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Bibliographic Details
Main Author:	Khrennikov, Andrei 1958- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] de Gruyter 2009
Edition:	2., rev. and extended ed.
Subjects:	Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis
Links:	http://deposit.dnb.de/cgi-bin/dokserv?id=3194509&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017374045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Literaturverz. S. 205 - 214
Physical Description:	XX, 217 S. 25 cm
ISBN:	9783110207484

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Record in the Search Index

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adam_text	CONTENTS 1 FOUNDATIONS OF PROBABILITY THEORY 1 1 A FEW WORDS ABOUT MEASURES 1 2 CLASSICAL AND ENSEMBLE DEFINITIONS OF PROBABILITY 1 2.1 CLASSICAL DEFINITIONOF PROBABILITY 1 2.2 ENSEMBLE (PROPORTIONAL) DEFINITION OF PROBABILITY 2 3 FREQUENCY THEORY OF PROBABILITY 4 4 KOLMOGOROV S MEASURE-THEORETICAL THEORY 8 5 KOLMOGOROV S IDEAS ON PROBABILITY 10 6 MEASURE-THEORETICAL APPROACH AND INTERPRETATIONSOF PROBABILITY 16 6.1 ENSEMBLE-FREQUENCY INTERPRETATION 16 6.2 MEASURE-THEORETICAL APPROACH AND THE ENSEMBLE INTERPRETATION . . 17 6.3 MEASURE-THEORETICAL APPROACH AND FREQUENCY PROBABILITY 17 6.4 MEASURE-THEORETICAL APPROACH AND ENSEMBLE-FREQUENCY INTERPRE- TATION 18 7 SUBJECTIVE (BAYESIAN) PROBABILITY THEORY 21 8 FOUNDATIONS OFRANDOMNESS 23 8.1 EXISTENCE OF COLLECTIVES; KAMKE S OBJECTION 23 8.2 GEOMETRIE AND FREQUENCY SPACES 26 8.3 VILLE S OBJECTION 26 8.4 ENSEMBLE PROBABILITY APPROACH TO RANDOMNESS 27 8.5 KOLMOGOROV COMPLEXITY 27 9 OPERATION OF COMBINING OF COLLECTIVES 29 10 INDEPENDENCE OF COLLECTIVES 32 11 FREQUENCY AND MEASURE - THEORETICAL VIEWPOINTS ON INDEPENDENCE ... 33 12 GENERALIZATIONOF THE OPERATION OF COMBINING . 35 13 COMPARATIVE PROBABILITY 35 2 QUANTUM PROBABILITIES 37 1 CLASSICAL AND QUANTUM PROBABILITY RULES 37 1.1 PROPERTIESOF PHYSICAL SYSTEMS 37 1.2 REALISM 37 1.3 EMPIRICISM 38 1. BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991725050 DIGITALISIERT DURCH XVIII CONTENTS 2 INTERPRETATION OF WAVE FUNCTION 42 2.1 ENSEMBLE REALIST INTERPRETATION - EINSTEINIAN INTERPRETATION . . . . 42 2.2 INDIVIDUAL REALISTS INTERPRETATION - LENINGRAD INTERPRETATION . . . 43 2.3 ENSEMBLE EMPIRICISTS INTERPRETATION - BOHRIAN INTERPRETATION . . . 43 2.4 VAEXJOE INTERPRETATION 44 2.5 INDIVIDUAL EMPIRICISTS INTERPRETATION - DIRAC-VON NEUMANN INTER- PRETATION 45 2.6 INDIVIDUAL INTERPRETATION AND SUBJECTIVE PROBABILITY - FUCHSIAN IN- TERPRETATION 45 2.7 PREPARATION AND MEASUREMENT PROCEDURES 46 2.8 FILTERS - PREPARATION VIA SELECTION 47 2.9 PREPARATION AND MEASUREMENT PROCEDURES IN QUANTUM FORMALISM . 47 3 CONTRADICTION BETWEEN QUANTUM AND CLASSICAL PROBABILITY CALCULI . . . 48 3.1 ENSEMBLE APPROACH: DISTURBANCE EFFECTS 49 3.2 ENSEMBLE APPROACH: NO CONDITIONAL PROBABILITIES 50 3.3 FREQUENCY PROBABILITY VIEWPOINT TO QUANTUM PROBABILISTIC RULE . . 52 3.4 KOLMOGOROV FORMALISM AND QUANTUM MEASUREMENTS 54 3.5 INTERFERENCE 55 3.6 NON-ERGODIC INTERPRETATION OF QUANTUM MECHANICS 56 4 PROBABILITIES WITH RESPECT TO OBJECTIVE CONDITIONS 57 4.1 FREQUENCY PROBABILITIES 58 4.2 NO CONDITIONAL PROBABILITIES, NO BAYES FORMULA 59 5 EINSTEIN-PODOLSKY-ROSEN PARADOX: PROBABILITY, REALITY AND LOCALITY . . . 61 6 BELL S INEQUALITY 65 6. CONTENTS XIX 3 NEGATIVE PROBABILITIES 85 1 THE ORIGIN OF NEGATIVE PROBABILITIES IN THE ENSEMBLE AND FREQUENCY THEORIES 85 1.1 ENSEMBLE APPROACH: FLUCTUATIONSOF FINITEAPPROXIMATIONS 85 1.2 ENSEMBLE APPROACH: SPLIT OF CONVENTIONAL PROBABILITIES 85 1.3 FREQUENCY APPROACH: IRREGULARITY OF BEHAVIOUR OF FREQUENCIES ... 