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23 - Interactions and Inequality

from Part IV - Nonlocal Realistic Theories

Published online by Cambridge University Press:  05 September 2016

By
Philip Pearle
Edited by
Mary Bell  and
Shan Gao
Philip Pearle
Affiliation:
Hamilton College
Shan Gao
Affiliation:
Chinese Academy of Sciences, Beijing
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Summary

Abstract

John Bell was a staunch supporter of the dynamical wave function collapse approach to making a well-defined quantum theory. Through letters from him, I reminisce on my handful of interactions with him, all of which were memorable tome. Then I discuss nonlocality, violation of Bell's inequality and some further implications within the framework of the CSL (continuous spontaneous localization) model of dynamical collapse.

Interactions

I was an instructor at Harvard with a newly minted Ph.D. from MIT, earned with an indifferent thesis on particle theory. It took me two years to come to terms with, dare I say it, the fact that I did not care about the S-matrix. I was going to be out of a job anyway in 1966 so, in the fall of 1965, I put my full energy into writing my very first paper, about what I did care: that, to my eyes there was something deeply wrong with the quantum theory I had been taught; that the rules of how to use it were inadequate. The title of the paper [1] was “Elimination of the reduction postulate from quantum theory and a framework for hidden variable theories.” It was a long title, because it was really two rather separate papers.

The first was based upon the perceived inadequacy that the collapse (reduction) postulate of the theory is ill-defined.

The second stated some postulates I thought a good hidden variable theory ought to obey, and gave a model for their satisfaction in a two-dimensional (i.e., spin-1/2) Hilbert space. Try as I might, I was not able to generalize my model to a higher-dimensional (i.e., spin-1) Hilbert space, but I put it out there for someone more clever than I to achieve. I sent the paper to a very few people who I thought might be interested. One was John Bell, and he replied (see Figure 23.1)!

So someone more clever than I pointed out that generalizing my model could not be achieved. I therefore excised the model and, after rewriting and retitling, published my very first paper [2]!

After a three-year stint at Case Institute of Technology, which graduated to become Case Western Reserve University while I was there, in 1969 I became ensconced at Hamilton College.

Type
Chapter
Information
Quantum Nonlocality and Reality
50 Years of Bell's Theorem
 , pp. 372 - 389
Publisher: Cambridge University Press
Print publication year: 2016

