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Unfinished Work: A Bequest

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Here are some topics in physics and philosophy on which my work is incomplete. I invite my friends in this assembly, and their colleagues and students, to continue the work and inform me about their progress.

1. There is a well known theorem of Wigner that a necessary condition for a quantity M of a physical system O to be measured without distortion (i.e., if O is in an eigenstate u of M just prior to the measurement then it remains in u immediately afterwards) is the commutation of M with any additive conserved quantity. This theorem has been generalized by Stein and Shimony by relaxing the condition “without distortion”, but the natural full generalization has neither been proven nor refuted by a counter-example.

2. In two-particle interferometry, using an ensemble of pairs of
particles in a pure entangled state ?, the fringe visibility V12
of pairs counted in coincidence may be defined analogously to the fringe visibility V1 of single particles, and a complementarity relation has been derived: V12 + V122 = 1. Generalizations of this complementarity relation to n-tuples (n ?2) of entangled particle are desired.

3. Relations have been explored among various reasonable definitions of “degree of entanglement”, but further systematization of these relations is desirable.

4. Bell’s Theorem shows that certain quantum mechanical predictions
cannot be derived in any “local realistic” theory, and experiments have overwhelmingly favored quantum mechanics in situations of theoretical conflict. Is it plausible to maintain “peaceful coexistence” between the nonlocality of quantum mechanics and the locality of relativity theory by citing the impossibility of using the former to send superluminal messages? But if this strategy fails, what is the proper adjudication of the conflict between these fundamental physical theories?

5. Stochastic modification of quantum dynamics (proposed by Ghirardi-Rimini-Weber, Gisin, Pearle, Wigner, Penrose, Károlyházy, and others) has been proposed as a promising program for solving the quantum mechanical measurement problem. But theoretical refinements of the proposed modifications are desirable as well as definitive experimental tests. Two promising areas of relevant experimental research are quantum gravity and variants of the “quantum telegraph” (an ensemble of atoms undergoing transitions between the ground state and a metastable state when exposed to appropriate laser beams).

6. Corinaldesi conjectured that the boson statistics of integral spin particles and the fermion statistics of half-integral spin particles
are consequences of their dynamics rather than of their kinematics
(the latter usually accepted because of Pauli’s spin and statistics theorem), so that obedience to the Pauli Exclusion Principle in a freshly formed ensemble of electrons would become increasingly strict as the ensemble ages. To test Corinaldesi’s conjecture it was proposed to form fresh ensembles of electrons by allowing a high velocity beam of Ne+ ions in a linear accelerator to be intersected by electrons from an electron gun, thereby neutralizing a subset of the ions. Transitions of electrons to the doubly occupied 1S shell in the complete Ne atoms will be monitored by suitable x-ray detectors at varying distances from the region of intersection, in order to scrutinize the conjectured diminution with time of violations of the Exclusion Principle. Refinements of this design and actual performance of the experiment are requested.

7. A test of the speculative conjecture that wave packet reduction
is a psycho-physical phenomenon, occurring only when a conscious
observer reads a measuring device, was performed in 1977 by three of my undergraduate students. They used a slow gamma emitter (about one emission per minute) monitored by a detector connected to registration devices in two separated rooms. There was a short time delay between the two registrations. The observer in the first room read his registration device in randomly chosen intervals of time and the observer in...