Foundations and interpretation of quantum mechanics : in the light of a critical-historical analysis of the problems and of a synthesis of the results ; with a foreword by Giorgio Parisi

The aim of this book is twofold: to provide a comprehensive account of the foundations of the theory and to outline a theoretical and philosophical interpretation suggested from the results of the last twenty years.There is a need to provide an account of the foundations of the theory because recent experience has largely confirmed the theory and offered a wealth of new discoveries and possibilities. On the other side, the following results have generated a new basis for discussing the problem of the interpretation: the new developments in measurement theory; the experimental generation of “Schrödinger cats”; recent developments which allow, for the first time, the simultaneous measurement of complementary observables; quantum information processing, teleportation and computation.To accomplish this task, the book combines historical, systematic and thematic approaches. The Aim Of This Book Is Twofold: To Provide A Comprehensive Account Of The Foundations Of The Theory And To Outline A Theoretical And Philosophical Interpretation Suggested From The Results Of The Last Twenty Years. There Is A Need To Provide An Account Of The Foundations Of The Theory Because Recent Experience Has Largely Confirmed The Theory And Offered A Wealth Of New Discoveries And Possibilities. On The Other Side, The Following Results Have Generated A New Basis For Discussing The Problem Of The Interpretation: The New Developments In Measurement Theory; The Experimental Generation Of Schrodinger Cats; Recent Recent Developments Which Allow, For The First Time, The Simultaneous Measurement Of Complementary Observables; Quantum Information Processing, Teleportation And Computation. To Accomplish This Task, The Book Combines Historical, Systematic And Thematic Approaches.--book Jacket. Historical Premise 1 -- 1 Short Review Of Classical Canonical Formalism 9 -- I Basic Formalism And Extensions Of Quantum Mechanics 13 -- 2 Where The Problems Begin 17 -- 2.1 Quantum Postulate 17 -- 2.2 Physical Consequences Of The Quantum Postulate 21 -- 2.3 Examination Of The Quantum Postulate 23 -- 3 Basic Quantum Mechanics 25 -- 3.1 Antecedents And First Experimental Results 25 -- 3.2 First Attempts At An Independent Formalism 29 -- 3.3 Matrix Mechanics And Observables 30 -- 3.4 Wave Mechanics 33 -- 3.5 States, Density Matrices And Projectors 40 -- 3.6 Unitary Transformations 47 -- 3.7 Distribution And Characteristic Functions 51 -- 3.8 Particles Statistics And Pauli Exclusion Principle 54 -- 3.9 Spin Theory 55 -- 3.10 Symmetries And Groups 60 -- 3.11 Scattering Matrix And Propagators 62 -- 4 Relativistic Quantum Mechanics 67 -- 4.1 Poincare Group 67 -- 4.2 Klein/gordon And Dirac Equations 69 -- 4.3 Field Formalism 71 -- 4.4 Relativistic Scattering 73 -- 4.5 Localization 76 -- 5 Quantum Optics 79 -- 5.1 General Formalism 79 -- 5.2 Quantum Optics In Phase Space 85 -- 5.3 Q-optics Experimental Apparatus And Methods 93 -- Ii Copenhagen Interpretation 95 -- 6 First Interpretations Of Quantum Mechanics 99 -- 6.1 Schrodinger's Interpretation 99 -- 6.2 Heisenberg's First Interpretation 102 -- 6.3 Some Observations