Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-848d4c4894-x24gv Total loading time: 0 Render date: 2024-05-25T07:32:51.591Z Has data issue: false hasContentIssue false

21 - Some Personal Reflections on Quantum Nonlocality and the Contributions of John Bell

from Part IV - Nonlocal Realistic Theories

Published online by Cambridge University Press:  05 September 2016

By
Basil J. Hiley
Edited by
Mary Bell  and
Shan Gao
Basil J. Hiley
Affiliation:
University of London
Shan Gao
Affiliation:
Chinese Academy of Sciences, Beijing
Get access

Summary

Abstract

I present the background of the Bohm approach that led John Bell to a study of quantum nonlocality, from which his famous inequalities emerged. I recall the early experiments done at Birkbeck with the aim of exploring the possibility of ‘spontaneous collapse’, a way suggested by Schrödinger to avoid the conclusion that quantum mechanics is grossly nonlocal. I also review some of the work that John did which directly impinged on my own investigations into the foundations of quantum mechanics and report some new investigations towards a more fundamental theory.

Introduction

My first encounter with quantum nonlocality was in discussions with David Bohm when I joined him as an assistant lecturer at Birkbeck in the sixties. Although my PhD thesis had been in condensed matter physics under the supervision of Cyril Domb, I had always been fascinated and puzzled by quantum phenomena, and when the opportunity to study the subject with Bohm came up, I took it. I would listen to the discussions between Bohm and Roger Penrose, who was at Birkbeck at the time, and it soon became clear that the prescribed interpretation of quantum mechanics that I was taught as an undergraduate left too many questions unanswered.

At that time there was a very strange atmosphere in the physics community. I was often informed that there were no problems with the interpretation of the quantum formalism. If I did not follow the well-prescribed rules of the quantum algorithm, I would be ‘wasting my time’. There was no alternative, just do it! But Louis de Broglie and David Bohm had shown there was another way. However, their views were strongly opposed by many, and as far as I could judge their reasons did not seem to be based on mathematics or on logic, but on a preconceived notion that the formalism was, in principle, the best we could do. The experimental data were bizarre when looked upon from the standpoint of classical physics, but the uncertainty principle somehow prevented us from examining the actual process in detail. Reality was somehow veiled (see [1]).Were we condemned to use a mere algorithm or was there an underlying ontology?

Type
Chapter
Information
Quantum Nonlocality and Reality
50 Years of Bell's Theorem
 , pp. 344 - 362
Publisher: Cambridge University Press
Print publication year: 2016

