QUANTUM PROBABILITY

References

[1]

L. Accardi, F. Frigerio and V. Gorini (eds.): Quantum Probability and Applications to the Quantum Theory of Irreversible Processes, Lecture Notes in Mathematics, Vol. 1055, Springer Verlag, Berlin-Heidelberg, 1984 

[2]

L. Accardi and W. von Waldenfells, (eds.): Quantum Probability and Applications, Lecture Notes in Mathematics, Vol. 1303, Springer Verlag, Berlin-Heidelberg, 1988 

[3]

L. Accardi and W. von Weidenfells (eds.): Quantum Probability and Applications, Lecture Notes in Mathematics, Vol. 1442, Springer Verlag, Berlin-Heidelberg, 1990 

[4]

W.L. Harper and C.A. Hooker (eds.): Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science, D. Reidel Publishing Co. Dordrecht, Holland, 1976 

[5]

L.E. Szabó: Is quantum mechanics compatible with a deterministic universe? Two interpretations of quantum probabilities. Foundations of Physics Letters 8 (1995) 421-440

EXPERIMENTAL TESTS OF BELL-TYPE THEOREMS

References

[1]

A. Aspect, P. Grangier and G. Roger: Experimental tests of realistic local theories via Bell's theorem Physical Review Letters 47 (1981) 460-467 

[2]

A. Aspect, P. Grangier and G. Roger: Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell's inequalities Physical Review Letters 48 (1982) 91-94 

[3]

A. Aspect, J. Dalibard and G. Roger: Experimental tests of Bell's inequalities using time-varying analyzers Physical Review Letters 49 (1982) 1804-1807 

[4]

J.F. Clauser, M.A. Horne and A. Shimony: Bell's theorem: experimantal tests and implications Reports on Progress in Physics 41 (1978) 1881-1927

BELL-TYPE THEOREMS AND HIDDEN VARIABLES

References

[1]

F.J. Belinfante: A Survey of Hidden Variable Theories, Pergamon Press, Oxford, 1973 

[2]

J.S. Bell (1964): On the Einstein-Podolsky-Rosen paradox Physics 1 (1964) 196-200 (reprinted in [5]) 

[3]

J.S. Bell (1966): On the problem of hidden variables in quantum mechanics Reviews in Modern Physics 38 (1966) 447-475 (reprinted in [5]) 

[4]

J.S. Bell: Introduction to the hidden variable question in Proceedings of the Interantional School of Physics ``Enrico Fermi", Course 49, ``Foundations of Quantum Mechanics", B. Espagnat (ed.), Academic Press, New York-London, 1971, 171-181 (reprinted in [5]) 

[5]

J.S. Bell: Speakable and unspeakable in quantum mechanics, Cambridge University Press, Cambridge, 1987 

[6]

J. Butterfield: A space-time approach to the Bell inequality in GENERAL [3] 114-144 

[7]

J. Butterfield: David Lewis Meets John Bell Philosophy of Science 59 (1992) 26-43 

[8]

J. Butterfield: Bell's Theorem: What it Takes British Journal for the Philosophy of Science 58 (1992) 41-83 

[9]

J. Butterfield: Outcome dependence and stochastic Einstein nonlocality in GENERAL [10] 385-424 

[10]

R. Clifton: Getting contextual and nonlocal elements-of-reality the easy way American Journal of Physics 61 (1993) 443-447 

[11]

G. Hellman: Einstein and Bell: Strengthening the case for microphysical randomness Synthese 53 (1982) 445-460 

[12]

G. Hellman: Stochastic Einstein-locality and the Bell theorems Synthese 53 (1982) 461-504. 

[13]

L.J. Landau: On the violation of Bell's inequality in quantum theory Physics Letters A120 (1987) 54-56 

[14]

L.E. Szabo, A. Fine: A local hidden variable theory for the GHZ experiment arXhiv.org/abs/quant-ph/0007102 

[15]

L.E. Szabo: A continuum local hideen variable model for the EPR experiments arXhiv.org/abs/quant-ph/0012042

LOGIC AND ALGEBRA OF QUANTUM MECHANICS

References

[1]

J.L. Bell and R.K. Clifton: Quasi-Boolean algebras and simultaneously definite properties in quantum mechanics International Journal of Theoretical Physics 34 (1985) 2409-2421 

[2]

G. Birkhoff and J. von Neumann: The logic of quantum mechanics Annals of Mathematics 37 (1936) 823-843 in [13] 105-125 

[3]

