A comment on “critique of home and sengupta's derivation of a Bell inequality”

Abstract

We clarify some aspects of our derivation of a Bell-type inequality, in response to a paper by Elby.

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References

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    A. Elby,Found. Phys. Lett. 3, 317 (1990).

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    D. Home and S. Sengupta,Phys. Lett. A 102, 159 (1984).

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    J. S. Bell,Physics 1, 195 (1964); reprinted inSpeakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge, 1987), p. 14.

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    A. Einstein, inDialectica 320 (1948); reprinted inThe Born-Einstein Letters (Macmillan, London, 1971), p. 172.

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    A. Einstein, ibid. p. 171.

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The following comments refer to Andrew Elby's discussion note immediately following our present paper.

(a) We wish to stress that physical distinction between NC and LC is particularly important in the case of local realist theories violating NC for any single system but satisfying LC for any correlated many-component system. Arguments given by Elby do not rule out a “reasonable” theory violating NC but obeying LC. Therefore, a physically meaningful possibility exists that while Bell's inequality derived from NC is violated for a single system, the inequality derived from LC is satisfied for correlated and spatially separated (non-interacting) systems. It is precisely this possibility which was explored by HS in deriving Bell's inequality from NC.

(b) Since Elby's formulation of locality condition necessarily involves a relativistic constraint at the level of individual measurements, it is pointless to discuss its compatibility with predictions derived from non-relativistic quantum mechanics, which is well known to allow superluminal communication by mechanisms such as wavepacket travel or spread. Recently this aspect has been discussed in depth by P. Ghose and D. Home,Phys. Rev. A 43, 6382 (1991). It needs to be stressed that our formulation of LC is in line with the “separability condition” articulated by Einstein in different contexts; see, for example,J. Franklin Inst. 221, 349 (1936), reprinted inIdeas and Opinions (Crown, New York, 1954), pp. 290–323.

On leave from: Department of Physics, Bose Institute, Calcutta 700009, India.

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Home, D., Sengupta, S. A comment on “critique of home and sengupta's derivation of a Bell inequality”. Found Phys Lett 4, 451–454 (1991). https://doi.org/10.1007/BF00691189

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Key words

  • Bell
  • Elby
  • noncontextual
  • locality
  • Home and Sengupta