  A Gedanken experiment is presented where an excited and a ground-state atom
are positioned such that, within the former's half-life time, they exchange a
photon with 50% probability. A measurement of their energy state will therefore
indicate in 50% of the cases that no photon was exchanged. Yet other
measurements would reveal that, by the mere possibility of exchange, the two
atoms have become entangled. Consequently, the "no exchange" result, apparently
precluding entanglement, is non-locally established between the atoms by this
very entanglement. This quantum-mechanical version of the ancient Liar Paradox
can be realized with already existing transmission schemes, with the addition
of Bell's theorem applied to the no-exchange cases. Under appropriate
probabilities, the initially-excited atom, still excited, can be entangled with
additional atoms time and again, or alternatively, exert multipartite nonlocal
correlations in an interaction free manner. When densely repeated several
times, this result also gives rise to the Quantum Zeno effect, again exerted
between distant atoms without photon exchange. We discuss these experiments as
variants of Interaction-Free-Measurement, now generalized for both spatial and
temporal uncertainties. We next employ weak measurements for elucidating the
paradox. Interpretational issues are discussed in the conclusion, and a
resolution is offered within the Two-State Vector Formalism and its new
Heisenberg framework.