M. Florig and S.J. Summers: On the statistical independence of algebras of observables Journal of Mathematical Physics 38 (1997) 1318-1328 

[4]

S. Kochen and E. Specker: The problem of hidden variables in quantum mechanics Journal of Mathematics and Mechanics 17 (1967) 59-67 

[5]

M. Pavicic: Bibliography on quantum logic International Journal of Theoretical Physics 31 (1992) 373-461 

[6]

M. Rédei: Quantum Logic in Algebraic Approach, Dordrecht: Kluwer Academic Publishers, 1998 

[7]

J. von Neumann: On rings of operators III Annals of Mathematics 41 (1940) 94-161 in [12] 6-119 

[8]

J. von Neumann: Continuous Geometry, Princeton University Press, Princeton, 1960 

[9]

J. von Neumann: Continuous geometries with transition probability Memoirs of the American Mathematical Society 34 No. 252 (1981) 1-210. 

[10]

J. von Neumann: Collected Works Vol. I. Logic, Theory of Sets and Quantum Mechanics, A.H. Taub (ed.), Pergamon Press, 1962 

[11]

J. von Neumann: Collected Works Vol. II. Operators, Ergodic Theory and Almost Periodic Functions in a Group, A.H. Taub (ed.), Pergamon Press, 1962 

[12]

J. von Neumann: Collected Works Vol. III. Rings of Operators, A.H. Taub (ed.), Pergamon Press, 1961 

[13]

J. von Neumann: Collected Works Vol. IV. Continuous Geometry and Other Topics, A.H. Taub (ed.), Pergamon Press, 1961

BRANCHING APPROACH TO BELL'S THEOREMS

References

[1]

N. Belnap: Branching space-time Synthese 92 (1992) 385-434 

[2]

N. Belnap and L.E. Szabó: Branching space-time analysis of the GHZ theorem Foundations of Physics 26 (1996) 989-1002 

[3]

T. Kowalski, T. Placek: Outcomes in branching space-time and GHZ-Bell theorems British Journal for the Philosophy of Science 50 (1999) 349-375 

[4]

T. Placek: Stochastic outcomes in branching spaec-time: analysis of Bell's theorem British Journal for the Philosophy of Science 51 (2000) 445-475

BELL'S THEOREMS IN QUANTUM FIELD THEORY

References

[1]

J. Butterfield: Vacuum correlations and outcome dependence in algebraic quantum field theory in GENERAL [4] 768-785 

[2]

R. Clifton, H. Halvorson: Generic Bell correlation between arbitrary local algebras in quantum field theory Journal of Mathematical Physics 41 (2000) 1711-1717 

[3]

R. Clifton, H. Halvorson, A. Kent: Non-local correlations are generic in infinite dimensional bipartite systems Physical Review A 61 (2000) 

[4]

F. Muller and J. Butterfield: Is algebraic relativistic quantum field theory stochastic Einstein local? Philosophy of Science 61 (1994) 457-474 

[5]

M. Rédei: Reichenbach's Common Cause Principle and quantum field theory Foundations of Physics 27 (1997) 1309-1321 

[6]

M. Rédei: Bell's inequalities, relativistic quantum field theory and the problem of hidden variables Philosophy of Science 58 (1991) 628-638 

[7]

S.J. Summers and R. Werner: The vacuum violates Bell's inequalities Physics Letters A110 (1985) 257-259 

[8]

S.J. Summers and R. Werner: Maximal violation of Bell's inequalities is generic in quantum field theory Communications in Mathematical Physics 110 (1987) 247-259 

[9]

S.J. Summers and R. Werner: Bell's inequalities and quantum field theory.I. General setting. Journal of Mathematical Physics 28 (1987) 2440-2447 

[10]

S.J. Summers and R. Werner: Bell's inequalities and quantum field theory.II. Bell's inequalities are maximally violated in the vacuum Journal of Mathematical Physics 28 (1987) 2448-2456 

[11]

S.J. Summers and R. Werner: Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions Annales de l'Institut Henri Poincaré - Physique theorique 49 (1988) 215-243 

[12]

S.J. Summers: Bell's inequalities and quantum field theory in [3] 393-413 

[13]

S.J. Summers: On the independence of local algebras in quantum field theory Reviews in Mathematical Physics 2 (1990) 201-247 

[14]

S.J. Summers and R. Werner: On Bell's inequalities and algebraic invariants Letters in Mathematical Physics 33 (1995) 321-334

