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John Stuart Bell

British physicist (1928–1990)

Born into a poor family in the Northern Irish capital of Belfast, Bell was encouraged by his mother to continue his education after leaving school at sixteen. Consequently, after working for a year as a laboratory assistant in the physics department of Queen's University, Belfast, he enrolled as a student and graduated in 1949. Rather than pursue a PhD and burden his family further, Bell began work immediately at the Atomic Energy Research Establishment at Harwell. He worked initially on the design of CERN's first accelerator, the Proton Synchrotron. He was also given a year's leave of absence to work on a doctorate at Birmingham University. On his return to Harwell he turned to the theoretical study of elementary particles. Bell moved to CERN in Geneva in 1960 where he remained for the rest of his life. He was accompanied by his wife, Mary Bell, also a physicist, who worked at CERN on accelerator design.

In 1964 Bell published what for many has become the single most important theoretical paper in physics to appear since 1945; it was entitled On the Einstein Podolsky Rosen Paradox. The title referred to a thought experiment proposed by Einstein and others in 1935 sharply challenging the basis of quantum theory. He proposed a principle of reality stating that: “If, without in any way disturbing a system we can predict with certainty … the value of a physical quantity then there exists an element of physical reality corresponding to this physical quantity.” For example, electrons have a spin that can take one of two values, conveniently classed as positive or negative. Spin, like angular momentum, is conserved. Consequently, if a particle with zero spin decays into an electron/positron (e/p+) pair, the two particles must have equal and opposite spins. Knowing, for example, that the electron has a negative spin, it can be inferred that the positron must have a positive spin.

But this, according to Einstein, gives us a way to measure the spin of a particle without disturbance. If the p+ spin is measured and found to be positive, the measurement may well disturb the p+, but on this basis the spin of the e can be concluded to be negative without in any way disturbing the e. It follows from Einstein's reality principle that the negative spin of e is a real property of the electron. This view, however, conflicts with the usual interpretation of quantum mechanics, which sees the spin of the electron as a superposition of both spin states, a condition only resolved when the electron is observed and the wave function collapses. Nor can it be said that the state of the electron is in any way influenced by the outcome of the observation of the positron's spin for, as no signal can travel faster than the speed of light, instantaneous communication between separated particles is impossible.

The theoretical physicist is therefore presented with an uncomfortable choice. He or she can accept that electrons have intrinsic spin, in accordance with the reality principle and against quantum mechanics, or adopt what Einstein scornfully termed a “spooky action at distance.” One weekend in 1964 Bell saw a way in which the matter could be resolved.

The spin of a particle is complicated in that it can be independently measured along three coordinates x, y, and z at right angles to each other. Further, a measurement of the electron's spin in the x direction will influence the spin of the positron in the x direction also; it will, however, have no effect on measurements along the y and z directions. Similar rules apply to measurements along the y and z axes. Bell argued that, if the reality principle is correct, then one would expect to find for a large number of observations:

x+y+ łe; (x+z+ + y+z+)
That is, the number of particles with a positive spin along the x and y axes, is smaller than the number found on both the x+z+ and y+z+ axes. The result is known variously as Bell's inequality and Bell's theorem. Although it proved impossible to test Bell's inequality in terms of the reactions described in the 1964 paper, later workers have produced equivalent formulations that are testable. The most convincing of these, the Aspect experiment performed by Alain Aspect of the Institute of Optics at the University of Paris in 1982, using correlations between polarized photons, established that the inequality did not hold. The conclusion seemed to be that nature preferred to act ‘spookily’ at a distance rather than using Einstein's reality principle.

At first Bell's five-page paper was ignored. Only when experimentalists such as John Clauser at Berkeley in 1969 took his work up did Bell's argument become widely known. Bell's views on his own work, more tentative and less extreme than those of many of his followers and popularizers, were collected in his Speakable and Unspeakable in Quantum Mechanics (1987).

 
 
Wikipedia: John Stewart Bell
John Bell (left) and Martinus Veltman (right) discussing Physics at CERN
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John Bell (left) and Martinus Veltman (right) discussing Physics at CERN

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

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, 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 theorem, 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
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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.

See also

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

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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