Concerning The Structure Of The Theory 103 -- 6.4 Born's Probabilistic Interpretation 104 -- 6.5 Ignorance And Statistical Interpretations 105 -- 6.6 Discussion Of The Ignorance And Statistical Interpretations 107 -- 7 Uncertainty Principle 117 -- 7.1 Heisenberg's Formulation 117 -- 7.2 Bohr's Interpretation Of The Principle 121 -- 7.3 Heisenberg's Interpretation: The Microscope Experiment 124 -- 7.4 Statistical Formulations Of The Uncertainty Principle 127 -- 7.5 Some Problems 128 -- 7.6 A New More General Formulation 131 -- 8 Complementarity Principle 135 -- 8.1 Definition Of Complementarity 135 -- 8.2 Complementarity Between Conjugate Observables 137 -- 8.3 Analysis Of The Wave/particle Dualism 138 -- 8.4 Complementarity Between Localization And Dynamic Laws 139 -- 8.5 Complementarity Between Separability And Phenomenon 142 -- 8.6 Conclusions On The Copenhagen Interpretation 150 -- Iii First Foundations Of Quantum Mechanics 151 -- 9 Qm Axiomatics 155 -- 9.1 Boolean Algebra And Some Other Technical Notions 155 -- 9.2 Qm Axiomatic And Quantum Logic 159 -- 9.3 Other Approaches 165 -- 9.4 Concluding Remarks On The Axiomatic 168 -- 9.5 Qm Logical Calculus 170 -- 10 Hilbert Spaces And Operators 173 -- 10.1 Is A Complex Hilbert Space Necessary? 173 -- 10.2 Time And Energy Operators 177 -- 10.3 Position Operator 187 -- 10.4 Angle Operator 189 -- 11 Classical And Quantum Probability: An Overview 191 -- 11.1 Introduction To The Concept Of Probability 191 -- 11.2 Classical Probability 194 -- 11.3 Qm Probability 196 -- 11.4 Generalization To S-dimensional Probabilities 197 -- 11.5 Gleason Theorem 199 -- 12 Geometric Phase 203 -- 12.1 Antecedents 203 -- 12.2 Berry's Contribution 205 -- 12.3 Generalization With Fiber Bundles 208 -- 12.4 Experiments And Conclusions 210 -- Iv Measurement Problem 211 -- 13 Some Preliminary Notions 215 -- 13.1 Measurement's Definition 215 -- 13.2 Elements Of The Measurement 215 -- 13.3 Steps Of The Measurement 215 -- 13.4 Premeasurement 216 -- 13.5 Types Of Measurement 217 -- 14 Von Neumann Theory And Its Refinements 219 -- 14.1 Von Neumann's Original Exposition 219 -- 14.2 Criticisms And Problems 231 -- 14.3 Value Reproducibility And Objectification 234 -- 15 Many World Interpretation 245 -- 15.1 Presentation Of The Interpretation 245 -- 15.2 Difficulties Of The Many-world Interpretation 248 -- 16 Solutions Using Classical Or Semiclassical Apparata 253 -- 16.1 Classicality As Superselection Rules 253 -- 16.2 Semiclassical Apparatus 256 -- 17 Decoherence 263 -- 17.1 A Recent And Yet Rich History 263 -- 17.2 Zurek's Solution 268 -- 17.3 Machida-namiki Model 279 -- 17.4 Cini's Model 281 -- 17.5 An Easy Computer Model 285 -- 17.6 Concluding Remarks On Decoherence 289 -- 18 Operational Stochastic Qm 291 -- 18.1 Fundamentals Of Operational Stochastic Quantum Mechanics 291 -- 18.2 Stochastic Analysis Of Non-commutativity And Complementarity 295 -- 18.3 Covariance, Conservation Laws And Measurement 297 -- 18.4 Sharpness And Unsharpness: Optimal Measurements 300 -- 18.5 Self-adjointness And Symmetry 301 -- 18.6 Informational Completeness And Measurement 302 -- 18.7 Statistical Treatment Of Definition And Observation 304 -- 18.8 Weak Measurement 311 -- 18.9 Discrimination Between Non-orthogonal States 316 -- 18.10 Stochastic Analysis