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] d'Espagnat, B. (2003), Veiled Reality: An Analysis of Present-Day Quantum Mechanical Concepts. Westview Press, Boulder, CO.
[2] Bohm, D. (1952), A suggested interpretation of the quantum theory in terms of hidden variables, I, Phys. Rev. 85, 166–79; and II, 85 180–93.Google Scholar
[3] Bohm, D., and Hiley, B.J. (1993), The Undivided Universe: An Ontological Interpretation of Quantum Mechanics, Routledge, London.
[4] Holland, Peter R. (1995), The Quantum Theory of Motion: An Account of the de Broglie–Bohm Causal Interpretation of Quantum Mechanics, Cambridge University Press, Cambridge.
[5] Durr, D., and Teufel, S. (2009), Bohmian Mechanics: The Physics and Mathematics of Quantum Theory, Springer, Dordrecht.
[6] Bell, J.S. (1964), On the Einstein–Podolsky–Rosen paradox, Physics 1, 195–200.
[7] von Neumann, J. (1955), Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, NJ.
[8] Wheeler, J.A. (1991), At Home in the Universe, AIP Press, New York, p. 286.
[9] Durr, D., Goldstein, S., N., Zanghi, (1992), Quantum equilibrium and the origin of absolute uncertainty, J. Stat. Phys. 67, 843–907.Google Scholar
[10] Dirac, P.M. (1973), in J., Mehra (ed.), The Physicist's Conception of Nature, Reidel, Dordrecht-Holland, p. 10.
[11] Einstein, A., Podolsky, B., and Rosen, N. (1935), Can quantum-mechanical description of physical reality be considered complete, Phys. Rev. 47, 777–80.Google Scholar
[12] Schrödinger, E. (1927), Energieaustausch nach der Wellenmechanik, Annalen der Physik (4) 388, 956–68.Google Scholar
[13] Schrödinger, E. (1936), Probability relations between separated systems, Proc. Cam. Phil. Soc. 32, 446–52.Google Scholar
[14] Bohr, N. (1935), Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 48, 696–702; repeated in a letter to Nature 36, 65 (July 1935).Google Scholar
[15] Bohm, D. (1951), Quantum Theory, Prentice-Hall, Englewood Cliffs, NJ.
[16] Langhoff, H. (1960), Die Linearpolarisation der Vernichtungsstrahlung von Positronen, Zeit. Phys. 160, 186–93.Google Scholar
[17] Kasday, L. (1972), Foundations of quantum mechanics, in Proc. Intern. School of Physics Enrico Fermi, Academic Press, New York, pp. 195–210.
[18] Hautojarvi, P., and Jauho, P. (1971), Positron annihilation, in International Conference on Queens University, Kingston, Canada, Kingston.
[19] Faraci, G., Gutkowski, D., Notarrigo, S., and Pennisi, A.R. (1974), An experimental test of the EPR paradox, Lett. Nuovo Cimento 9 (15), 607–11.Google Scholar
[20] Wilson, A.R., Lowe, J., and Butt, D.K. (1976), Measurement of the relative planes of polarization of annihilation quanta as a function of separation distance, J. Phys. G: Nucl. Phys. 2 (9), 613.Google Scholar
[21] Furry, W.H. (1936), Note on the quantum-mechanical theory of measurement, Phys. Rev. 49, 393–9.Google Scholar
[22] Bohm, D., and Aharonov, Y. (1957), Discussion of experimental proof for the paradox of Einstein, Rosen, and Podolsky, Phys. Rev. 108 (4), 1070.Google Scholar
[23] Paramananda, V., and Butt, D.K. (1987), Quantum correlations, non-locality and the EPR paradox, J. Phys. G: Nucl. Phys. 13, 449–52.Google Scholar
[24] Ursin, R., Tiefenbacher, F., Schmitt-Manderbach, T., Weier, H., Scheidl, T., Lindenthal, M., Blauensteiner, B., Jennewein, T., Perdigues, J., Trojek, P., Omer, B., Furst, M., Meyenburg, M., Rarity, J., Sodnik, Z., Barbieri, C., Weinfurter, H., and Zeilinger, A. (2007), Entanglement-based quantum communication over 144 km, Nat. Phys. 3, 481–6.Google Scholar
[25] Schrödinger, E. (1935), Discussion of probability relations between separated systems, Proc. Cam. Phil. Soc. 31, 555–63.Google Scholar
[26] Bell, J.S. (1987), Beables for quantum field theory, in B.J., Hiley and D., Peat (eds.), Quantum Implications: Essays in Honour of David Bohm, Routledge & Kegan Paul, London, pp. 227–34.
[27] Bohr, N. (1961), Atomic Physics and Human Knowledge, Science Editions, New York, p. 50.
