New Insights on Time-Symmetry in Quantum Mechanics

The " time-asymmetry " attributed to the standard formulation of Quantum Mechanics (QM) was inherited from a reasonable tendency learned from Classical Mechanics (CM) to predict the future based on initial conditions: once the equations of motion are fixed in CM, then the initial and final conditions are not independent, only one can be fixed arbitrarily. In contrast, as a result of the uncertainty principle, the relationship between initial and final conditions within QM can be one-to-many: two " identical " particles with identical environments can subsequently exhibit different properties under identical measurements. These subsequent identical measurements provide fundamentally new information about the system which could not in principle be obtained from the initial conditions. Although this lack of causal relations seemed to conflict with basic tenets of science, many justified it by arguing " nature is capricious. " This lead to Einstein's objection " God doesn't play dice. " Nevertheless, after 100 years of experimental verification, QM has won over Einstein's objection. QM's " time-asymmetry " is the assumption that measurements only have consequences after they are performed, i.e. towards the future. Nevertheless , a positive spin was placed on QM's non-trivial relationship between initial and final conditions by Aharonov, Bergmann and Lebowitz (ABL) [2] who showed that the new information obtained from measurements was also relevant for the past of every quantum-system and not just the future. This inspired ABL to re-formulate QM in terms of Pre-and-Post-Selected-ensembles. The traditional paradigm for ensembles is to simply prepare systems in a particular state and thereafter subject them to a variety of experiments. These are " pre-selected-only-ensembles. " For pre-and-post-selected-ensembles, we add one more step, a subsequent measurement or post-selection. By collecting only a subset of the outcomes for this later measurement, we see that the " pre-selected-only-ensemble " can be divided into sub-ensembles according to the results of this subsequent " post-selection-measurement. " Because pre-and-post-selected-ensembles are the most refined