As a result of the uncertainty principle, the relationship between initial and final conditions within quantum mechanics can be one-to-many: two "identical" particles with identical environments can subsequently exhibit different properties under identical measurements. These subsequent identical measurements or post-selections provide fundamentally new information about the system which could not in principle be obtained from the initial conditions. Because pre- and post-selected-ensembles are the most refined quantum ensemble, they are of fundamental importance and subsequently led to the Time-Symmetric re-formulation of Quantum Mechanics which provides a complete description of a quantum-system at a given moment by using two wavefunctions instead of one. We also review the problem of interference using the Heisenberg picture and highlight some new aspects through the use of pre-selection, post-selection, weak measurements, and modular variables. We present a physical explanation for the different behaviors of a single particle when the distant lit is open or closed: instead of having a quantum wave that passes through all slits, we have a localized particle with non-local interactions with the other slit(s).
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