Positronium is a sort of an atom but a very exotic one, with only a fleeting existence. Like an atom of hydrogen it consists of two elementary particles with equal and opposite electric charges. Like an atom of hydrogen one of these particles is an electron, familiar (as far as any subatomic particle is "familiar") as a constituent of the atoms around us. Unlike a hydrogen atom the positively charged particle is a positron. A positron has the same mass as an electron but a positive, rather than a negative charge. It is the electron's antimatter counterpart, a sort of evil twin. When an electron and a positron come together they cancel one another out (the word used is "annihilate") and the mass of both particles is converted into energy, in the form of light, according to Einstein's most famous relation E = mc2.
Antimatter sounds like something out of science fiction (and one of its most famous occurrences must certainly be in the propulsion unit of the Starship Enterprise). Nonetheless it exists. The first discovery of a positively charged electron was in 1932 by the American scientist Carl Anderson. Now they are put to work every day in our hospitals (know somebody who's had a PET scan? Guess what the "P" in "PET" stands for).
Natural processes produce positrons, as do events in man-made particle accelerators. My own interest focuses on the energetic events of solar flares, in which positrons are sometimes produced. Once they exist, positrons don't hang around for very long. There's usually an electron for them to annihilate with. But before annihilating, for a ten-millionth of a second or less, the positron and the electron orbit one another as an atom of positronium. I like to think of them in a sort of dance, eyeball to eyeball, each recognising in the other its equal, its opposite and its imminent extinction. Finally they annihilate one another, producing a spectrum line in gamma-rays that we can detect and learn from.
Composed only of two very simple objects, the positronium atom gives very precise tests of the quantum theory of electromagnetism, so it has been studied in great detail in the laboratory. It lets us test very precisely elements of our basic understanding of the world.
Matter and anti-matter can both exist but there is more matter than anti-matter. If there were equal amounts of both, they would have annihilated each other very early in the history of the Universe. The Universe would be filled with light but there wouldn't be atoms and molecules i.e. ourselves. So the question, "why is there more matter than anti-matter" is a fundamental question about the Universe.
After all this I'm both sad and a bit cross to discover talk of "positronium homeopathy". In its yin-and-yang components, its brief existence, its annihilation, and the matter-antimatter asymmetry at which it hints, positronium is a very beautiful and exotic aspect of the physical world. There's more than enough real, deep beauty and weirdness there without making up a lazy, unsubstantiated fairy story.
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