This paper describes a toy, consisting of a pair of magic tesseracts, that can be used to perform an amazing trick that defies explanation in conventional terms. An account of the toy, and the trick possible with it, is given in nontechnical terms that should be accessible to a layman. An explanation is then given, for physicists, of how this trick can be interpreted as a proof of Bell’s theorem. An appendix (again intended for physicists) describes the internal machinery of the toy and how it works its magic.
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Bell’s theorem has served as a fertile source of magic tricks in the past. Notable examples are Mermin’s tricks based on a singlet state of two qubits (Ref. 13), on the Greenberger–Horne–Zeilinger state of three qubits (Ref. 11, and on Hardy’s nonmaximally entangled state of two qubits (Ref. 14). Vaidman, Aharanov, and Albert (Ref. 15) presented an ingenious trick based on an EPR state of two qubits; this example was later generalized by Mermin (Ref. 16), who pointed out the connection between this trick and the BKS theorem.
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The reason for carrying out each experiment during a prearranged (and narrow) time slot is to ensure that Alice and Bob’s tesseracts, which are very far apart, don’t have sufficient time to exchange information with each other once measurements on either have begun. The ability to exchange such information would provide a ready explanation for the magic to be revealed shortly.
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It may be worth pointing out that measuring arbitrary observables on a particle of arbitrary spin has been shown to be possible in principle. The paper by
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© 2001 American Association of Physics Teachers.
2001
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