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Physicists Prove Surprising Rule of Threes

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Back in 1970, Soviet nuclear physicist Vitaly Efimov had a theory regarding trios of particles that was just recently proven by a group of experimental physicists. via Quanta Magazine:

More than 40 years after a Soviet nuclear physicist proposed an outlandish theory that trios of particles can arrange themselves in an infinite nesting-doll configuration, experimentalists have reported strong evidence that this bizarre state of matter is real.

In 1970, Vitaly Efimov was manipulating the equations of quantum mechanics in an attempt to calculate the behavior of sets of three particles, such as the protons and neutrons that populate atomic nuclei, when he discovered a law that pertained not only to nuclear ingredients but also, under the right conditions, to any trio of particles in nature.

While most forces act between pairs, such as the north and south poles of a magnet or a planet and its sun, Efimov identified an effect that requires three components to spring into action. Together, the components form a state of matter similar to Borromean rings, an ancient symbol of three interconnected circles in which no two are directly linked. The so-called Efimov “trimer” could consist of a trio of protons, a triatomic molecule or any other set of three particles, as long as their properties were tuned to the right values. And in a surprising flourish, this hypothetical state of matter exhibited an unheard-of feature: the ability to range in size from practically infinitesimal to infinite.

“It’s a pretty wild idea,” said Randy Hulet, a physics professor at Rice University in Houston. “You get this infinite series of molecules.”

Efimov had shown that when three particles come together, a special confluence of their forces creates the Borromean rings effect: Though one is not enough, the effects of two particles can conspire to bind a third. The nesting-doll feature — called discrete scale invariance — arose from a symmetry in the equation describing the forces between three particles. If the particles satisfied the equation when spaced a certain distance apart, then the same particles spaced 22.7 times farther apart were also a solution. This number, called a “scaling factor,” emerged from the mathematics as inexplicably as pi, the ratio between a circle’s circumference and diameter.

“It’s like layers of an onion,” Hulet said. “You see molecules at one layer. Peel the layer away, and you see that there’s a molecule there 22.7 times smaller. Every time you peel away a layer, you find another molecule.”

Efimov published his theory in a Soviet journal as well as the Western publication Physics Letters B. At first, almost no one believed it.

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