Borromean rings consist of
three circles linked as a group, with no two circles interlinked; removal of one ring results in the separation of all three. Named for the
Borromeo family of 15th century Italy which featured the rings on its
coat of arms, the symbol has had
a long and varied history. The rings have appeared everywhere from
medieval Christian iconography to
Norse rune stones to
the pillars of Hindu temples. In more recent times, Borromean rings have attracted formal study in the fields of
topology,
chemistry and (strangely enough) quantum mechanics.
So-called Borromean nuclei, found
in certain shortly-lived isotopes, feature a core nucleus surrounded by a
halo of two additional nucleons. Like their namesake, Borromean nuclei form a loosely-bound
3-body system in the absence of 2-body bound states, and the removal of one body causes the system to fall apart.
A similar phenomenon is the
Efimov state, named after the
Russian physicist that
predicted it 35 years prior to its discovery, and
first observed in
triads of ultracold cesium atoms. Interestingly, the Efimov state
does not depend on the size or identity of the particles; it occurs at
an infinite number of regular intervals along the scales of binding energy and length, just as the same note appears at different octaves.
A final example of Borromean rings occurs in certain types of
quantum entanglement, where particles are bound by information rather than energy. In the
Greenberger-Horne-Zeilinger state, for instance, measuring the z-axis
spin of one of three entangled particles is equivalent to
cutting one ring of a Borromean set (
PDF), resulting in the other two particles becoming disentangled. Measurement in other ways results in the triad
collapsing into other linking configurations, such as the Hopf link, (3,3)-torus link, and 3-ring chain shown
here.
It is currently unclear whether the relationship between quantum entanglement and topological links is significant or incidental.
Some think it could have repercussions for the field of
quantum computing. Others are less conservative in their speculation, suggesting that Borromean links could be
just one form of hyperstructure in a
whole new hierarchy of matter.
posted by Relay at 7:03 PM on January 8, 2011 [3 favorites]