[28] Bell, J.S. (1990), Against measurement, in A.I., Miller (ed.), Sixty-Two Years of Uncertainty: Historical, Philosophical, and Physical Inquiries into the Foundations of Quantum Mechanics, NATO ASI Series 226, pp. 17–31.
[29] Ghirardi, G.C., Rimini, A., and Weber, T. (1986), Unified dynamics for microscopic and macroscopic systems, Phys. Rev. D 34, 470–91.Google Scholar
[30] Bohm, D.J., Hiley, B.J., and Kaloyerou, P.N. (1987), An ontological basis for the quantum theory: II. A causal interpretation of quantum fields, Phys. Rep. 144, 349–75.Google Scholar
[31] Kaloyerou, P.N. (1994), The causal interpretation of the electromagnetic field, Phys. Rep. 244, 287–385.Google Scholar
[32] Bohm, D., Schiller, R. and Tiomno, J. (1955), A causal interpretation of the Pauli equation (A) and (B), Nuovo Cim. Supp. 1, 48–66 and 67–91.Google Scholar
[33] Dewdney, C., Holland, P.R., and Kyprianidis, A. (1987), A causal account of Nonloc A. Einstein–Podolsky–Rosen spin correlations, J. Phys. A: Math. Gen. 20, 4717– 32.Google Scholar
[34] Dewdney, C., Holland, P.R., Kyprianidis, A., and Vigier, J.-P. (1988). Spin and nonlocality in quantum mechanics, Nature 336, 536–44.Google Scholar
[35] Bohm, D. (1962), Classical and nonclassical concepts in the quantum theory, Brit. J. Phil. Sci. 12 (48), 265–80.Google Scholar
[36] de Broglie, L. (1960), Non-linearWave Mechanics: A Causal Interpretation, Elsevier, Amsterdam.
[37] Hestenes, D. (2003), Space–time physics with geometric algebra, Am. J. Phys. 7, 691–714.Google Scholar
[38] Hiley, B.J., and Callaghan, R.E. (2011), The clifford algebra approach to quantum mechanics: B. The Dirac particle and its relation to the Bohm approach, arXiv: Mathsph: 1011.4033.
[39] Hiley, B.J., and Callaghan, R.E. (2012), Clifford algebras and the Dirac– Bohm quantum Hamilton–Jacobi equation, Foundations of Physics 42, 192–208.Google Scholar
[40] Dirac, P.M. (1947), The Principles of Quantum Mechanics, Oxford University Press, Oxford, p. 80.
[41] Frohlich, H. (1967), Microscopic derivation of the equations of hydrodynamics, Physica 37, 215–26.Google Scholar
[42] Bell, J.S. (1980), De Broglie–Bohm, delayed-choice double slit experiment and the density matrix, Int. J. Quant. Chem, Quant. Chem. Symp. 14, 155–9.Google Scholar
[43] Hiley, B.J. (2013), Bohmian non-commutative dynamics: History and new developments, arXiv 1303.6057.
[44] Tucker, R.W. (1988), Closed currents, vector fields and phenomena, Found. Phys. 18, 8–20.Google Scholar
[45] von Neumann, J. (1931), Die Eindeutigkeit der Schrödingerschen Operatoren, Mathematische Annalen 104, 570–87.Google Scholar
[46] de Gosson, M. (2001), The Principles of Newtonian and Quantum Mechanics: The Need for Planck's Constant, Imperial College Press, London.
[47] de Gosson, M. (2010), Symplectic Methods in Harmonic Analysis and in Mathematical Physics, Birkhauser Verlag, Basel.
[48] Weyl, H. (1928), Quantenmechanik und Gruppentheorie, Zeit. für Physik 46, 1–46.Google Scholar
[49] Moyal, J.E. (1949), Quantum mechanics as a statistical theory, Proceedings of the Cambridge Philosophical Society 45, 99–123.
[50] Bohm, D., and Hiley, B.J. (1981), On a quantum algebraic approach to a generalised phase space, Found. Phys. 11, 179–203.Google Scholar
[51] Hiley, B.J. (2015), On the relationship between the Moyal algebra and the quantum operator algebra of von Neumann, Journal of Computational Electronics 14, 869–78; arXiv 1211.2098.Google Scholar
[52] Bell, J.S. (1986), EPR correlations and EPW distributions, Ann. N.Y. Acad. Sci. 480, 263–6.Google Scholar
[53] Bohm, D., and Hiley, B.J. (1975), On the intuitive understanding of nonlocality as implied by quantum theory, Found. Phys. 5, 93–109.Google Scholar
[54] Crumeyrolle, A. (1990), Orthogonal and Symplectic Clifford Algebras: Spinor Structures, Kluwer, Dordrecht.
[55] Guillemin, V.W., and Sternberg, S. (1984), Symplectic Techniques in Physics, Cambridge University Press, Cambridge.
[56] de Gosson, M., and Hiley, B.J. (2011), Imprints of the quantum world in classical mechanics, Found. Phys. 41, 1415–36.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×