1.0:Feynman's question

$\qquad$von Neuman, Einstein

1.1:Quantum language

$\qquad$Dsecartes, the philosophy of probability and statistics, the philosophy of quantum mechanics,

1.2(1):Axioms 1 and 2 (measurement and causality ) and interpretation

$\qquad$measurement, causal relation, Lord Kelvin, metaphysics, Descartes=Kant philosophy,

1.2(2):Linguistic interpretation

$\qquad$the interpretation of quantum mechanics, cookbook, Kolmogorov's extension theorem,

1.2(3):Summary

$\qquad$Kant, a priori judgment, sell, continental rationlism, British empiricism,

1.3:Example (Hot or Cold?)

$\qquad$ translation from ordinary language to quantum language

2.0: Axiom 1( measurement ); Abstract

$\qquad$ Newtonian mechanics, von Neumann's "Mathematical foundations of quantum mechanics"

2.1: Basic structure $[{\mathcal A} \subseteq$ $ \overline{\mathcal A} \subseteq B(H)]$( General Theory)

$\qquad$ Newtonian mechanics, von Neumann's "Mathematical foundations of quantum mechanics", Hilbert space, operator algebra, basic structure,

2.2: Quantum basic structure $[{\mathcal C}(H) \subseteq$ $ B(H) \subseteq B(H)]$

$\qquad$ Dirac notation, complete orthonormal sysyte, trace operator, compact operator,

2.3: Classical basic structure $[C_0(\Omega ) \subseteq$ $ L^\infty ( \Omega, \nu ) \subseteq B(H)]$

$\qquad$ commutative $C^*$-algebra, commutative $W^*$-algebra, Gelfand theorem, spectrum, point measure,

2.4: State and observable

$\qquad$ John Locke, the primary ( sencondary ) quality, Plato, Aristotle, dualism, observable (= measureing instrument), sample space

2.5: Examples of observables

$\qquad$ existence observable, Berkeley , Einstein and Tagore's conversation, exact observable,

2.6: System quantity

$\qquad$ system quantity, Hermite matrix, specral decomposition,

2.7: Axiom 1 ; No science without measurements

$\qquad$ Born, the probabilistic interpretation of quantum mechanics, Einstein, the god does not throw dice, The Bohr?Einstein debates

2.8: Classicalexamples ( urn problem, etc.)

$\qquad$ urn problem, Wonder of man's linguistic competence

2.9: Stern=Gerlach experiment

$\qquad$ spin observable,

2.10: de Broglie paradox

$\qquad$ there is something faster than ligh, non-locality, Stop being bothered!

3.0: Linguistic interpretation; Abstract

$\qquad$ fifth Solvay conference

3.1: The linguistic interpretation

$\qquad$Kant, a priori judgment, sell, continental rationlism, British empiricism,dualism, Descartes' figure, Parmenides, Whitehead,

3.2: Tensor operator algebra

$\qquad$ tensor Hilbert space, tensor basic structure,

3.3.1: Only one observable

$\qquad$ Kolmogorv's extension theore, simultaneous observable,

3.3.2: state doesnot move

$\qquad$ Parmenides, Herakleitos, quasi-product observable,

3.3.3: Only one state

$\qquad$ parallel measurement, erdodic,

4.0: Linguistic interpretation; quantum system

$\qquad$ Descartes' figure,

4.1: Kolmogorov extension theorem

$\qquad$ Parmenides, infinite simultaneous observable

4.2: The law of large numbers

$\qquad$ Bernoulli, Galileo, Mean,variance,unbiased variance, Robertson uncertainty relation

4.3.1: Why is Heisenberg's uncertainty principle famous?

$\qquad$ Heisenberg's uncertainty principle is doubtful, Heisenberg's thought experiment due to γ-ray microscope

4.3.2: Mathematical formulation of Heisenberg's uncertainty principle

$\qquad$approximately simultaneous measurement

4.3.3: except approximately simultaneous measurement

$\qquad$Ozawa inequality, EPR-paradox,

4.4: EPR-paradox

$\qquad$entangled state, there is something faster than light, Bohr-Einstein debates

4.5: Bell's inequalirty

$\qquad$there is no relation between Bell's inequality and Bell's argument, hiden variable, Shut up and calculate

5.0: Fisher statistics (abstract)

$\qquad$measurement and inference are the two sides of a coin

5.1: Urn problem

$\qquad$Population(=system), paramenter (=state), normal measurement, student distribution, Gsset,

