  Supported by results obtained with semi-classical quantization techniques,
and with a quantum mechanical "square-root Klein-Gordon" operator, it is argued
that Positronium (Ps) may exhibit a proper quantum-mechanical ground state
whose energy level lies $\approx 2m c^2$ below its "hydrogenic (pseudo-) ground
state" energy, where $m$ is the empirical rest mass of the electron. While the
familiar hydrogenic pseudo-ground state of Ps is caused by the Coulomb
attraction of electron and anti-electron, modified by small spin-spin and
radiative QED corrections, the proper ground state is caused by the magnetic
attraction between electron and anti-electron, which dominates over the
electric one at short distances. This finding suggests that the familiar
"annihilation" of electron and anti-electron is, in reality, simply yet another
transition between two atomic energy levels, with the energy difference
radiated off in form of photons --- except that the energy difference is huge:
about 1 MeV instead of the few eV in a hydrogenic transition. In their proper
ground state configuration the two particles would be so close that they would
electromagnetically neutralize each other for most practical purposes, thus
giving the appearance of an annihilation. Once in such a tightly bound state
such pairs would hardly interact with normal matter and not be noticeable ---
except through their gravitational effects in bulk! If the existence of such a
low-energy ground state is confirmed it would imply that a significant part of
the mysterious "dark matter" in the universe may consist of such
matter-antimatter bound states.
