A uniqueness theorem for 'no collapse' interpretations of quantum mechanics

Studies in History and Philosophy of Science Part B - Studies in History and Philosophy of Modern Physics

Volumn 27, Issue 2, 1996, Pages 181-219

  Bub, Jeffrey ^a   Clifton, Rob ^b  

^a UNIVERSITY OF MARYLAND   (United States)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

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[No Author keywords available]

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EID: 0030160837     PISSN: 13552198     EISSN: 18792502     Source Type: Journal    
DOI: 10.1016/1355-2198(95)00019-4     Document Type: Article

References (90)

1. 1 P.A.M. Dirac, Quantum Mechanics (Oxford: Clarendon Press, 1958), 4th edn, pp. 46-47; J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton: Princeton University Press, 1955), p. 253.
2. 1 P.A.M. Dirac, Quantum Mechanics (Oxford: Clarendon Press, 1958), 4th edn, pp. 46-47; J. von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton: Princeton University Press, 1955), p. 253.
3. 2 See Dirac, op. cit., p. 36; and von Neumann, op. cit., pp. 351 and 418.
4. 2 See Dirac, op. cit., p. 36; and von Neumann, op. cit., pp. 351 and 418.
5. 3 E.g. D. Bohm and J. Bub, 'A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory', Reviews of Modern Physics 38 (1966), 470-469; G. C. Ghirardi, A. Rimini and T. Weber, 'Unified Dynamics for Microscopic and Macroscopic Systems', Physical Review D34 (1966), 470-491.
6. 3 E.g. D. Bohm and J. Bub, 'A Proposed Solution of the Measurement Problem in Quantum Mechanics by a Hidden Variable Theory', Reviews of Modern Physics 38 (1966), 470-469; G. C. Ghirardi, A. Rimini and T. Weber, 'Unified Dynamics for Microscopic and Macroscopic Systems', Physical Review D34 (1966), 470-491.
7. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
8. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
9. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
10. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
11. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
12. 4 The idea of a modal interpretation of quantum mechanics was first introduced by van Fraassen. [B. van Fraassen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', Synthese 42 (1979), 155-165; 'A Modal Interpretation of Quantum Mechanics', in E. Beltrametti and B. van Fraassen (eds), Current Issues in Quantum Logic (Singapore: World Scientific, 1981), pp. 229-258. See also B. van Fraassen, Quantum Mechanics: An Empiricist View (Oxford: Oxford University Press, 1991)]. We have in mind here specifically the interpretations developed by Kochen and by Dieks. [S. Kochen, 'A New Interpretation of Quantum Mechanics', in P. Lahti, and P. Mittelstaedt (eds), Symposium on the Foundations of Modern Physics (Singapore: World Scientific, 1985), pp. 151-169; D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', Foundations of Physics 19 (1989), 1397-1423; D. Dieks, 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', Physical Review A49 (1994), 2290-2300.]
13. 5 D. Bohm, 'A Suggested Interpretation of Quantum Theory in Terms of 'Hidden Variables': Parts I and II', Physical Review 85 (1952), 166-179, 180-193. Different formulations of Bohm's theory treat observables such as spin differently. We discuss these differences in Section 3.
14. 6 N. Bohr, Atomic Physics and Human Knowledge (New York: Wiley, 1958).
15. 7 S. Kochen and E. P. Specker, 'The Problem of Hidden Variables in Quantum Mechanics', Journal of Mathematics and Mechanics 17 (1967), 59-87.
16. 8 J. S. Bell, 'On the Problem of Hidden Variables in Quantum Mechanics', Reviews of Modern Physics 38 (1966), 447-475. Reprinted in Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987).
17. 9 J. S. Bell, 'On the Einstein-Podolsky-Rosen Paradox', Physics 1 (1964), 195-200. Reprinted in Speakable and Unspeakable in Quantum Mechanics, op. cit. Note that this article, published two years before the 1966 review article, was actually written after the review article.