5.2: Fisher's maximum likrlihoof method

$\qquad$Born and Fisher,

5.3: Examples of Fisher's maximum likrlihoof method<

$\qquad$urn problem, normal measurement
/a>

5.4: Moment method

$\qquad$ unnatual but useful

5.5: Monty Hall problem: High school student puzzle

$\qquad$measurement is the metaphysical concept

5.6: Two envelope problem: High school student puzzle

$\qquad$"symmetrical" is non-sense without world description, Copernican revolution, Heliocentrism, Geocentric model

6.0: Confidence interval and statistical hypothesis testing ( Abstract )

$\qquad$"null hypothesis vs. alternative hypothesis" and "one-sided test and two-sided test"

6.1: Review: classical quantum language

$\qquad$Gauss integral, image observable, $\chi^2$-distribution,

6.2: The reverse relation between confidence interval and statistical hypothesis

$\qquad$ semi-metric, estimator and system quantity, rejection region

6.3(1): Population mean (Confidence interval and statistical hypothesis testing)

$\qquad$simultaneous normal measurement, Gauss integral,

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

$\qquad$"null hypothesis vs. alternative hypothesis" and "one-sided test and two-sided test

7.0: ANOVA(Analysis of variance) ( Abstract )

7.1: Zero way ANOVA (= Student $t$-distribution )

$\qquad$ $\;\;\; F$-distribution with $(1,n-1)$ degree of freedom= the student $t$-distribution with $(n-1)$ degree of freedom

7.2: The one way ANOVA

$\qquad$ $F$-distribution, Gayss integral,

7.3(1): The two way ANOVA

$\qquad$ $F$-distribution, Gayss integral,

7.3(2): The two way ANOVA

$\qquad$ $F$-distribution, Gayss integral,

7.4: Supplement (Gauss integral )

$\qquad$ $F$-distribution, Gayss integral,

8.0: Practical logic - Do you believe in syllogism?

$\qquad$Socrates is mortal

8.1: Marginal observable and quasi-product observable

$\qquad$quasi-product observable, projection observable,

8.2: Properties of quasi-product observables

$\qquad$ tomato

8.3: The definition of "implication "

$\qquad$ Contraposition

8.4: Cogito-- "I think, therefore I am" is doubtful

$\qquad$ Descartes figure, Heidegger, Augustinus, Bergson, What we cannot speak about we must pass over in silence.

8.5: Combined observable -- Only one measurement is permitted

$\qquad$ combined observable, Bell's inequality,

8.6: Syllogism-- Does Socrates die?

$\qquad$variants of syllogism,

8.7: Syllogism does not hold in quantum systems

$\qquad$ EPR-paradox, non-locality,

9.0: Mixed measurement theory ($\supset$Bayesian statistics)

9.1: Mixed measurement theory ( Bayesian statistics )

9.2: Simple examples in mixed measurements

$\qquad$ urn problem,

9.3: St. Petersburg two envelope problem

$\qquad$symmetricity

9.4: Bayesian statistics is to use Bayes theorem

$\qquad$Bayes theorem

9.5: Two envelope problem (Bayes' method)

$\qquad$Bayes theorem

9.6:Monty Hall problem ( Bayesian approach )

$\qquad$Bayes theorem

9.7:Monty Hall problem ( The principle of equal weight )

$\qquad$ the case that you throw dice

9.8: Averaging information ( Entropy )

$\qquad$ Shanon

9.9: Fisher statistics: Monty Hall problem [three prisoners problem]

$\qquad$ Descartes figure

9.10:Bayesian statistics: Monty Hall problem [three prisoners problem]

$\qquad$ Descartes figure

9.11: Equal probability: Monty Hall problem [three prisoners problem]

$\qquad$ Descartes figure

9.12: Bertrand's paradox( "randomness" depends on how you look at)

10.0: Causality (Abstract)

$\qquad$ Anti-realism

10.1: The most important unsolved problem---what is causality?