86 1.4 FREQUENCY APPROACH: SPLIT OF MISES PROBABILITIES 87 1.5 WHERE ARE NEGATIVE PROBABILITIES? 87 1.6 THE FORMULA OF TOTAL PROBABILITY AS AN AVERAGE PROCEDURE 88 1.7 NEGATIVE PROBABILITIES AND THE PRINCIPLE OF COMPLEMENTARITY . ... 90 1.8 HISTORY OF NEGATIVE PROBABILITIES IN PHYSICS 93 2 SIGNED PROBABILISTIC MEASURES AND EINSTEIN-PODOLSKY-ROSEN PARADOX 94 3 WIGNER PHASE-SPACE DISTRIBUTION AND NEGATIVE PROBABILITY 101 4 DIRAC S WORLD WITH NEGATIVE PROBABILITIES 107 5 NEGATIVE PROBABILITIES AND LOCALIZATION 110 4 P-ADIC PROBABILITY THEORY 113 1 NON-ARCHIMEDEAN NUMBER SYSTEMS; P-ADIC NUMBERS 115 2 FREQUENCY PROBABILITY THEORY 119 3 ENSEMBLE PROBABILITY . 122 3.1 ENSEMBLES OF INFINITE VOLUMES 122 3.2 THE RULES FOR WORKING WITH P-ADIC PROBABILITIES 126 3.3 NEGATIVE PROBABILITIES AND P-ADIC ENSEMBLE PROBABILITIES 130 4 MEASURES 131 5 P-ADIC PROBABILITY SPACE 137 5 TESTS FOR RANDOMNESS FOR P-ADIC PROBABILITY THEORY 140 1 P-ADI XX CONTENTS 2 5-SEQUENCES (COLLECTIVES) AND CORRESPONDING PROBABILITIES 166 3 FORMULA OF TOTAL PROBABILITY AND MEASURES OF SUPPLEMENTARITY 167 4 SUPPLEMENTARY PHYSICAL OBSERVABLES 171 5 PRINCIPLE OF SUPPLEMENTARITY 172 6 SUPPLEMENTARITY AND KOLMOGOROVNESS 173 7 QUANTUM-LIKE REPRESENTATION 178 1 TRIGONOMETRIE, HYPERBOLIC, AND HYPER-TRIGONOMETRIC CONTEXTS 178 2 QUANTUM-LIKE REPRESENTATION ALGORITHM - QLRA 180 2.1 PROBABILISTIC DATA ABOUT CONTEXT 180 2.2 CONSTRUCTION OF COMPLEX PROBABILISTIC AMPLITUDES . 181 3 HUBERT SPACE REPRESENTATION OF FE-OBSERVABLE . 183 3.1 BORN SRULE . 183 3.2 FUNDAMENTAL PHYSICAL OBSERVABLE: VIEWS OF DE BROGLIE AND BOEHM 183 3.3 6-OBSERVABLE AS MULTIPLICATION OPERATOR 184 3.4 INTERFERENCE 185 4 HUBERT SPACE REPRESENTATION OFA -OBSERVABLE 185 4.1 CONVENTIONAL QUANTUM AND QUANTUM-LIKE REPRESENTATIONS 185 4.2 A-BASIS FROM INTERFERENCE 186 4.3 NECESSARY AND SUFFICIENT CONDITIONS FOR BORN S RULE 187 4.4 CHOICE OF PROBABILISTIC PHASES 189 4.5 CONTEXTUAL DEPENDENCE OF A-BASIS 189 4.6 EXISTENCE OF QUANTUM-LIKE REPRESENTATION WITH BORN S RULE FOR BOTH REFERENCE OBSERVABLES 190 4.7 PATHOLOGIES 191 5 PROPERTIES OF MAPPING OF TRIGONOMETRIC CONTEXTS INTO COMPLEX AMPLITUDES 192 5.1 CLASSICAL-LIKE CONTEXTS 192 5.2 NON-INJECTIVITY OF REPRESENTATION MAP 193 6 NON-DOUBLY STOCHASTIC MATRIX: QUANTUM-LIKE REPRESENTATIONS 193 7
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author	Khrennikov, Andrei 1958-
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discipline	Physik Mathematik
edition	2., rev. and extended ed.
format	Book
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isbn	9783110207484
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publisher	de Gruyter
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spellingShingle	Khrennikov, Andrei 1958- Interpretations of probability Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd
subject_GND	(DE-588)4079013-7
title	Interpretations of probability
title_auth	Interpretations of probability
title_exact_search	Interpretations of probability
title_full	Interpretations of probability Andrei Khrennikov
title_fullStr	Interpretations of probability Andrei Khrennikov
title_full_unstemmed	Interpretations of probability Andrei Khrennikov
title_short	Interpretations of probability
title_sort	interpretations of probability
topic	Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd
topic_facet	Wahrscheinlichkeitstheorie Quantentheorie Probabilities Quantum theory p-adic analysis
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