## What is the Copenhagen interpretation? --- Linguistic Copenhagen Interpretation of Quantum Mechanics; Quantum language (by Shiro. ISHIKAWA; Keio university)

Recently I proposed gquantum languageh (or,g the linguistic Copenhagen interpretation of quantum mechanicsh), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology and the dualistic turn of statistics. Namely, quantum language is the scientific final goal of dualistic idealism. It has a great power to describe classical systems as well as quantum systems. Thus, I believe that quantum language is the language in which science is written. Our present purpose is to examine and assert our belief (i.e.,gscientific proposition can be written by quantum langaugeh). I believe that our research is one of the most important themes of philosophy of science.

CONTENTS
§ 1 [Animistic worldview] → [Mechanical worldview] → [Linguistic worldview]

We have a more than 3000-year history concerning the research of worldviews. And this study has been always located at the central position of science and philosophy. The first paradigm shift (i.e., the leap from "the animistic worldview (life dwells on things) " of the Middle Ages) is the mechanical worldview, which was owed to Galileo, Bacon, Descartes, Newton, and so on. This paradigm shift is very powerful, and hence, it opened the door from the Middle Ages to the Modern Ages (see ① in Fig.1). Here, the mechanical word view is characterized as.

(A): Study every (non-physical) science, modeled on physics. It is simple, but, as the norm of the best description of the world, it has dominated the modern science until today.
If it be so, everyone may dream to propose the scond paradigm shift, however, it may not be easy. In fact, it is not difficult to enumerate shattered dreams such as catastrophe theory, fuzzy theory, complex system theory, chaos theory and so on. However, It is not stopped that we strive against instinct of liking to tell "grand narratives". That is, we cannot stop to investigate the paradigm shift.
Here we assert that the linguistic worldview in Fig. 1 due to the quantum language (=measurement theory), which is the final stage of the linguistic series in Fig. 1, is the scond paradigm shift.

§ 2 The beginning of things: Heisenberg's uncertainty principle

Our starting point is the discovery ( 20 years ago) of the mathematical formulation of Heisenberg's uncertainty principle (cf. ref. [1]). This discovery urged us to investigate the following problem:

(B):        What is quantum mechanics?     Or, what is the standard interpretation of quantum mechanics?

Quantum mechanics has various interpretations ( such as the Copenhagen interpretation, the many worlds interpretation, etc.). This fact may be negligible in applications. But it is serious for the formulation of Heisenberg's uncertainty principle. That is, the "errors" depend on the interpretation (e.g., the wavefunction collapse is accepted or not?) ). Thus, we now think that we should have argued about Heisenberg's uncertainty relation under a certain firm interpretation of quantum mechanics in ref. [1].

§ 3 In the beginning was the word --- the miraculous power of language ---

Quantum mechanics was born about 90 years ago. However, we may be possessed with the surprising prejudice. That is, we may convince "Quantum mechanics is physics." Writing the conclusion first, we say that the linguistic worldview (i.e., the in Fig. 1) is,

 (C): In the beginning there exists the language called "quantum language". And world is described and constructed by the language.

(cf. Refs.[2, 3]). Although the explanation of quantum language is omitted here, it suffices to consider that it is composed of two spells (concerning "measurement" and "causality") and the linguistic interpretation. What we can do in quantum language (=measurement theory) is only to trust in man's linguistic competence. Fig 1 says that quantum language has the following three aspects:

 [⑦ Fig 1]: The ture colors of the Copenhagen interpretation. That is, the Copenhagen interpretation does not belong to physics!    (Even if "the true quantum mechanics" exists in the direction of ⑤, I believe that it is the relativistic quantum mechanics that does not need "interpretation") [⑧ Fig 1]: The final goal of the dualistic idealism ( Descartes=Kant philosophy) [⑨ Fig 1]: Theoretical statistics of the future

This language has a great power to describe ordinary phenomena as well as quantum phenomena. For example, economics is created by describing economical phenomena in quantum language.

