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Why are we interested in positronium?

Because a positron is the anti-twin of an electron, they annihilate when they find each other, as seen in the GIF below. All their mass is converted into energy, in the form of two photons, seen in pink.

GIF courtesy of C.A. Quarles of TCU

They do not annihilate immediately because it takes the particles a while to find each other. It is during the time they are looking for each other that they can form positronium ... the particles in this animation have formed positronium when they begin circling each other. Positronium, abbreviated as Ps, has a maximum lifespan of about 10^-8 seconds before the electron and positron annihilate.