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

In recent years, a number of authors have studied pre- and postselected 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. (C) 2008 Elsevier Ltd. All rights reserved.