Also,

• economics is created by describing economical phenomena in quantum language.
• quantum mechanics is created by describing quantum phenomena in quantum language.
• psychology is created by describing psychological phenomena in quantum language.
• EEEEEEEEEEEEE

(see Fig 2). We assert that this is the true picture of quantum mechanics, and we are convinced that this is just the answer to the question (B). Therefore, the "⑦ →" in Fig. 1 is a historical circumstance. and thus, the true direction is the "← ⑦"(where we consider the usual quantum mechanics and not the quantum physics beyond the ⑤ in Fig. 1). That is, (C)=[Fig.2]=(D), namely,
 (D):
Thus, the linguistic worldview (C) (= in Fig. 1) asserts that

• Science (more precisely, non-physical science) is to describe the world by quantum language.

Therefore,

• the metaphysics called quantum language is located in the center of science.

Again note that the linguistic worldview (C) (= in Fig. 1)is due to the great human's power of linguistics.

If quantum mechanics is regarded as physics, we cannot understand the reason that there are several paradoxes and interpretations in quantum mechanics. For example, we think that Schrödinger's cat does not live in the linguistic worldview since it can not be described by quantum mechanics. (Recall Wittgenstein's saying: "The limits of my language mean the limits of my world"). Also, we consider that the dualism is not fit for physics. Such idea is not only due to us but also Einstein, who never regarded quantum mechanics as physics.

§ 4 Mechanical worldview (A) vs. linguistic worldview (C)

For example, some philosophers has been studying "Achilles and the tortoise (cf. the above (D))" during about 2500 years. If you think that they are too stupid to understand the geometric series, you are an ordinary person, i.e., the believer of the mechanical worldview (A). That is, you do not know that the philosophers has been making efforts to discover another worldview rather than the mechanical worldview (A) (cf. [11]). Also, under the mechanical worldview (A), we cannot answer the question "What is statistics? or "What is (non-physical) space-time?" That is, the quantum language is necessary to answer these questions (cf. [7-9, 12-14]). Moreover, we cannot understand the dualistic idealism (in the main stream of the philosophy) without the linguistic worldview (C) (cf. [4,14]). This is the reason that there are no understandable books concerning dualistic idealism. Since unsolved problems are easily solved under the (C), we believe that the linguistic worldview (C) is superior to the mechanical worldview(A). Also, it should be noted that the mechanical worldview (A) has no room in Fig. 1. Thus, it is improper to consider the mechanical worldview (A) as a kind of worldview.
Dr. Hawking said in his best seller book [A Brief History of Time: From the Big Bang to Black Holes, Bantam, Boston, 1990]:
 (E): Philosophers reduced the scope of their inquiries so much that Wittgenstein the most famous philosopher this century, said "The sole remaining task for philosophy is the analysis of language." What a comedown from the great tradition of philosophy from Aristotle to Kant!

We think that this is not only his opinion but also most scientists' opinion. However, we do not agree to his opinion, since we know the development such as "Kant ⇒ Wittgenstein ⇒ The linguistic worldview " in Fig. 1.

§ 5 The end of grand narratives --- 3000-year final answer ---

Now we believe that the proof of "the ⑩ in Fig. 1" has been almost completed. Therefore, the countdown of the two ends of grand narratives (⑤ and ⑩ in Fig.1) started. In the above sense (i.e., the linguistic series acquires the linguistic worldview (C)), we dare to declare

"the happy end of grand narratives"

However, science has already rushed into post modern time[=the ages of small narratives = the ages of sciences(i.e., engineering, social sciences, bio, etc.) in (D)]. Thus, we think that science is not over.

[References]
The refs. [2,3,4,24,27,29] may be easiest to understand. The [24 (or 23), 29] clarified the similaities and differences between so called Copenhagen interpretation and the linguistic interpretation. Also, [8] is the text for undergraduate students. Almost all my outcomes are written in the preprints [26, 28] (the lecture note of the master course in Dept of Math. Keio university).

My favorite papers are [24,29], which can be read without the knowledge of quantum language [25].

