.1: Finite realized causal observable
12.2 Double-slit experiment
12.3: Wilson cloud chamber in double slit experiment
12.4: Two kinds of absurdness ---idealism and dualism
13.0: Fisher statistic (II)
13.1: "Inference = Control" in quantum language
13.2: Regression analysis
14.0: Regression analysis
14.1: Infinite realized causal observable in classical systems
14.2: Is Brownian motion a motion?
14.3: The Schrödinger picture of the sequential deterministic causal operator
14.4 : Zeno's paradoxes---Flying arrow is not moving
15.0: Least-squares method and Regression analysis
15.1 The least squares method
15.2: Regression analysis in quantum language
15.3: Regression analysis(distribution , confidence interval and statistical hypothesis testing)
15.4: Generalized linear model
16.0: Kalman filter
16.1: Bayes=Kalman method (in $L^\infty(\Omega, m)$)
16.2: Problem establishment (concrete calculation)
16.3: Bayes=Kalman operator
16.4: Calculation: prediction part
16.5: Calculation: Smoothing part
17.0: Equilibrium statistical mechanics

17.1: Equilibrium statistical mechanics (Causality)
17.2: Equilibrium statistical mechanics (Probability)
18.0: The reliability in psychological test
18.1: Reliability in psychological tests
18.1.3: Reliability coefficient
18.2: Correlation coefficient: How to calculate the reliability coefficient
19.0: How to describe "brief"
19.1: Belief, probability and odds
19.2: The principle of equal odds weight
20.1: Two kinds of ( realistic and linguistic ) world- views
20.2: The summary of quantum language
20.3: Quantum language is located at the center of science



:INDEX





CONTENTS (FC2-version )