The transactional interpretation, counterfactuals, and weak values in quantum theory

In recent years, a number of authors have studied pre- and post-selected quantum systems and associated time symmetry considerations. In this context, numerous paradoxes have arisen which raise questions about what can be inferred about such a system based on theoretically calculated quantities such as the Aharonov–Bergmann–Lebowitz (ABL) probabilities; and, more recently, “weak values”—time-symmetric quantities applicable to pre- and post-selected systems. This paper applies to some of these problems a time-symmetric interpretation of quantum theory: the “transactional interpretation” (TI) of Cramer, first proposed in 1980. The TI picture supports the conclusion that weak values are properly interpreted as multiple-time amplitudes rather than as generalized expectation values. It also prompts a stricter constraint on the counterfactual usage of the ABL rule than the consistency of the associated family of histories, which has previously been regarded as sufficient.