 [1]: S. Ishikawa, "Uncertainty Relations in Simultaneous Measurements for Arbitrary Observables," Rep. Math. Phys., Vol. 29, No. 3, pp. 257-273 (1991) doi: 10.1016/0034-4877(91)90046-P, [PDF download]
 [2]: S. Ishikawa, "A New Interpretation of Quantum Mechanics," Journal of Quantum Information Science, Vol. 1 No. 2, 2011, pp. 35-42. doi: 10.4236/jqis.2011.12005 ( download free)
 [3]: S. Ishikawa, "The linguistic interpretation of quantum mechanics," arXiv:1204.3892v1[physics.hist-ph] , (2012) ( download free)
 [4]: S. Ishikawa, "Quantum Mechanics and the Philosophy of Language: Reconsideration of Traditional Philosophies," Journal of quantum information science, Vol. 2, No. 1, 2012, pp.2-9. doi: 10.4236/jqis.2012.21002 ( download free)
 [5]: S. Ishikawa, "Fuzzy Inferences by Algebraic Method," Fuzzy Sets and Systems, Vol. 87, No. 2, 1997, pp.181-200. doi: 10.1016/S0165-0114(96)00035-8 , [PDF download]
 [6]: S. Ishikawa, "A Quantum Mechanical Approach to Fuzzy Theory," Fuzzy Sets and Systems, Vol. 90, No. 3, 1997, pp. 277-306. doi: 10.1016/S0165-0114(96)00114-5 , [PDF download]
 [7]: S. Ishikawa, "Statistics in measurements," Fuzzy sets and systems, Vol. 116, No. 2, 141-154 (2000). doi:10.1016/S0165-0114(98)00280-2 , [PDF download]
 [8]: S. Ishikawa, "Mathematical Foundations of Measurement Theory," Keio University Press Inc. 335pages, 2006. http://www.keio-up.co.jp/kup/mfomt/
 [9]: S. Ishikawa, "A Measurement Theoretical Foundation of Statistics," Applied Mathematics, Vol. 3, No. 3, 2012, pp. 283-292. doi: 10.4236/am.2012.33044 ( download free)
 [10]: S. Ishikawa, "Ergodic Hypothesis and Equilibrium Statistical Mechanics in the Quantum Mechanical World View," World Journal of Mechanics, Vol. 2, No. 2, 2012, pp. 125-130. doi:10.4236/wjm.2012.22014 ( download free)
 [11]: S. Ishikawa, "Zeno's paradoxes in the Mechanical World View," arXiv:1205.1290v1 [physics.hist-ph] , (2012) ( download free)
 [12]: SS. Ishikawa, "Monty Hall Problem and the Principle of Equal Probability in Measurement Theory," Applied Mathematics , Vol. 3, No. 7, 2012, pp. 788-794. doi:10.4236/am.2012.37117 ( download free)
 [13]: S. Ishikawa, "What is statistics?; The Answer by Quantum Language," arXiv:1207.0407v1 [physics.data-an] , 2012 ( download free)
 [14]: S. Ishikawa: "Measurement Theory in the Science of Philosophy," arXiv:1209.3483v1[physics.hist-ph] ,( 2012) (download free)
 [15]: S. Ishikawa: "Heisenberg uncertainty principle and quantum Zeno effects in the linguistic interpretation of quantum mechanics," http://arxiv.org/abs/1308.5469[quant-ph] ,( 2013) (download free)
 [16]: S. Ishikawa: "A quantum linguistic characterization of the reverse relation between confidence interval and hypothesis testing," http://arxiv.org/abs/1401.2709[math.ST] ,( 2014) (download free)
 [17]: S. Ishikawa: "ANOVA (analysis of variance) in the quantum linguistic formulation of statistics," http://arxiv.org/abs/1402.0606[math.ST] ,( 2014) (download free)
 [18]: S. Ishikawa: "Regression analysis in quantum language," http://arxiv.org/abs/1403.0060[math.ST] ,( 2014) (download free)
 [19]: S. Ishikawa, K. Kikuchi: "Kalman filter in quantum language," http://arxiv.org/abs/1404.2664[math.ST] ,( 2014) (download free)
 [20]: S. Ishikawa: "The double-slit quantum eraser experiments and Hardy's paradox in the quantum linguistic interpretation," http://arxiv.org/abs/1407.5143[quantum-ph] ,( 2014) (download free)
