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6. Collapse and the Quantum Mechanics Formalism


The ``collapse'' or reduction of the state vector of a quantum system to a definite state as the result of a measurement was first perceived in the operational procedures of the quantum formalism by John von Neumann[6]. He observed that in orthodox quantum formalism one represents a post-measurement quantum system with a state vector that is qualitatively different from that used to represents the pre-measurement quantum system. In a very interesting contribution to this Conference, Prof. Ballentine[7] demonstrates that while collapse is implicit in the formalism, the mechanism of state vector collapse in an individual quantum event is not, strictly speaking, a part of the formalism. Either, he argues, the formalism of quantum mechanics must be considered applicable only to a statistically large number of similar quantum events, or else one must supply an additional process, an extension of the formalism of quantum mechanics, to provide the collapse mechanism for individual events. He gave an example of such a process which involved an ``extra'' stochastic field.

This discussion is relevant to the transactional interpretation because the TI might be viewed as supplying a mechanism for state vector collapse. That appears to contradict Ballentine's requirement of an additional mechanism. Actually, there is no such contradiction. The TI's nonlocal collapse mechanism is strictly at the interpretational level. It cannot supply mechanisms missing from the formalism. The problem that Ballentine poses, that of accommodating collapse for a single quantum event, is one that must be addressed by the formalism. The transactional interpretation would then have to be considered in the context of such a revised formalism to decide if a conflict exists.

John G. Cramer
Tue Apr 30 12:12:30 PDT 1996