Gravity, Energy Conservation, and Parameter Values in Collapse Models

Foundations of Physics

Volumn 26, Issue 3, 1996, Pages 291-305

  Pearle, Philip ^a   Squires, Euan ^b  

^a HAMILTON COLLEGE   (United States)

^b DURHAM UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010706415     PISSN: 00159018     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02069474     Document Type: Article

References (34)

1. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
2. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
3. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
4. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
5. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
6. This prescription is crude because it is based upon the undefined notion of measurement by an apparatus to determine which events can occur and upon the imprecise statement "after the measurement is completed" to indicate when the event and its accompanying collapse take place (note that the Born rule gives, not an absolute probability per second of an event, but rather the conditional probability of an event if one occurs). The currently fashionable "decoherence" schemes provide no essential improvement, possessing comparable undefined and imprecise features. See, e.g., F. Dowker and A. Kent, Phys. Rev. Lett. 75, 3038 (1995); I. Giardina and A. Rimini, "On the existence of inequivalent classical domains," Pavia preprint FNT/T-95/22; P. Pearle, A. J. Phys. 35, 742 (1967) and in Quantum-Classical Correspondence, Proceedings of the 4th Drexel Symposium on Quantum Nonintegrability, D. H. Feng and B. L. Hu, eds. (World Scientific, Singapore, 1995); E. Squire, in Stochastic Evolution of Quantum States in Open Systems and in Measurement Processes, L. Diosi and B. Lukacs, eds. (World Scientific, Singapore, 1994); A. Venugopalan, Phys. Rev. A 50, 2742 (1994).
7. P. Pearle, Phys. Rev. A 39, 2277 (1989).
8. G. C. Ghirardi, P. Pearle, and A. Rimini, Phys. Rev. A 42, 78 (1990).
9. G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 167; P. Pearle, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 193; G. C. Ghirardi and P. Pearle, in Proceedings of the Philosophy of Science Foundation 1990, Volume 2, A. Fine, M. Forbes, and L. Wessels, eds. (PSA Association, Michigan, 1992), p. 19 and p. 35; P. Pearle, in The Interpretation of Quantum Theory: Where Do We Stand, L. Accardi, ed. (Istituto della Enciclopedia Italiana, Roma, 1994), p. 187.
10. G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 167; P. Pearle, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 193; G. C. Ghirardi and P. Pearle, in Proceedings of the Philosophy of Science Foundation 1990, Volume 2, A. Fine, M. Forbes, and L. Wessels, eds. (PSA Association, Michigan, 1992), p. 19 and p. 35; P. Pearle, in The Interpretation of Quantum Theory: Where Do We Stand, L. Accardi, ed. (Istituto della Enciclopedia Italiana, Roma, 1994), p. 187.
11. G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 167; P. Pearle, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 193; G. C. Ghirardi and P. Pearle, in Proceedings of the Philosophy of Science Foundation 1990, Volume 2, A. Fine, M. Forbes, and L. Wessels, eds. (PSA Association, Michigan, 1992), p. 19 and p. 35; P. Pearle, in The Interpretation of Quantum Theory: Where Do We Stand, L. Accardi, ed. (Istituto della Enciclopedia Italiana, Roma, 1994), p. 187.
12. G. C. Ghirardi and A. Rimini, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 167; P. Pearle, in Sixty-Two Years of Uncertainty, A. Miller, ed. (Plenum, New York, 1990), p. 193; G. C. Ghirardi and P. Pearle, in Proceedings of the Philosophy of Science Foundation 1990, Volume 2, A. Fine, M. Forbes, and L. Wessels, eds. (PSA Association, Michigan, 1992), p. 19 and p. 35; P. Pearle, in The Interpretation of Quantum Theory: Where Do We Stand, L. Accardi, ed. (Istituto della Enciclopedia Italiana, Roma, 1994), p. 187.
13. (6) and indeed one factor in their choice of parameters was to keep it below experimental limits.
14. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986); Phys. Rev. D 36, 3287 (1987); Found. Phys. 18, 1 (1988); J. S. Bell, in Schrodinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987) and in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.
15. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986); Phys. Rev. D 36, 3287 (1987); Found. Phys. 18, 1 (1988); J. S. Bell, in Schrodinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987) and in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.
16. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986); Phys. Rev. D 36, 3287 (1987); Found. Phys. 18, 1 (1988); J. S. Bell, in Schrodinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987) and in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.
17. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986); Phys. Rev. D 36, 3287 (1987); Found. Phys. 18, 1 (1988); J. S. Bell, in Schrodinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987) and in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.
18. G. C. Ghirardi, A. Rimini, and T. Weber, Phys. Rev. D 34, 470 (1986); Phys. Rev. D 36, 3287 (1987); Found. Phys. 18, 1 (1988); J. S. Bell, in Schrodinger-Centenary Celebration of a Polymath, C. W. Kilmister, ed. (Cambridge University Press, Cambridge, 1987) and in Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 167.
19. T. W. B. Kibble, in Quantum Gravity II, A Second Oxford Symposium, C. J. Isham, R. Penrose, and D. W. Sciama, eds. (Clarendon Press, Oxford, 1981), p. 63.
20. D. N. Page and C. D. Geilker, Phys. Rev. Lett. 47, 979 (1981).
21. L. Diosi, Phys. Rev. A 40, 1165 (1989).
22. G. C. Ghirardi, R. Grassi, and A. Rimini, Phys. Rev. A 42, 1057 (1990).
23. This energy gain is compensated by a loss of gravitational potential energy supplied by the vacuum. The appearance of, e.g., a Planck mass monopole means that the vacuum supplies both the Planck mass-energy and the (negative) monopole-particle mutual gravitational energy. The energy gain of a particle during its brief period of acceleration by the monopole comes from a decrease of this mutual gravitational energy. Thus, the subsequent absorption of the monopole by the vacuum entails a net loss of gravitational energy of the vacuum.
24. F. Karolyhazy, Nuovo Cimento A 42, 1506 (1966); F. Karolyhazy, A Frenkel, and B. Lukacs, in Physics as Natural Philosophy, A. Slumony and H. Feshbach, eds. (M.I.T. Press, Cambridge, 1982), p. 204; in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon, Oxfod, 1986), p. 109; A. Frenkel, Found. Phys. 20, 159 (1990).
25. F. Karolyhazy, Nuovo Cimento A 42, 1506 (1966); F. Karolyhazy, A Frenkel, and B. Lukacs, in Physics as Natural Philosophy, A. Slumony and H. Feshbach, eds. (M.I.T. Press, Cambridge, 1982), p. 204; in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon, Oxfod, 1986), p. 109; A. Frenkel, Found. Phys. 20, 159 (1990).
26. F. Karolyhazy, Nuovo Cimento A 42, 1506 (1966); F. Karolyhazy, A Frenkel, and B. Lukacs, in Physics as Natural Philosophy, A. Slumony and H. Feshbach, eds. (M.I.T. Press, Cambridge, 1982), p. 204; in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon, Oxfod, 1986), p. 109; A. Frenkel, Found. Phys. 20, 159 (1990).
27. F. Karolyhazy, Nuovo Cimento A 42, 1506 (1966); F. Karolyhazy, A Frenkel, and B. Lukacs, in Physics as Natural Philosophy, A. Slumony and H. Feshbach, eds. (M.I.T. Press, Cambridge, 1982), p. 204; in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon, Oxfod, 1986), p. 109; A. Frenkel, Found. Phys. 20, 159 (1990).
28. R. Penrose, in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon Press, Oxford, 1986), p. 129; The Emperor's New Mind (Oxford University Press, Oxford, 1992); Shadows of the Mind (Oxford University Press, Oxford, 1994).
29. R. Penrose, in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon Press, Oxford, 1986), p. 129; The Emperor's New Mind (Oxford University Press, Oxford, 1992); Shadows of the Mind (Oxford University Press, Oxford, 1994).
30. R. Penrose, in Quantum Concepts in Space and Time, R. Penrose and C. J. Isham, eds. (Clarendon Press, Oxford, 1986), p. 129; The Emperor's New Mind (Oxford University Press, Oxford, 1992); Shadows of the Mind (Oxford University Press, Oxford, 1994).
31. P. Pearle, Phys. Rev. A 48, 913 (1993); in Perspectives on Quantum Reality, R. Clifton, ed. (Kluwer Academic, Dordrecht, 1996).
32. P. Pearle, Phys. Rev. A 48, 913 (1993); in Perspectives on Quantum Reality, R. Clifton, ed. (Kluwer Academic, Dordrecht, 1996).
33. P. Pearle and E. Squires, Phys. Rev. Lett. 73, 1 (1994).
34. B. Collett, P. Pearle, F. Avignone, and S. Nussinov. Found. Phys. 25, 1399 (1995).