 [21]: S. Ishikawa: "The Final Solutions of Monty Hall Problem and Three Prisoners Problem," arXiv:1408.0963v1 [stat.OT] ,( 2014) (download free)
 [22]: S. Ishikawa: "The two envelopes paradox in non-Bayesian and Bayesian statistics," arXiv:1408.4916v4 [stat.OT] ,( 2014) (download free)
 [23]: S. Ishikawa: "Linguistic interpretation of quantum mechanics: Quantum language," KSTS/RR-15/001 [Reseach Report; Keio Math] ,( 2015), 416 pages (download free) or, KSTS/RR-15/001 [S. Ishikawa]
 [24]: S. Ishikawa, "Linguistic interpretation of quantum mechanics; Projection Postulate," Journal of Quantum Information Science, Vol. 5 No. 4, 2015, pp. 150-155. DOI: 10.4236/jqis.2015.54017 (download free)    Also, see Reseach Report; Keio Math [KSTS/RR-15/009](S. Ishikawa ). ( download free) ,arXiv:1511.07777 [physics.gen-ph] ,( 2015), (download free)
[25]: S. Ishikawa: "Linguistic interpretation of quantum mechanics: Quantum language [ver. 2]," Research Report, Keio Math. [KSTS/RR-16/001] ,( 2016), 426 pages (download free) or, Research Report, Keio Math. [KSTS/RR-16/001] (S. Ishikawa)
S. Ishikawa: "Linguistic interpretation of quantum mechanics: Quantum language [ver. 3]," Research Report, Keio Math. [KSTS/RR-17/007] ,( 2017), 426 pages (download free) or, Research Report, Keio Math. [KSTS/RR-17/007] (S. Ishikawa)
The html version is seen in the right side bar. Also, this preprint is the draf of the following book.
 ♦ Shiro Ishikawa, "Linguistic Interpretation of Quantum Mechanics - Towards World-Description in Quantum Language -" Shiho-Shuppan Publisher 2016, ( 405 pages)
 [26]: S. Ishikawa: "History of Western Philosophy from the quantum theoretical point of view," Reseach Report; Keio Math [KSTS/RR-16/005] ,( 2016), 141 pages (download free) or, Reseach Report; Keio Math [KSTS/RR-16/005](S. Ishikawa )    or,   Philpapers (2016)
 [27]: S. Ishikawa: "A final solution to the mind-body problem by quantum language" Journal of quantum information science, Vo.7 No.2 2017, 48-56 (download free), The preprint is as follows: Reseach Report; Keio Math [KSTS/RR-17/003](S. Ishikawa )(download free),
 [28]: S. Ishikawa: "History of Western Philosophy from the quantum theoretical point of view, Versin 2" Reseach Report; Keio Math [KSTS/RR-17/004](S. Ishikawa ) ,( 2017), 139 pages (download free)
 [29]: S. Ishikawa: "Bell's inequality should be reconsidered in quantum language" Journal of quantum information science, Vo.7 No.4 2017, 140-154 (download free), The preprint is as follows: Reseach Report; Keio Math [KSTS/RR-17/006](S. Ishikawa )(download free),
 [30]: S. Ishikawa: "Leibniz-Clarke Correspondence, Brain in a Vat, Five-Minute Hypothesis, McTaggartfs Paradox, etc. Are Clarified in Quantum Language" Open Journal of philosophy, Vo.8 No.5 2018, 466-480 (download free),
 [31]: S. Ishikawa: "Leibniz-Clarke Correspondence, Brain in a Vat, Five-Minute Hypothesis, McTaggartfs Paradox, etc. Are Clarified in Quantum Language [Revised version]" Keio Reseach report; 2018; KSTS/RR-18/001, 1-15
 [32]: S. Ishikawa: "Linguistic Copenhagen interpretation of quantum mechanics: Quantum language [ver. 4]," Research Report, Keio Math. [KSTS/RR-18/002] ,( 2018), 430 pages (download free) or, Research Report, Keio Math. [KSTS/RR-18/002] (S. Ishikawa) This [32] is compilation of "quantum language" in the present

