The particle arriving from the future: Aharonov's two-state vector
In a time-symmetric formulation of quantum mechanics, the present is described by one state evolving from the past and another evolving backwards from a future boundary.
Aharonov, Bergmann and Lebowitz introduced the formalism in 1964; it reproduces standard quantum predictions for pre- and post-selected systems.
It does not provide a controllable channel for sending messages into the past.
Two envelopes around the present
Ordinary calculation evolves an initial state forward. The two-state vector formalism adds a second vector determined by a later measurement and evolved backward.
Pre-selection and post-selection
Preparing many identical particles and retaining only a chosen final outcome creates an ensemble constrained from both ends of the experiment.
A very gentle interaction reveals almost nothing in one trial but yields a weak value across many selected trials, sometimes outside the ordinary eigenvalue range.
The framework is time-symmetric without allowing yesterday to receive a chosen message. It treats a quantum history as bounded by both initial and final conditions.