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References

[1] P., Pearle, How stands collapse, I, J. Phys. A: Math. Theor. 40, 3189 (2007) contains a bit of an autobiographical account of how I came to care about this, a more detailed account of this paper, as well as other professional events in my life touched upon here. One other place I have written autobiographically is P., Pearle, Tales and tails 388 Interactions and Inequality and stuff and nonsense, in R.S. Cohen, M. Horne, and J. Stachel (eds.), Experimental Metaphysics: Quantum Mechanical Studies for Abner Shimony (Kluwer, Dordrecht 1997), p. 143.Google Scholar
[2] P., Pearle, Alternative to the orthodox interpretation of quantum theory, Am. J. Phys. 35, 742 (1967).Google Scholar
[3] P., Pearle, Reduction of the state vector by a nonlinear Schrödinger equation, Phys. Rev. D 13, 857 (1976).Google Scholar
[4] R, Penrose, Time asymmetry and quantum gravity, in C., Isham, R., Penrose, and D.W., Sciama (eds.), Quantum Gravity 2, A Second Oxford Symposium (Clarendon, Oxford 1981), p. 244.
[5] J.S., Bell, Are there quantum jumps? in C.W., Kilmister (ed.), Schrödinger: Centenary Celebration of a Polymath (Cambridge University Press, Cambridge 1987), p. 41.
[6] C. Dove and E.J. Squires, A local model of explicit wavefunction collapse, quantph/9605047.
[7] R., Tumulka, A relativistic version of the Ghirardi–Rimini–Weber model, J. Statist. Phys. 125, 825 (2006).Google Scholar
[8] P., Pearle, Combining stochastic dynamical state-vector reduction with spontaneous localization, Phys. Rev. A 39, 2277 (1989).Google Scholar
[9] G.C., Ghirardi, P., Pearle, and A., Rimini, Markov processes in Hilbert space and continuous spontaneous localization of systems of identical particles, Phys. Rev. A 42, 78 (1990).Google Scholar
[10] C., Dove and E.J., Squires, Symmetric versions of explicit wavefunction collapse models, Found. Phys. 25, 1267 (1995).Google Scholar
[11] J.S., Bell, Against “measurement,” in Arthur I., Miller (ed.), Sixty-Two Years of Uncertainty (Plenum, New York 1990), p. 17.
[12] P., Pearle, On the time it takes a state vector to reduce, J. Statist. Phys. 41, 719 (1985).Google Scholar
[13] G.C., Ghirardi and T. Weber, An interpretation which is appropriate for dynamical reduction theories, in R.S. Cohen, M. Horne and J. Stachel (eds.), Potentiality, Entanglement and Passion-at-a-Distance: Quantum Mechanical Studies for Abner Shimony Vol. 2 (Kluwer, Dordrecht 1997), p. 89; G.C., Ghirardi, R., Grassi and F., Benatti, Describing the macroscopic world: Closing the circle within the dynamical reduction program, Found. Phys. 25, 5 (1995); P., Pearle, Tales and tails and stuff and nonsense, in R.S. Cohen, M. Horne and J. Stachel (eds.), Experimental Metaphysics, Quantum Mechanical Studies for Abner Shimony Vol. 1 (Kluwer, Dordrecht 1997), p. 143; P., Pearle, How stands collapse, II, inW.C. Myrvold and J. Christian (eds.), Quantum Reality, Relativistic Causality and Closing the Epistemic Circle: Essays in Honour of Abner Shimony (Springer, New York, 2009), p. 257.Google Scholar
[14] P., Pearle, Toward a relativistic theory of statevector reduction, in Arthur I., Miller (ed.), Sixty-Two Years of Uncertainty (Plenum, New York) (1990), p. 193.
[15] G.C., Ghirardi, R., Grassi and P., Pearle, Relativistic dynamical reduction models: General framework and examples, Found. Phys. 20, 1271 (1990).Google Scholar
[16] David Mermin's most recent belief is expressed in C.A., Fuchs, N.D., Mermin, and R., Schack, An introduction to QBism with an application to the locality of quantum mechanics, Am. J. Phys. 82, 749 (2014).Google Scholar
[17] For a recent introduction, see P., Pearle, Collapse, miscellany, in D., Struppa and J., Tollakson (eds.), Quantum Theory: a Two Time Success Story. Yakir Aharonov Festschrift, eds. D., Struppa, J., Tollakson (Springer, Milan 2013), p. 131.
[18] P., Canate, P., Pearle and D., Sudarsky, Continuous spontaneous localization wave function collapse model as a mechanism for the emergence of cosmological asymmetries in inflation, Phys. Rev. D 87, 104024 (2013).Google Scholar
[19] Bedingham has considered this in the context of a relativistic CSL-type model: D., Bedingham, Stochastic particle annihilation: A model of state reduction in relativistic quantum field theory, J. Phys. A: Math. Theor. 40, 647 (2007): Relativistic state reduction model, J. Phys.: Conference Series 306, 012034 (2011).Google Scholar
[20] J.S., Bell, On the Einstein–Podolsky–Rosen paradox, Physics 1, 195 (1964).Google Scholar
[21] K., Hornberger, S., Gerlich, P., Haslinger, S., Nimmrichter and M., Arndt, Colloquium: Quantum interference of clusters and molecules, Rev. Mod. Phys. 84, 157 (2012); J. Bateman, S. Nimmrichter,K.Hornberger and H. Ulbricht,Near-field interferometry of a free-falling nanoparticle from a point-like source, Nature Commun. 5, 4788 (2014).Google Scholar

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