## The Rule of Three Proved By Physicists 80

An anonymous reader writes

*"In 1970, Russian physicist Vitaly Efimov developed mathematical proof (PDF) that any three-particle substance, referred to as a trimer, will scale up or down in size by a factor of 22.7 and that if the particles are not all of the same type, 'the scaling factor of 22.7 decreases according to the particles' relative masses.' In 2006, physicists in Austria proved that Efimov's trimers can be created in laser-cooled environments. And now, in 2014, physicists in Austria, Germany, and the U.S. have physical proof that Efimov's trimers do indeed scale by a factor of 22.7 if they are comprised of the same particles or a lower ratio relative to their particles' masses if they are comprised of a mixture of different particles (abstract 1, abstract 2, abstract 3). 22.7 — a.k.a., the rule of three — now appears to be as significant as pi."*
## Re:Pi? (Score:3, Informative)

http://rsta.royalsocietypublishing.org/content/369/1946/2679.full

If you check section three, you'll be able to compute that the number in question is 22.6943825963666951931....

## Re:Clueless (Score:5, Informative)

I found the summary confusing but the article made more sense.

The theory was that there exist configurations of three particles that is stable in a strange sort of way. The strange part is that if a certain configuration was stable then putting the particles in the same configuration but the distances blown up by a certain factor (22.7 if the three particles were the same) gives another stable configuration. So you can keep blowing up the distances in multiples of 22.7 and would get an infinite sequence of stable configurations. These configurations are necessarily quantum and not classical since the distances involved would be much larger than the range of the forces between the particles. (Although even the initial distances are large too, if i understood correctly, you would agree that they _will_ get pretty large at some point).

Now some independent groups have shown the existence of such states with the required blowup. Since similar-particle setup required cooling things down to the limit of present day technology, only _one_ configuration was observed initially. Someone used a system of different particles resulting in a blowup factor less than 22.7 allowing them to observe _three_ of these configurations, essentially validating the theory.

Hope that made sense (IANAP).