Bridget Armozel mentioned the transactional interpretation of quantum mechanics. In this note, I want to partially assess the consistency of the transactional interpretation with Rand’s metaphysics. I rely here on John G. Cramer’s presentation (1986) of the transactional interpretation in Reviews of Modern Physics 58(3):647–87.
The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet it is relativistically invariant and fully causal. . . . The transactional interpretation permits quantum mechanical wave functions to be interpreted as real waves physically present in space rather than as “mathematical representations of knowledge” as in the Copenhagen interpretation. (647, emphasis added)
The transactional interpretation accepts a principle of contrafactual definiteness (CFD): “For the various possible measurements (perhaps of noncommuting variables) which might have been performed on a quantum system, each would have produced a definite (but unknown and possibly random) observational result. . . . [CFD] is completely compatible with the mathematics of quantum mechanics, but it is in some conflict with the positivistic element of the Copenhagen interpretation” (648). It is also in conflict with the following interpretations: Hidden Variables; Guide-Wave (de Broglie); Collapse of State Vector (von Neumann); Many-Worlds; and Advanced-Wave (de Beauregard or Davidon).
An interpretation of quantum mechanics must provide a physical interpretation of the mathematical formalism. This enables experimental tests. A second function of an interpretation is to “define the domain of applicability of the formalism” and to “interpret the unobservables in such a way as to avoid paradoxes and contradictions” (650).
Is the CFD principle, which is a central component of the transactional interpretation, consistent with Rand’s metaphysics as stated in her published works? CFD is certainly consistent with Rand’s view that external reality exists and has definite objective characteristics whether we measure them or not. The possible conflict between Rand’s metaphysics and CFD would be in the latter’s factor of definite but possibly random observational results. The transactional interpretation takes the mathematical state vector, which carries canonically conjugate quantities, to be a real wave. That means that the Heisenberg uncertainty relations (dispersion relations) implied in Schrödinger’s equation (see Jody Gomez’s post #0) are indeterminacy relations in external objective reality.
Rand takes the law of causality to be her rich law of identity applied to action. She states the law of causality this way: “All the countless forms, motions, combinations and dissolutions of elements within the universe—from a floating speck of dust to the formation of a galaxy to the emergence of life—are caused and determined by the identities of the elements involved” (1973). If by determined Rand means to say that every particular result of an experiment, even the particular values of canonically conjugate quantities, is uniquely determined prior to the instant of the experimental test, then her version of the principle of causality (and her version of identity) would need a modest adjustment to accommodate the CFD principle in the transactional interpretation of quantum mechanics.
A second central component of the transactional interpretation is its abandonment, in the quantum regime, of the principle of locality, which has borne much good fruit in classical physics. The transactional interpretation embraces correlations established faster-than-light between parts of a physical state vector separated by spacelike or negative timelike intervals. Rand’s metaphysics is not in conflict with this sort of physical nonlocality.
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