The Rise and Fall of Time-Symmetrized Quantum Mechanics

Abstract

In the context of a discussion of time symmetry in the quantum mechanical measurement process, Aharonov et al. (1964) derived an expression concerning probabilities for the outcomes of measurements conducted on systems which have been pre- and postselected on the basis of both preceding and succeeding measurements. Recent literature has claimed that a resulting “time-symmetrized” interpretation of quantum mechanics has significant implications for some basic issues, such as contextuality and determinateness, in elementary, nonrelativistic quantum mechanics. Bub and Brown (1986) have shown that under the standard interpretation of the aforementioned expression, these claims employ ensembles which are not well defined. It is argued here that under a counterfactual interpretation of the expression, these claims may be understood as employing well-defined ensembles; it is shown, however, that such an interpretation cannot be reconciled with the standard interpretation of quantum mechanics.

Measurements, disturbances and the quantum three box paradox

“…Perhaps more importantly, Sharp and Shanks [SS93], and Cohen [Coh95] demonstrated that attempting to combine post-selective inferences when Bob's measurements disturb Alice's measurement results, will in general lead to inconsistent probabilistic predictions.…”

“…As the paradigm example of a quantum pre-and post-selection (PPS) paradox there has been much discussion of its meaning. Questions raised include the validity of the counterfactual use of the ABL rule [SS93,Coh95,Kas03], connections to quantum contextuality proofs and measurement disturbance [LS05b,LS05a] and whether classical systems can simulate the essential properties of a PPS paradox [Kir03,LS05a].…”

Objective probabilities, quantum counterfactuals, and the ABL rule—A response to R. E. Kastner

“…Ruth Kastner [4,5,6] and others [7,8,9] have raised objections concerning the appropriateness of probability assignments to counterfactuals based on the ABL rule. The first objection I will address is this [6]: Since the Q measurement is not actually made, the following rule should be used instead of the ABL rule (6):…”

“…That she thinks differently about the background conditions is obvious from her discussion [5] of the experiment considered by Sharp and Shanks [7]. In this experiment spin- 1 2 particles are prepared at time t 1 with probability measure |a + and subjected at time t 2 to a measurement of their spin component along the b axis.…”

“…I have argued that the objective probabilities associated with attributions of results to unperformed measurements should be calculated according to the ABL rule, first derived by Aharonov, Bergmann, and Lebowitz [3]. Ruth Kastner [4,5,6] and others [7,8,9] have raised objections concerning the appropriateness of probability assignments to counterfactuals based on the ABL rule. In the present article I re-derive the ABL rule, clarify the meaning of objective probabilities and the significance of their existence, and respond to these objections.…”