Linguistic Copenhagen interprettion of quantum mechanics ( Shiro Ishikawa; Keio University )

Shiro Ishikawa, "Linguistic Copenhagen Interpretation of Quantum Mechanics : Quantum language [ver.4]" KSTS/RR-18/002 (2018, Research Report in Dept. Math. Keio Univ.)

:[English PDF]+ [English HTML]+ [Japanese HTML]+ [Japanese PDF; KOARA(c䃁fBA) 2018]

0.1: Preface[Japanese PDF; KOARA 2018]
1.0: 1.0:Feynman's question1.0:t@C}mւ̉[Japanese PDF; KOARA 2018]
1.1:Quantum language(1.1:ʎq)
1.2(1):Axioms 1 and 2 (measurement and causality ) and interpretation: y1.2(1):ꃋ[12(ƈʊ֌W)Ƃ̉߁z
1.2(2):Linguistic interpretationy1.2(2):I(Ryn[Q)߁z
1.2(3):Summaryy1.2(3):vz
1.3:Example (Hot or Cold?)y1.3:(MH@₽H)z
2.0: Axiom 1( measurement ); Abstract 2.0: ꃋ[1()z[Japanese PDF; KOARA 2018]
2.1: Basic structure $[{\mathcal A} \subseteq$ $\overline{\mathcal A} \subseteq B(H)]$( General Theory)y2.1: {\$[{\mathcal A} \subseteq$ $\overline{\mathcal A} \subseteq B(H)]$(ʘ_)z
2.2: Quantum basic structure $[{\mathcal C}(H) \subseteq$ $B(H) \subseteq B(H)]$y2.2: ʎq{\$[{\mathcal C}(H) \subseteq$ $B(H) \subseteq B(H)]$z
2.3: Classical basic structure $[C_0(\Omega ) \subseteq$ $L^\infty ( \Omega, \nu ) \subseteq B(H)]$y2.3: ÓT{\$[C_0(\Omega ) \subseteq$ $L^\infty ( \Omega, \nu ) \subseteq B(H)]$z
2.4: State and observabley2.4: ԂƊϑʁz
2.5: Examples of observablesy2.5: ϑʂ̗z
2.6: System quantityy2.6: VXeʁz
2.7: Axiom 1 ; No science without measurementsy2.7: ꃋ[1G薳āAȊwz
2.8: Classicalexamples ( urn problem, etc.) y2.8: ÓTn̗(, etc.) z
2.9: Stern=Gerlach experimenty2.9: Ve=Qbn̎z
3.0: Linguistic interpretation; Abstract y3.0:I;AuXgNgz[Japanese PDF; KOARA 2018]
3.1: The linguistic interpretationy3.1:I(Ryn[Q)߁z
3.2: Tensor operator algebray3.2:e\͍pf㐔z
3.3.1: Only one observabley3.3.1:ϑʂ͈z
3.3.2: state doesnot movey3.3.2:Ԃ͓Ȃz
3.3.3: Only one state y3.3.3:Ԃ͈ z
4.0: Linguistic interpretation; quantum systemsy4.0:I;ʎqnz[Japanese PDF; KOARA 2018]
4.1: Kolmogorov extension theoremy4.1:RSt̊g藝z
4.2: The law of large numbersy4.2:吔̖@z
4.3.1: Why is Heisenberg's uncertainty principle famous?y4.3.1:nC[xO̕sm萫͉̗LȂ̂Hz
4.3.2: Mathematical formulation of Heisenberg's uncertainty principley4.3.2:nC[xO̕sm萫̐wI莮z
4.3.3: except approximately simultaneous measurementy4.3.3:nC[xO̕sm萫jꍇz
4.5: Bell's inequalirty y4.5: x̕sz
5.0: Fisher statistics (abstract)y5.0:tBbV[vwz[Japanese PDF; KOARA 2018]
5.1: Urn problemy5.1:z
5.2: Fisher's maximum likrlihoof methody5.2:tBbV[̍Ŗޖ@z
5.3: Examples of Fisher's maximum likrlihoof methody5.3:tBbV[̍Ŗޖ@̗z
5.4: Moment method y5.4:[g@z
5.5: Monty Hall problem: High school student puzzle y5.5:eBz[:ZpYz
5.6: Two envelope problem: High school student puzzle y5.6:̕:ZpYz
6.0: Confidence interval and statistical hypothesis testing y6.0:MԂƉz
6.1: Review: classical quantum language y6.1:K: ÓTʎqz
6.2: The reverse relation between confidence interval and statistical hypothesis y6.2:MԂƉ̋t֌Wz
6.3(1): Population mean (Confidence interval and statistical hypothesis testing)y6.3(1):ꕽ(I:MԂƉ)z
