In a Viewpoint article, "Weak measurements just got stronger", for This Week in Physics ( April 27, 2009) Sandu Popescu, Physics 2, 32 (2009) In the weird world of quantum mechanics, looking at time flowing backwards allows us to look
forward to precision measurements:
In 1964 when Yakir Aharonov, Peter Bergman, and Joel Lebowitz started to think seriously about the issue of the arrow of time in quantum mechanics [1]—whether time only flows from the past to the future or also from the future to the past—none of them could have possibly imagined that their esoteric quest would one day lead to one of the most powerful amplification methods in physics. But in the weird, unpredictable, yet wonderful way in which physics works, one is a direct, logical, consequence of the other. As reported in Physical Review Letters by P. Ben Dixon, David J. Starling, Andrew N. Jordan, and John C. Howell at the University of Rochester this amplification method makes it possible to measure angles of a few hundred femtoradians and displacements of 20 femtometers, about the size of an atomic nucleus [2].
[ ... ]
Viewed from one angle, this story is all about fundamental philosophical ideas. Does the spin indeed have a value larger than 1/2 or is the result simply an error in the imprecise measuring device used? Does the spin indeed have both the x spin component and the z one well defined? And, above all, does time indeed flow in two directions in quantum mechanics? To be sure, the strange outcome of the measurement of Sπ/4 in this pre- and post-selected ensemble could indeed be obtained as an error in the measurement, an error in which the pointer of the measuring apparatus moved more than it should have. The explanation can be fully given by standard quantum mechanics, involving regular past-to-future-only flow of time. But the explanation is cumbersome and involves very intricate interference effects in the measuring device. Assuming that time flows in two directions tremendously simplifies the problem. As far as I can tell, Aharonov, Albert, and Vaidman hold the view that one should indeed accept this strange flow of time. I fully agree. Not everybody agrees though, and this is one of the most profound controversies in quantum mechanics.Viewed from one angle, this story is all about fundamental philosophical ideas. Does the spin indeed have a value larger than 1/2 or is the result simply an error in the imprecise measuring device used? Does the spin indeed have both the x spin component and the z one well defined? And, above all, does time indeed flow in two directions in quantum mechanics? To be sure, the strange outcome of the measurement of Sπ/4 in this pre- and post-selected ensemble could indeed be obtained as an error in the measurement, an error in which the pointer of the measuring apparatus moved more than it should have. The explanation can be fully given by standard quantum mechanics, involving regular past-to-future-only flow of time. But the explanation is cumbersome and involves very intricate interference effects in the measuring device. Assuming that time flows in two directions tremendously simplifies the problem. As far as I can tell, Aharonov, Albert, and Vaidman hold the view that one should indeed accept this strange flow of time. I fully agree. Not everybody agrees though, and this is one of the most profound controversies in quantum mechanics.
