Phys. Rev. A 89, 024102 (2014)

Don't dwell on the past — especially when it is poorly defined, as in the case of quantum particles. Traditionally, referring to a particle between measurements has not made much sense, but in the context of delayed-choice experiments the issue cannot be ignored.

Lev Vaidman suggested that the history of a particle would be betrayed by the weak trace it leaves along its path: any interaction with the environment should leave some trace and, provided that it is weak enough not to disturb the overall evolution of the system, ensemble measurements on pre- and post-selected particles would reveal that trace. He illustrated the idea using photons travelling within a nested Mach–Zehnder interferometer: as the photons are reflected by the mirrors in the interferometer arms, their paths are exposed by the mirror vibrations.

Vaidman now provides an interpretation of these results in terms of the overlap between forward and backward evolving wavefunctions. Intriguingly, the particle can exist not only within the overlap, but also in adjacent regions — suggesting a weaker 'secondary presence' that, despite not leaving a trace of its own, would still affect the particle.