PROBABILISTIC CAUSALITY

References

[1]

G. Fleming and J. Butterfield: Is there superluminal causation in quantum theory? in [14] 203-207 

[2]

G. Hofer-Szabó, M. Rédei and L.E. Szabó: On Reichenbach's common cause principle and Reichenbach's notion of common cause The British Journal for the Philosophy of Science 50 (1999) 377-3999 

[3]

M. Rédei: Reichenbach's Common Cause Principle and quantum field theory Foundations of Physics 27 (1997) 1309-1321 

[4]

M. Rédei: Are prohibitions of superluminal causation by stochastic Einstein locality and by absence of Lewisian probabilistic counterfactual causation equivalent? Philosophy of Science 60 (1993) 608-618 

[5]

M. Rédei: Is there counterfactual superluminal causation in relativistic quantum field theory? in GENERAL [2] 29-42 

[6]

H. Reichenbach: The Direction of Time, University of California Press, Los Angeles, 1956

[7]

W.C. Salmon: Probabilistic causality Pacific Philosophical Quarterly 61 (1980) 50-74 

[8]

P. Suppes and M. Zanotti: On the determinism of hidden variables with strict correlation and conditional statistical independence in GENERAL [15] 

[9]

B.C. Van Fraassen: When is a correlation not a mystery? in GENERAL [7] 113-128 

[10]

B.C. Van Fraassen: The charybdis of realism: epistemological implications of Bell's inequality in GENERAL [3] 97-113

GENERAL

References

[1]

E.G. Beltrametti and G. Cassinelli: The Logic of Quantum Mechanics, Addison-Wesley, 1981 

[2]

R. Clifton (ed.): Perspectives on Quantum Reality: Relativistic, Non-Relativistic and Field Theoretic, Kluwer Academic Publishers, 1966 

[3]

J. Cushing and E. McMullin (eds.): Philosophical Consequences of Quantum Theory, University of Notre Dame Press, Notre Dame, IN, 1989 

[4]

D.M. Greenberger and A. Zeilinger (eds.): Fundamental Problems in Quantum Theory, Annals of the New York Academy of Sciences, 755 (1994) 

[5]

R. Haag: Local Quantum Physics. Fields, Particles, Algebras, Springer Verlag, Berlin, 1992 

[6]

M. Jammer: The Philosophy of Quantum Mechanics, Wiley Interscience, New York, 1974 

[7]

P. Lahti and P. Mittelstaedt (eds.): Symposium on the Foundations of Modern Physics, World Scientific, Singapore, 1985 

[8]

D. Lewis: Counterfactuals, Blackwell, Oxford, 1973 

[9]

D. Lewis: Collected Papers. Volume II., Oxford University Press, Oxford, 1986 

[10]

D. Prawitz and D. Westerdahl (eds.): Logic and Philosophy of Science in Uppsala, Kluwer, Dordrecht, Holland, 1994 

[11]

M. Redhead: Incompleteness, Non-locality and Realism: Prolegomenon to the Philosophy of Quantum Mechanics, Claredon Press, Oxford, 1987 

[12]

B.C. van Fraassen: Quantum Mechanics: An Empiricist View , Claredon Press, Oxford, 1991 

[13]

J. von Neumann Mathematische Grundlagen der Quantenmechanik, Springer Verlag, Heidelberg, 1932 

[14]

A. Van Der Merwe, F. Selleri and G. Tarozzi (eds.): Bell's Theorem and the Foundations of Modern Physics, World Scientific, Singapore, 1992 

[15]

P. Suppes (ed.): Logic and Probability in Quantum Mechanics, D. Reidel Publishing Co. Dordrecht, Holland, 1976

[16]

H. R. Brown, E. Sjoeqvist, G. Bacciagaluppi: Remarks on identical particles in de Broglie-Bohm theory,  quant-ph/9811054 

[17]

G. Bacciagaluppi, M. Dickson: Dynamics for Density Operator Interpretations of Quantum Theory,  quant-ph/9711048 

[18]

L. Henderson: Two-state teleportation,  quant-ph/9910028 

[19]

L. Henderson, V. Vedral: Information: Relative Entropy of Entanglement and Irreversibility, quant-ph/9909011 

[20]

F. Laudisa: The EPR Argument in a Relational Interpretation of Quantum Mechanics, quant-ph/0011016 

[21]

F. Laudisa: A Note on Nonlocality, Causation and Lorentz-Invariance, PSA98  -  PDF