18. 10 D. M. Greenberger, M. A. Horne and A. Zeilinger, 'Going Beyond Bell's Theorem', in M. Kafatos (ed.), Bell's Theorem, Quantum Theory, and Conceptions of the Universe (Dordrecht: Kluwer, 1989), pp. 73-76.
19. 11 L. Hardy, 'Quantum Mechanics, Local Realistic Theories, and Lorentz-Invariant Theories', Physical Review Letters 68 (1992), 2981-2984.
20. 12 The proof is unpublished. For a reference, see A. Peres, Quantum Theory: Concepts and Methods (Dordrecht: Kluwer, 1993), p. 197.
21. 13 A. Peres, op. cit., Chap. 7.
22. 14 M. Kernaghan, 'Bell-Kochen-Specker Theorem with 20 Vectors', Journal of Physics A: Math. Gen. 27 (1994), L829.
23. 15 R. Clifton, 'Getting Contextual and Nonlocal Elements of Reality the Easy Way', American Journal of Physics 61 (1993), 443-447.
24. 16 N. D. Mermin, 'Hidden Variables and the Two Theorems of John Bell', Reviews of Modern Physics 65 (1993), 803-815. Note that the Mermin proofs, which are conceptually very simple, are not nearly so economical as the Peres proofs in terms of the number of rays.
25. 17 See H. Brown, 'Bell's Other Theorem and its Connections with Nonlocality. Part I', in A. van der Merwe, F. Selleri and G. Tarozzi (eds), Bell's Theorem and the Foundations of Modern Physics (Singapore: World Scientific, 1992), pp. 104-116 for an interesting discussion of 'no-go' theorems, especially the Mermin proofs, and Peres, op. cit., p. 212, for an account of Penrose's 40-ray proof for a spin-3/2 system. See also J. Zimba and R. Penrose, 'On Bell Non-Locality Without Probabilities: More Curious Geometry', Studies in History and Philosophy of Modern Physics 24 (1993), 697-720.
26. 17 See H. Brown, 'Bell's Other Theorem and its Connections with Nonlocality. Part I', in A. van der Merwe, F. Selleri and G. Tarozzi (eds), Bell's Theorem and the Foundations of Modern Physics (Singapore: World Scientific, 1992), pp. 104-116 for an interesting discussion of 'no-go' theorems, especially the Mermin proofs, and Peres, op. cit., p. 212, for an account of Penrose's 40-ray proof for a spin-3/2 system. See also J. Zimba and R. Penrose, 'On Bell Non-Locality Without Probabilities: More Curious Geometry', Studies in History and Philosophy of Modern Physics 24 (1993), 697-720.
27. 17 See H. Brown, 'Bell's Other Theorem and its Connections with Nonlocality. Part I', in A. van der Merwe, F. Selleri and G. Tarozzi (eds), Bell's Theorem and the Foundations of Modern Physics (Singapore: World Scientific, 1992), pp. 104-116 for an interesting discussion of 'no-go' theorems, especially the Mermin proofs, and Peres, op. cit., p. 212, for an account of Penrose's 40-ray proof for a spin-3/2 system. See also J. Zimba and R. Penrose, 'On Bell Non-Locality Without Probabilities: More Curious Geometry', Studies in History and Philosophy of Modern Physics 24 (1993), 697-720.
28. 18 The uniqueness theorem supersedes earlier related results by one of us. See J. Bub, 'Quantum Mechanics Without the Projection Postulate', Foundations of Physics 22 (1992), 737-754; J. Bub, 'On the Structure of Quantal Proposition Systems', Foundations of Physics 24 (1994), 1261-1280; J. Bub, 'How to Interpret Quantum Mechanics', Erkenntnis 41 (1994), 253-273.
29. 18 The uniqueness theorem supersedes earlier related results by one of us. See J. Bub, 'Quantum Mechanics Without the Projection Postulate', Foundations of Physics 22 (1992), 737-754; J. Bub, 'On the Structure of Quantal Proposition Systems', Foundations of Physics 24 (1994), 1261-1280; J. Bub, 'How to Interpret Quantum Mechanics', Erkenntnis 41 (1994), 253-273.
30. 18 The uniqueness theorem supersedes earlier related results by one of us. See J. Bub, 'Quantum Mechanics Without the Projection Postulate', Foundations of Physics 22 (1992), 737-754; J. Bub, 'On the Structure of Quantal Proposition Systems', Foundations of Physics 24 (1994), 1261-1280; J. Bub, 'How to Interpret Quantum Mechanics', Erkenntnis 41 (1994), 253-273.
31. 19 J. S. Bell, 'On the Problem of Hidden Variables in Quantum Mechanics', op. cit.