Of Spin 317 -- 19 Non Demolition Measurement Theory 323 -- 19.1 Brief History 323 -- 19.2 More On The Measurement Process 324 -- 19.3 Indirect Measurement 326 -- 19.4 Principles Of Non-demolition Measurement 327 -- 19.5 Evaluation Of The Minimal Measurement Error 333 -- 19.6 Qnd-measurement And The Uncertainty Principle 335 -- 19.7 Experimental Context 339 -- 19.8 Zeno Paradox 339 -- 19.9 Boundaries Between Apparatus And Object 347 -- 20 Information Without Interaction 353 -- 20.1 Renninger's Experiment 353 -- 20.2 Interaction-free Interferometry 354 -- 20.3 More Recent Experiments 355 -- V Microphysics/macrophysics 359 -- Schrodinger's Analysis 361 -- A Short Discussion 362 -- 21 Decoherence And Thermodynamics 365 -- 21.1 Heat Baths And Master Equation 365 -- 21.2 Baths Of Harmonic Oscillators 369 -- 21.3 Damping 375 -- 21.4 Ignorance And Dynamics: Baths And Damping 378 -- 21.5 Unruh/zurek Model 379 -- 21.6 Another Model 382 -- 21.7 Measure Of Decoherence 386 -- 22 Quantum Jumps 393 -- 22.2 Interpretation Of Quantum Jumps And Trajectories 400 -- 22.3 Models And Experiments: Jumps As Telegraph Signals 401 -- 23 Reductions To Classical Case 403 -- 23.1 Classical Stochastic Theories 403 -- 23.2 Ghirardi/rimini/weber 408 -- 23.3 Stochastic Non-linear Jump-theories 411 -- 24 Generation Of The Cat 413 -- 24.1 How To Construct A Schrodinger Cat 413 -- 24.2 Short History 414 -- 24.3 Detailed Exposition Of A Performed Experiment 417 -- 24.4 Schrodinger Cats And Decoherence 422 -- Vi Time And Qm 429 -- 25 Consistent And Decohering Histories 433 -- 25.1 Consistent Histories 433 -- 25.2 Gell-mann/hartle's Model 435 -- 25.3 Yamada/takagi Theorem 441 -- 26 Delayed Choice 445 -- 26.1 Theoretical Problem 445 -- 26.2 Proposed Delayed Choice Experiments 447 -- 26.3 A Delayed Choice Performed Experiment 450 -- 26.4 Lessons Of The Delayed Choice 452 -- 27 Reversibility And Irreversibility 457 -- 27.1 A Spin Experiment 457 -- 27.2 Haunted Measurements 459 -- 27.3 Schrodinger Cats And Revival Behaviour 461 -- 27.4 Montecarlo Methods 463 -- Vii Wave/particle Dualism 467 -- 28 Reality Of Quantum Waves And States 471 -- 28.1 De Broglie's Pilot Wave 471 -- 28.2 Non-linear Solutions 478 -- 28.3 Empty Waves 482 -- 28.4 Meaning Of The Wave Function 489 -- 28.5 Measurement Of The Density Matrix 495 -- 28.6 Classical Waves Or Quantum Waves? 501 -- 29 Indeterminacy Of Quantum Waves And States 505 -- 29.1 Three-valued Logic 505 -- 29.2 Ontological Aspects 508 -- 30 Between Wave And Particle 513 -- 30.1 Wootters/zurek Gedankenexperiment 513 -- 30.2 Inequality Between Predictability And Visibility 516 -- 30.3 Stochastic Complementarity Visibility/predictability 521 -- 30.4 Beginning Of An Ontological Interpretation 525 -- Viii Completeness And Determinism 527 -- 31 Einstein/podolsky/rosen Argument 531 -- 31.2 Argument 534 -- 31.3 Bohm's Reformulation 536 -- 31.4 Wave Function And Density Matrix 538 -- 32 Examination And Interpretation Of Hidden Variable Theories 543 -- 32.1 Basic Definitions Of The Hidden Variable Problem 543 -- 32.2 First Proofs 544 -- 32.3 A Corollary Of The Gleason Theorem 547 -- 32.4 Kochen/specker Theorem 550 -- 32.5 Other Proofs 555 -- 32.6 Interpretation Of Hidden-variable Theories 556 -- 33 Stochastic Generalization 565 -- 33.1 General Statement Of The