$\qquad$ Parmenides, Herakleitos, Aristotle, purpose, Galileo, Bacon, Hume, Kant, Copernican revolution,

10.2: Causality---Mathematical preparation

$\qquad$Causal operator, Heisenberg picture and the Schrödinger picture
10.2.2: Simple example---Finite causal operator is represented bymatrix

$\qquad$ Causal map, Heisenberg picture and the Schrödinger picture

10.3:Axiom 2---Smoke is not located on the place which does not have fire

$\qquad$ final cause, evolution theory, dialectic, entropy increase, multiple markov process, time-lag process

10.4: Kinetic equation (in classical mechanics and quantum mechanics)

$\qquad$Newtonian equation(=Hamilton's canonical equation), Schrödinger equation,Heisenberg's kinetic equation

10.5: Exercise:Solve Schrödinger equation by variable separation method

$\qquad$Schrödinger equation in a box

10.6:Random walk and quantum decoherence

$\qquad$non-deterministic causal operator

10.7: Leibniz=Clarke Correspondence: What is space-time?

$\qquad$ realistic view vs. linguistic view, Newton's absolutism , Leibniz's relationalism, McTaggart's paradox, Einstein=Bohr debates

11.0: Measurement and causality (Abstract)

$\qquad$ the relationship between measurement and causality

11.1: The Heisenberg picture and the Schrödinger picture

$\qquad$ Parmenides, there is no movement

11.2:Wave function collapse (= Projection postulate )

11.3:de Broglie's paradox(non-locality=faster-than-light)

$\qquad$ there is something faster than light

11.4: Quantum Zeno effect

$\qquad$ watched pot effect

11.5: Schrödinger's cat, Wigner's friend and Laplace's demon

$\qquad$Schrödinger's cat( quantum decoherence), Wigner's friend(What we cannot speak about we must pass over in silence)

11.6: Wheeler's Delayed choice experiment: "Particle or wave?" is a foolish question

$\qquad$What we cannot speak about we must pass over in silence

11.7: quantum eraser experiment

12.0: Realized causal observable in general theory

$\qquad$ the relationship between measurement and causality

12.1: Finite realized causal observable

$\qquad$ existence observable, Berkeley , Einstein and Tagore's conversation, exact observable,

12.2 Double-slit experiment

$\qquad$seni-ordered tree

12.3: Wilson cloud chamber in double slit experiment

$\qquad$approximately simultaneous measurement

12.4: Two kinds of absurdness ---idealism and dualism

$\qquad$A spectator does not go up to the stage, Fit feet to shoes, There are no facts, only interpretations. Click,

13.0: Fisher statistic (II)

$\qquad$ regression analysis, "inference" in the relation of "measurement" and "causality"

13.1: "Inference = Control" in quantum language

13.2: Regression analysis

$\qquad$ regression analysis $=$ inference $+$ realized causal operator

14.0: Classical causal relation

$\qquad$ Zeno's paradox

14.1: Infinite realized causal observable in classical systems

$\qquad$Kolmogorov extension theorem

14.2: Is Brownian motion a motion?

$\qquad$non-deterministic causal operator
14.3: The Schrödinger picture of the sequential deterministic causal operator

$\qquad$Why does Newtonian mechanics have measurement?

14.4 : Zeno's paradoxes---Flying arrow is not moving

$\qquad$ Zeno's pardox $\Leftrightarrow$ quantum language

15.0 :Least-squares method and Regression analysis

$\qquad$ explanational variable, response variable

15.1 The least squares method

$\qquad$ too easy, thus somewhat difficult

15.2: Regression analysis in quantum language

$\qquad$ classical deterministic causality, parallel measurement,

15.3: Regression analysis(distribution , confidence interval and statistical hypothesis testing)

$\qquad$ student-distribution

15.4: Generalized linear model

$\qquad$ explanational variable, response variable

16.0: Abstract (16.0: Kalman filter)

$\qquad$ classical non-deterministic causality in Bayesian statistics

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:The reliability in psychological test

$\qquad$ system error, measurement error, reliability

17.1: Reliability in psychological tests

$\qquad$ group test (=parallel measurement), test observable

17.1.3: Reliability coefficient

17.2: Correlation coefficient: How to calculate the reliability coefficient

18.0: how to describe "brief"

$\qquad$ odds

18.1: Belief, probability and odds

$\qquad$the " probability" that Japan will win the victory in the next FIFA World Cup

18.2: The principle of equal odds weight

$\qquad$Monty Hall problem

19.1 Two kinds of ( realistic and linguistic ) world- views

$\qquad$The necessariness of the philosophy of dualistic idearism

19.2: The summary of quantum language

$\qquad$The linguistic interpretation

19.3: Quantum language is located at the center of science

$\qquad$Dr. Hawking, Quantum language is only one useful philosophy

## Linguistic interpretation of quantum mechanics; Quantum language

#
**
Contents and key-words
**

**Contents and key-words**