32. 20 D. Bohm and J. Bub, 'A Refutation of the Proof by Jauch and Piron that Hidden Variables Can Be Excluded in Quantum Mechanics', Reviews of Modern Physics 38 (1966), 470-475.
33. 21 J. M. Jauch and C. Piron, 'Can Hidden Variables be Excluded in Quantum Mechanics?', Helvetica Physica Acta 36 (1963), 827-837.
34. 22 J. S. Bell, 'On the Problem of Hidden Variables in Quantum Mechanics', op. cit., p. 452.
35. 23 J. S. Bell, 'On the Einstein-Podolsky-Rosen Paradox', op. cit.
36. 24 Dirac, op. cit., p. 36; and von Neumann, op. cit., pp. 351 and 418.
37. 24 Dirac, op. cit., p. 36; and von Neumann, op. cit., pp. 351 and 418.
38. 25 The terminology is Van Fraassen's. See B. van Fraassen, Quantum Mechanics: An Empiricist View, op. cit., p. 275.
39. 26 B. van Fraassen, ibid., p. 279.
40. 27 First formulated in B. van Fraaasen, 'Hidden Variables and the Modal Interpretation of Quantum Statistics', op. cit.
41. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
42. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
43. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
44. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
45. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
46. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
47. 28 S. Kochen, 'A New Interpretation of Quantum Mechanics', op. cit.; H. Krips, The Metaphysics of Quantum Theory (Oxford: Clarendon Press, 1987); R. Healey, The Philosophy of Quantum Mechanics (Cambridge: Cambridge University Press, 1988); D. Dieks, 'Quantum Mechanics Without the Projection Postulate and Its Realistic Interpretation', op. cit.; 'Modal Interpretation of Quantum Mechanics, Measurements, and Macroscopic Behavior', op. cit.; J. Bub, 'Quantum Mechanics Without the Projection Postulate', op. cit.; 'How to Interpret Quantum Mechanics', op. cit.
48. 29 R. Clifton, 'Independently Motivating the Kochen-Dieks Modal Interpretation of Quantum Mechanics', British Journal for the Philosophy of Science 46 (1995), 33-57.
49. 30 R. Clifton, 'Independently Motivating the Kochen-Dieks Modal Interpretation of Quantum Mechanics', op. cit.
50. 31 The spectral measure of W is the Boolean algebra generated by SR(W).
51. 32 D. Bohm, 'A Suggested Interpretation of Quantum Theory in Terms of 'Hidden Variables': Parts I and II', op. cit.
52. 33 T. Epstein, 'The Causal Interpretation of Quantum Mechanics', Physical Review 89 (1952), 319 and Physical Review 91 (1953), 985.
53. 33 T. Epstein, 'The Causal Interpretation of Quantum Mechanics', Physical Review 89 (1952), 319 and Physical Review 91 (1953), 985.
54. 34 A. Stone, 'Does the Bohm Theory Solve the Measurement Problem?', Philosophy of Science 61 (1994), 250-266.
55. 35 D. Dieks, 'Modal Interpretations of Quantum Mechanics, Measurements, and Macroscopic Behavior' op. cit.; P.E. Vermaas, 'Unique Transition Probabilities in the Modal Interpretation', Studies in History and Philosophy of Modem Physics 27 (1996) 133-159; G. Bacciagaluppi and M. Dickson, 'Modal Interpretations with Dynamics', manuscript.
56. 35 D. Dieks, 'Modal Interpretations of Quantum Mechanics, Measurements, and Macroscopic Behavior' op. cit.; P.E. Vermaas, 'Unique Transition Probabilities in the Modal Interpretation', Studies in History and Philosophy of Modem Physics 27 (1996) 133-159; G. Bacciagaluppi and M. Dickson, 'Modal Interpretations with Dynamics', manuscript.
57. 35 D. Dieks, 'Modal Interpretations of Quantum Mechanics, Measurements, and Macroscopic Behavior' op. cit.; P.E. Vermaas, 'Unique Transition Probabilities in the Modal Interpretation', Studies in History and Philosophy of Modem Physics 27 (1996) 133-159; G. Bacciagaluppi and M. Dickson, 'Modal Interpretations with Dynamics', manuscript.
58. 36 The symbol 'R' here should not, of course, be confused with the symbol 'R' for the preferred determinate observable.
59. 37 J. C. Vink, 'Quantum Mechanics in Terms of Discrete Beables', Physical Review A48 (1993), 1808-1818.