6.3(2): Population mean (Confidence interval and statistical hypothesis testing) y6.3(2):ꕽ(II:MԂƉ) z
6.4(1): Population variance (Confidence interval and statistical hypothesis testing)y6.4(1):ꕪU(I:MԂƉ)z
6.4(2): Population variance (Confidence interval and statistical hypothesis testing) y6.4(2):ꕪU(II:MԂƉ)z
6.5: Difference of population means (Confidence interval and statistical hypothesis y6.5:ꕽς̍(MԂƉ)z
6.6: Student $t$-distribution of population meany6.6:ꕽς̃X[fg$t$-zz
7.0: ANOVA(Analysis of variance) ( Abstract )y7.0:ANOVA(U):AuXgNgz
7.1: Zero way ANOVA (= Student $t$-distribution )y7.1: 댳U(=X[fg$t$-z)z
7.2: The one way ANOVA y7.2: ꌳÚz
7.3(1): The two way ANOVAy7.3(1):񌳕U(I)z
7.3(2): The two way ANOVA y7.3(2):񌳕U(II)z
7.4: Supplement (Gauss integral ) y7.4:(KEXϕ) z
8.0: Practical logic - Do you believe in syllogism?y8.0:H_ - Oi_@M܂? z[Japanese PDF; KOARA 2018]
8.1: Marginal observable and quasi-product observable y8.1:ӊϑʂƋ[ϊϑʁz
8.2: Properties of quasi-product observablesy8.2: [ϊϑʂ̐z
8.3: The definition of "implication "y8.3:"܈"̒z
8.4: Cogito-- I think, therefore I amy8.4: RMg---vÂɂ݂z
8.5: Combined observable -- Only one measurement is permittedy8.5: ϑ -- ͈񂾂z
8.6: Syllogism-- Does Socrates die? y8.6: Oi_@-- \NeX͎ʂ? z
8.7: Syllogism does not hold in quantum systemsy8.7: Oi_@͗ʎqnłNGz
9.0: Mixed measurement theory ($\supset$Bayesian statistics)y9.0:($\supset$xCYv)z[Japanese PDF; KOARA 2018]
9.1: Mixed measurement theory ( Bayesian statistics ) y 9.1:($\supset$xCYv)z
9.2: Simple examples in mixed measurementsy9.2:̊ȒPȗz
9.3: St. Petersburg two envelope problemy9.3:ZgyeXuO̓̕z
9.4: Bayesian statistics is to use Bayes theoremy9.4:xCYvƂ̓xCY̒藝gƁz
9.5: Two envelope problem (Bayes' method)y9.5:̕(xCY̕@)z
9.6:Monty Hall problem ( Bayesian approach )y9.6:eBz[(xCY̕@)z
9.7:Monty Hall problem ( The principle of equal weight ) y9.7:eBz[(m̌) z
9.8: Averaging information ( Entropy )y9.8:Ϗ(Ggs[ )z
9.9: Fisher statistics: Monty Hall problem [three prisoners problem]y9.9:tBbV[v: eBz[ [Ol̖]z
9.10:Bayesian statistics: Monty Hall problem [three prisoners problem] y9.10:xCYvF eBz[ [Ol̖]z
9.11: Equal probability}: Monty Hall problem [three prisoners problem] y9.11:m̌: eBz[ [Ol̖] z
9.12: Bertrand's paradox( "randomness" depends on how you look at)y9.12:xg̃phbNX( "_"͌)z
10.0: Causality (Abstract)y10.0:ʊ֌Wz[Japanese PDF; KOARA 2018]
10.1: The most important unsolved problem---what is causality?y10.1:ʊ֌WƂ͉H---Ȋw̍ŏdvz
10.2: Causality---Mathematical preparation y10.2:ʊ֌W---wIz
10.2.2: Simple example---Finite causal operator is represented bymatrixy10.2.2:ȒPȗ---s\z
10.3:Axiom 2---Smoke is not located on the place which does not have firey10.3:ꃋ[2---΂̂ȂƂɉ͗Ȃz
10.4: Kinetic equation (in classical mechanics and quantum mechanics)y10.4:(ÓTnƗʎqn)^z
10.5: Exercise:Solve Schrödinger equation by variable separation methody10.5:K:ϐ@ɂV[fBK[̉z
10.6:Random walk and quantum decoherencey10.6:ƗʎqfRq[Xz
