John Stewart Bell

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John Stewart Bell (June 28, 1928 – October 1, 1990) was a physicist, and the originator of Bell's Theorem, one of the most important theorems in quantum physics.

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[edit] Life and work

He was born in Belfast, Northern Ireland, and graduated in experimental physics at the Queen's University of Belfast, in 1948. He went on to complete a PhD at the University of Birmingham, specialising in nuclear physics and quantum field theory. His career began with the British Atomic Energy Agency, in Malvern, Britain's, then Harwell Laboratory. After several years he moved to the European Center for Nuclear Research (CERN, Conseil Européen pour la Recherche Nucléaire). Here he worked almost exclusively on theoretical particle physics and on accelerator design, but found time to pursue a major avocation, investigating the fundamentals of quantum theory.

In 1964, after a year's leave from CERN that he spent at Stanford University, the University of Wisconsin-Madison and Brandeis University, he wrote a paper entitled "On the Einstein-Podolsky-Rosen Paradox"[1]. In this work, he showed that the carrying forward EPR's analysis[2] permits one to derive the famous Bell's inequality. This inequality, derived from some basic philosophical assumptions, conflicts with the predictions of quantum mechanics.

There is some disagreement regarding what Bell's inequality—in conjunction with the EPR paradox—can be said to imply. Bell held that not only local hidden variables, but any and all local theoretical explanations must conflict with quantum theory: "It is known that with Bohm's example of EPR correlations, involving particles with spin, there is an irreducible nonlocality."[3] According to an alternate interpretation, not all local theories in general, but only local hidden variables have shown incompatibility with quantum theory.

Despite the fact that hidden variable schemes are often associated with the issue of indeterminism, or uncertainty, Bell was instead concerned with the fact that orthodox quantum mechanics is a subjective theory, and the concept of measurement figures prominently in its formulation. It was not that Bell found measurement unacceptable in itself. He objected to its appearance at quantum mechanics' most fundamental theoretical level, which he insisted must be concerned only with sharply-defined mathematical quantities and unambiguous physical concepts.

In Bell's words: "The concept of 'measurement' becomes so fuzzy on reflection that it is quite surprising to have it appearing in physical theory at the most fundamental level... does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?"[4]

Bell was impressed that within Bohm’s hidden variable theory, reference to this concept was not needed, and it was this which sparked his interest in the field of research.

But if he were to thoroughly explore the viability of Bohm's theory, Bell needed to answer the challenge of the so-called impossibility proofs against hidden variables. Bell addressed these in a paper entitled "On the Problem of Hidden Variables in Quantum Mechanics".[5] Here he showed that von Neumann’s argument[6] does not prove impossibility, as it claims. The argument fails in this regard due to its reliance on a physically unreasonable assumption. In this same work, Bell showed that a stronger effort at such a proof (based upon Gleason's theorem) also fails to eliminate the hidden variables program. (The flaw in von Neumann's proof was previously discovered by Grete Hermann in 1935, but did not become common knowledge until rediscovered by Bell.)

If these attempts to disprove hidden variables failed, can Bell's resolution of the EPR paradox be considered a success? The answer to this question hinges on the interpretation. According to Bell's position, quantum mechanics itself has been demonstrated to be irreducibly nonlocal. Therefore, one cannot fault a hidden variables scheme if, as Bohm's does, it includes "superluminal signalling", i.e., nonlocality.

The alternative interpretation would disagree with this conclusion. It does not assess the EPR/Bell world as having proven the nonlocality of quantum theory. It would claim that by keeping the standard interpretation and avoiding hidden variables, one retains locality, and they base arguments against hidden variables on this notion.

In 1972 the first of many experiments that have shown a violation of Bell's Inequality was conducted. Again, the meaning of this violation differs according to its interpretation. Bell himself concludes: "It now seems that the non-locality is deeply rooted in quantum mechanics itself and will persist in any completion."[7] The alternative view is that the experiment means the elimination of local hidden variable theories.

Bell remained interested in objective 'observer-free' quantum mechanics. He stressed that at the most fundamental level, physical theories ought not to be concerned with observables, but with 'be-ables': "The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on 'observation'."[8] He remained impressed with Bohm's hidden variables as an example of such a scheme and he attacked the more subjective alternatives such as the Copenhagen and Everett "many-worlds" interpretations.[9]

Blue plaque honouring John Bell at the Queen's University of Belfast
Blue plaque honouring John Bell at the Queen's University of Belfast

Bell seemed to be quite comfortable with the notion that future experiments would continue to agree with quantum mechanics and violate his inequalities. Referring to the Bell test experiments, he remarked:

"It is difficult for me to believe that quantum mechanics, working very well for currently practical set-ups, will nevertheless fail badly with improvements in counter efficiency ..."[10]

Some people continue to believe that agreement with Bell's inequalities might yet be saved. They argue that in the future much more precise experiments could reveal that one of the known loopholes, for example the so-called "fair sampling loophole", had been biasing the interpretations. This latter loophole, first publicized by Philip Pearle in 1970[11], is such that increases in counter efficiency decrease the measured quantum correlation, eventually destroying the empirical match with quantum mechanics. Most mainstream physicists are highly skeptical about all these "loopholes", admitting their existence but continuing to believe that Bell's inequalities must fail.

Bell died unexpectedly of a cerebral hemorrhage in Belfast in 1990. His contribution to the issues raised by EPR was significant. Some regard him as having demonstrated the failure of local realism (local hidden variables). Bell's own interpretation is that locality itself met its demise.

[edit] See also

[edit] Notes

  1. ^ John Bell, Speakable and Unspeakable in Quantum Mechanics, p. 14
  2. ^ Einstein, et al., "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?"
  3. ^ Bell, p. 196
  4. ^ Bell, p. 117
  5. ^ Bell, p.1
  6. ^ John von Neumann, Mathematical Foundations of Quantum Mechanics
  7. ^ Bell, p. 132
  8. ^ Bell, p. 174
  9. ^ Bell, p. 92, 133, 181
  10. ^ Bell, p. 109
  11. ^ Philip Pearle, Hidden-Variable Example Based upon Data Rejection

[edit] References

  • Aczel, Amir D, Entanglement: The Greatest Mystery in Physics (2001), New York: Four Walls Eight Windows
  • Bell, John S, Speakable and Unspeakable in Quantum Mechanics (1987), Cambridge University Press, ISBN 0-521-36869-3, 2004 edition with introduction by Alain Aspect and two additional papers: ISBN 0-521-52338-9
  • Einstein, Podolsky, Rosen, "Can Quantum Mechanical Description of Physical Reality Be Considered Complete?", Phys. Rev. 47, 777 (1935).
  • von Neumann, John, Mathematical Foundations of Quantum Mechanics (1932), Princeton University Press 1996 edition: ISBN 0-691-02893-1
  • Pearle, Philip, Hidden-Variable Example Based upon Data Rejection, Physical Review D, 2, 1418-25 (1970)

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