  A novel prediction is derived by the Two-State-Vector-Formalism (TSVF) for a
particle superposed over three boxes. Under appropriate pre- and
postselections, and with tunneling enabled between two of the boxes, it is
possible to derive not only one, but three predictions for three different
times within the intermediate interval. These predictions are moreover
contradictory. The particle (when looked for using a projective measurement)
seems to disappear from the first box where it would have been previously found
with certainty, appearing instead within the third box, to which no tunneling
is possible, and later re-appearing within the second. It turns out that local
measurement (i.e. opening one of the boxes) fails to indicate the particle's
presence, but subtler measurements performed on the two boxes together reveal
the particle's nonlocal modular momentum spatially separated from its mass.
Another advance of this setting is that, unlike other predictions of the TSVF
that rely on weak and/or counterfactual measurements, the present one uses
actual projective measurements. This outcome is then corroborated by adding
weak measurements and the Aharonov-Bohm effect. The results strengthen the
recently suggested time-symmetric Heisenberg ontology based on nonlocal
deterministic operators. They can be also tested using the newly developed
quantum router.