10.7: Leibniz=Clarke Correspondence: What is space-time? y10.7:Ƃ͉H---Cvjbc=N[N_z
11.0: Measurement and causality (Abstract)y11.0:Pƈʊ֌Wz[Japanese PDF; KOARA 2018]
11.1: The Heisenberg picture and the Schrödinger picturey11.1:nC[xOƃV[fBK[z
11.2: Wave function collapse ( = Projection postulate )y11.2:ˉe@( g̎k)z
11.4: Quantum Zeno effecty11.4:ʎq[mʁz
11.5: Schrödinger's cat, Wigner's friend and Laplace's demony11.5:V[fBK[̔LAEBOi[̗FlAvẌz
11.6: Wheeler's Delayed choice experiment: "Particle or wave?" is a foolish questiony11.6:EB[[̒xI: "q org?"͋z
12.0: Realized causal observable in general theoryy12.0:ʊϑz[Japanese PDF; KOARA 2018]
12.1: Finite realized causal observabley12.1: Lʊϑʁz
12.2 Double-slit experiment y12.2 dXbg z
12.3: Wilson cloud chamber in double slit experimenty12.3: EB\̖z
12.4: Two kinds of absurdness ---idealism and dualismy12.4: 񌳘_ƊϔO_̃gf ---z
13.0: Fisher statistic (II)y13.0:tBbV[v (II)z[Japanese PDF; KOARA 2018]
13.1: "Inference = Control" in quantum languagey13.1: " = "Ǝvz
13.2: Regression analysisy13.2: A={ʊϑʁz
14.0: Regression analysisy14.0:ÓTʊ֌W{ z[Japanese PDF; KOARA 2018]
14.1: Infinite realized causal observable in classical systemsy14.1: ʊϑʁz
14.2: Is Brownian motion a motion?y14.2: uE^Ƃ͉?z
14.3: The Schrödinger picture of the sequential deterministic causal operatory14.3: Iʍpf̃V[fBK[z
14.4 : Zeno's paradoxes---Flying arrow is not moving y14.4 : [m̃phbNX---ALXƋTz
15.0: Least-squares method and Regression analysisy15.0 :ŏ@ƉÁFAuXgNgz
15.1 The least squares methody15.1 ŏ@FȒPēz
15.2: Regression analysis in quantum languagey15.2: ŏ@A͂ցz
15.3: Regression analysis(distribution , confidence interval and statistical hypothesis testing)y15.3: A(z,M,)z
15.4: Generalized linear modely15.4: ʐ`fz
16.0: Kalman filter y16.0:J}tB^[FAuXgNg Abstract (16.0: Kalman filter)z
16.1: Bayes=Kalman method (in $L^\infty(\Omega, m)$)y16.1: xCYJ}̕@(in $L^\infty(\Omega, m)$)z
16.2: Problem establishment (concrete calculation)y16.2: J}tB^[̖ݒ(̓IvZ)z
16.3: Bayes=Kalman operatory16.3: xCYJ}pfz
16.4: Calculation: prediction part y16.4: vZ: \ z
16.5: Calculation: Smoothing party16.5: vZ: z
17.0: Equilibrium statistical mechanics [Japanese PDF; KOARA 2018]

17.1: Equilibrium statistical mechanics (Causality)
17.2: Equilibrium statistical mechanics (Probability)
18.0: The reliability in psychological test y17.0:SvFAuXgNgz
18.1: Reliability in psychological tests y17.1: SeXg̐M z
18.1.3: Reliability coefficienty17.1.3: Sv̐MWz
18.2: Correlation coefficient: How to calculate the reliability coefficient
19.0: How to describe "brief"y18.0: "MO"̊mFAuXgNgz
19.1: Belief, probability and oddsy18.1: MO, m, IbYz[Japanese PDF; KOARA 2018]
19.2: The principle of equal odds weighty18.2: m̌(II)z
20.1: Two kinds of ( realistic and linguistic ) world- viewsy19.1 ƂF@̐ELq@(ݓIƌI)z[Japanese PDF; KOARA 2018]
20.2: The summary of quantum language y19.2: ʎq̂܂Ƃ z
20.3: Quantum language is located at the center of sciencey19.3: ȊwƂ́AʎqŘbƁz