60. 38 J. S. Bell, 'Beables for Quantum Field Theory', in Speakable and Unspeakable in Quantum Mechanics, op. cit., pp. 173-180. See pp. 176-177.
61. 39 In J. S. Bell, 'Beables for Quantum Field Theory', op. cit.
62. 40 E. Nelson, 'Derivation of the Schrödinger Equation from Newtonian Mechanics', Physical Review 150 (1966), 1079-1085.
63. 41 For a discussion, see J. Bub, 'Interference, Noncommutativity, and Determinateness in Quantum Mechanics', Topoi 14 (1995), 39-43.
64. 42 D. Bohm, R. Schiller and J. Tiomno, 'A Causal Interpretation of the Pauli Equation', Suppl. Nuovo Cimenta 1 (1955), 48-66.
65. 43 C. Dewdney, 'Constraints on Quantum Hidden-Variables and the Bohm Theory', Journal of Physics A: Math. Gen. 25 (1992), 3615-3626.
66. 44 P. R. Holland and J. P. Vigier, The Quantum Potential and Signalling in the Einstein-Podolsky-Rosen Experiment', Foundations of Physics 18 (1988), 741-749.
67. 45 D. Bohm and B. J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory (London: Routledge, 1993).
68. 46 J. S. Bell, 'Quantum Mechanics for Cosmologists'; and 'On the Impossible Pilot Wave', in Speakable and Unspeakable in Quantum Mechanics, op. cit.
69. 47 D. Dürr, S. Goldstein and N. Zanghi, 'Quantum Equilibrium and the Origin of Absolute Uncertainty', Journal of Statistical Physics 67 (1992), 843-907.
70. 48 D. Albert, Quantum Mechanics and Experience (Cambridge, MA: Harvard University Press, 1992).
71. 49 J. T. Cushing, Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony (Chicago: University of Chicago Press, 1994).
72. 50 C. Pagonis and R. Clifton, 'Unremarkable Contextualism: Dispositions in the Bohm Theory', Foundations of Physics 25 (1995), 281-296.
73. 51 A. R. Swift and R. Wright, 'Generalized Stern-Gerlach Experiments and the Observability of Arbitrary Spin Operators', Journal of Mathematical Physics 21 (1980), 77-82.
74. 52 D. Bohm, Quantum Theory (Englewood Cliffs, NJ: Prentice-Hall, 1951).
75. 53 See Chap. 6, 'Measurement as a Special Case of Quantum Process', in D. Bohm and B. J. Hiley, The Undivided Universe: An Ontological Interpretation of Quantum Theory, op. cit., pp. 97-133.
76. 54 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, op. cit., p. 41.
77. 55 A. Einstein, B. Podolsky and N. Rosen, 'Can Quantum-Mechanical Description of Physical Reality be Considered Complete?', Physical Review 47 (1935), 777-780.
78. 56 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge: Cambridge University Press, 1987), p. 174.
79. 57 D. Bohm and B. J. Hiley, The Undivided Universe: An Onlological Interpretation of Quantum Theory op. cit., p. 41.
80. 58 A. Einstein, in Albert Einstein: Philosopher-Scientist, P.A. Schilpp (ed.) (Illinois: Open Court, 1991), 3rd edn, pp. 681-682.
81. 59 A. Einstein, Dialectica 2 (1948), 320-324. Translated as 'Quantum Mechanics and Reality', in M. Born (ed.), The Born-Einstein Letters (London: Walker & Co., 1971), p. 192.
82. 59 A. Einstein, Dialectica 2 (1948), 320-324. Translated as 'Quantum Mechanics and Reality', in M. Born (ed.), The Born-Einstein Letters (London: Walker & Co., 1971), p. 192.
83. 60 A . Fine, The Shaky Game: Einstein, Realism, and the Quantum Theory (Chicago: University of Chicago Press, 1986).
84. 61 M. Jammer, The Philosophy of Quantum Mechanics (New York: Wiley, 1974).
85. 62 A. Einstein, in M. Born (ed.), The Born-Einstein Letters (London: Walker & Co., 1971), p. 192.
86. 63 J. S. Bell, Speakable and Unspeakable in Quantum Mechanics, op. cit., p. 89.
87. 64 N. Bohr, Dialectica 2 (1948), 312-319.
88. 65 W. Pauli, Dialectica 2 (1948), 307-311.
89. 66 It could also be argued that the complementarity interpretation does not really solve the measurement problem, unlike the other 'no collapse' interpretations we have been discussing (excluding the orthodox Dirac-von Neumann interpretation), since Bohr gives no measurement-independent prescription for what R should be taken to be. We concentrate on recovering other aspects of this interpretation, once Bohr's choice of R is granted.
90. 67 See Bohr, op. cit., p. 316.