Problem 565 -- 33.2 Stochastic Quantum Mechanics In Phase Space 569 -- Ix Problem Of Non-locality 579 -- 34 Initial Criticisms Of The Einstein/podolsky/rosen Argument 583 -- 34.1 Schrodinger's Answer 583 -- 34.2 Bohr's Answer 584 -- 34.3 Bub's Formulation 585 -- 35 Bell Inequalities 589 -- 35.1 Second Bell Theorem 589 -- 35.2 Refinements Of Bell Theorem 592 -- 35.3 Experimental Tests 600 -- 35.4 Loopholes 607 -- 35.5 Fine's Theorems 615 -- 35.6 Hidden-variable Theories And Classicality 618 -- 36 Problem Of Separability As Such 621 -- 36.1 Stapp Theorem 621 -- 36.2 Problem Of Counterfactuals 624 -- 36.3 Relationship Between Stapp Theorem And Bell Theorem 625 -- 36.4 Other Proofs On The Same General Lines As Stapp's Proof 628 -- 36.5 Eberhard Theorem 633 -- 36.6 Hidden Variables And Lorentz Invariance 635 -- 36.7 Context-dependent Entanglement 640 -- 37 More Exact Bounds For The Inequalities 643 -- 37.1 Introduction To The Problem 643 -- 37.2 Tsirelson Theorem 643 -- 37.3 Landau Theorem 645 -- 37.4 Hillery/yurke Theorem 647 -- 37.5 Conditions For Separability 649 -- 38 Entanglement With Pure States And With Mixtures 651 -- 38.1 Pure States 651 -- 38.2 Mixed States 653 -- 38.3 Purification Procedures 657 -- 39 Generalized Bell Inequalities 659 -- 39.1 Pykacz/santos Theorems 659. Gennaro Auletta ; With A Foreword By Giorgio Parisi. Includes Bibliographical References (p. 803-932) And Indexes.

the Aim Of This Book Is Twofold: To Provide A Comprehensive Account Of The Foundations Of The Theory And To Outline A Theoretical And Philosophical Interpretation Suggested From The Results Of The Last Twenty Years. There Is A Need To Provide An Account Of The Foundations Of The Theory Because Recent Experience Has Largely Confirmed The Theory And Offered A Wealth Of New Discoveries And Possibilities. On The Other Side, The Following Results Have Generated A New Basis For Discussing The Problem Of The Interpretation: The New Developments In Measurement Theory; The Experimental Generation Of Schrodinger Cats; Recent Developments Which Allow, For The First Time, The Simultaneous Measurement Of Complementary Observables; Quantum Information Processing, Teleportation And Computation. To Accomplish This Task, The Book Combines Historical, Systematic And Thematic Approaches.

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aulette (u. La Sapienza, Rome I, Italy) Believes That The Theoretical And Experimental Developments Of Quantum Mechanics Over The Past Two Decades Has Permitted For The First Time The Testing Of A Number Of Philosophical Postulates And Assumptions That Were Made In The Field From The Beginning But Never Proved. Without Presuming To Forge A Unity Of Thinking, Or Wanting To Sacrifice The Richness Of Theoretical And Experimental Results To The Tyranny Of One, He Begins The Task Of Finding Some Points Of Convergence Between Different Areas And Approaches. His Critique Is Arranged Chronologically, Discussing Basic Formulations And Extensions, The Copenhagen Interpretation, First Foundations, The Measurement Problem, Microphysics And Macrophysics (including The Generation Of The Cat), Time, The Wave/particle Dualism, Completeness And Determinism, The Problem Of Non-locality, And Information. Annotation C. Book News, Inc., Portland, Or (booknews.com)