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The Resource Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource)
Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource)
Resource Information
The item Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.This item is available to borrow from all library branches.
Resource Information
The item Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Manitoba Libraries.
This item is available to borrow from all library branches.
 Summary
 The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known nogo theorems: the impossibility to establish a finer description of microphenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum nonlocality). Also, possible applications of the contextual probabilistic model and its quantumlike representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed
 Language

 eng
 eng
 Edition
 1st ed. 2009.
 Extent
 1 online resource (378 p.)
 Note
 Description based upon print version of record
 Contents

 Quantum and Classical Probability
 Quantum Mechanics: Postulates and Interpretations
 Classical Probability Theories
 Contextual Probability and QuantumLike Models
 Contextual Probability and Interference
 QuantumLike Representation of Contextual Probabilistic Model
 Ensemble Representation of Contextual Statistical Model
 Latent QuantumLike Structure in the Kolmogorov Model
 Interference of Probabilities from Law of Large Numbers
 Bell’s Inequality
 Probabilistic Analysis of Bell’s Argument
 Bell’s Inequality for Conditional Probabilities
 Frequency Probabilistic Analysis of BellType Considerations
 Original EPRExperiment: Local Realistic Model
 Interrelation between Classical and Quantum Probabilities
 Discrete Time Dynamics
 Noncommutative Probability in Classical Disordered Systems
 Derivation of Schrödinger’s Equation in the Contextual Probabilistic Framework
 Hyperbolic Quantum Mechanics
 Representation of Contextual Statistical Model by Hyperbolic Amplitudes
 Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics
 Isbn
 9786612364853
 Label
 Contextual Approach to Quantum Formalism
 Title
 Contextual Approach to Quantum Formalism
 Statement of responsibility
 by Andrei Y. Khrennikov
 Language

 eng
 eng
 Summary
 The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell’s inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known nogo theorems: the impossibility to establish a finer description of microphenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell’s theorem (including quantum nonlocality). Also, possible applications of the contextual probabilistic model and its quantumlike representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed
 http://library.link/vocab/creatorName
 Khrennikov, Andrei Y
 Dewey number

 519.2
 530.12
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 MhlRmAI1Bsk
 Language note
 English
 LC call number
 QC173.96174.52
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Fundamental Theories of Physics,
 Series volume
 160
 http://library.link/vocab/subjectName

 Quantum theory
 Distribution (Probability theory
 Quantum Physics
 Elementary Particles, Quantum Field Theory
 Probability Theory and Stochastic Processes
 Quantum Information Technology, Spintronics
 Complex Systems
 Theoretical, Mathematical and Computational Physics
 Label
 Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p.325347) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Quantum and Classical Probability  Quantum Mechanics: Postulates and Interpretations  Classical Probability Theories  Contextual Probability and QuantumLike Models  Contextual Probability and Interference  QuantumLike Representation of Contextual Probabilistic Model  Ensemble Representation of Contextual Statistical Model  Latent QuantumLike Structure in the Kolmogorov Model  Interference of Probabilities from Law of Large Numbers  Bell’s Inequality  Probabilistic Analysis of Bell’s Argument  Bell’s Inequality for Conditional Probabilities  Frequency Probabilistic Analysis of BellType Considerations  Original EPRExperiment: Local Realistic Model  Interrelation between Classical and Quantum Probabilities  Discrete Time Dynamics  Noncommutative Probability in Classical Disordered Systems  Derivation of Schrödinger’s Equation in the Contextual Probabilistic Framework  Hyperbolic Quantum Mechanics  Representation of Contextual Statistical Model by Hyperbolic Amplitudes  Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics
 Dimensions
 unknown
 Edition
 1st ed. 2009.
 Extent
 1 online resource (378 p.)
 Form of item
 online
 Isbn
 9786612364853
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781402095931
 Specific material designation
 remote
 System control number

 (CKB)1000000000754171
 (EBL)450739
 (OCoLC)434090511
 (SSID)ssj0000129923
 (PQKBManifestationID)11139124
 (PQKBTitleCode)TC0000129923
 (PQKBWorkID)10100223
 (PQKB)10244917
 (SSID)ssj0000769070
 (PQKBManifestationID)12308381
 (PQKBTitleCode)TC0000769070
 (PQKBWorkID)10767625
 (PQKB)10545714
 (DEHe213)9781402095931
 (MiAaPQ)EBC450739
 (EXLCZ)991000000000754171
 Label
 Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p.325347) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 Quantum and Classical Probability  Quantum Mechanics: Postulates and Interpretations  Classical Probability Theories  Contextual Probability and QuantumLike Models  Contextual Probability and Interference  QuantumLike Representation of Contextual Probabilistic Model  Ensemble Representation of Contextual Statistical Model  Latent QuantumLike Structure in the Kolmogorov Model  Interference of Probabilities from Law of Large Numbers  Bell’s Inequality  Probabilistic Analysis of Bell’s Argument  Bell’s Inequality for Conditional Probabilities  Frequency Probabilistic Analysis of BellType Considerations  Original EPRExperiment: Local Realistic Model  Interrelation between Classical and Quantum Probabilities  Discrete Time Dynamics  Noncommutative Probability in Classical Disordered Systems  Derivation of Schrödinger’s Equation in the Contextual Probabilistic Framework  Hyperbolic Quantum Mechanics  Representation of Contextual Statistical Model by Hyperbolic Amplitudes  Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics
 Dimensions
 unknown
 Edition
 1st ed. 2009.
 Extent
 1 online resource (378 p.)
 Form of item
 online
 Isbn
 9786612364853
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781402095931
 Specific material designation
 remote
 System control number

 (CKB)1000000000754171
 (EBL)450739
 (OCoLC)434090511
 (SSID)ssj0000129923
 (PQKBManifestationID)11139124
 (PQKBTitleCode)TC0000129923
 (PQKBWorkID)10100223
 (PQKB)10244917
 (SSID)ssj0000769070
 (PQKBManifestationID)12308381
 (PQKBTitleCode)TC0000769070
 (PQKBWorkID)10767625
 (PQKB)10545714
 (DEHe213)9781402095931
 (MiAaPQ)EBC450739
 (EXLCZ)991000000000754171
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.lib.umanitoba.ca/portal/ContextualApproachtoQuantumFormalismby/gnnzuSsQV6k/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.lib.umanitoba.ca/portal/ContextualApproachtoQuantumFormalismby/gnnzuSsQV6k/">Contextual Approach to Quantum Formalism, by Andrei Y. Khrennikov, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.lib.umanitoba.ca/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.lib.umanitoba.ca/">University of Manitoba Libraries</a></span></span></span></span></div>