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Borromean Rings and Quantum Mechanics
January 8, 2011 6:52 PM   Subscribe

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 dephlogisticated (24 comments total) 55 users marked this as a favorite

 
And they can also be found on John Bonham's drumset.
posted by Relay at 7:03 PM on January 8, 2011 [3 favorites]


Don't forget Borromean Rings made out of DNA (5 yrs before the smaller co-ordination chemistry based syntheses)
posted by lalochezia at 7:05 PM on January 8, 2011 [1 favorite]


And Lacan loved them too!
posted by Obscure Reference at 7:11 PM on January 8, 2011 [2 favorites]


I sure could go for a cold Ballantine Ale right now.
posted by TedW at 7:12 PM on January 8, 2011 [1 favorite]


Early in a Knot Theory course I had to draw set of four rings, no two linked. I remember poring over every crossing, and I'm sure it wasn't 100% when I turned it in. Since then I've thought of a much nicer way to do it, which I'm sure isn't optimal and, if it is, definitely isn't original. Think of a pair of rubber bands, one on each hand between thumb and forefinger, but passed behind each other so your hands are bound together. Tie a loop of string through one of them to free one hand, and add another rubber band through the thumb and forefinger positions of the other hand. Continue adding rubber bands in this end, and finally end with a loop of string on this end. You should have a chain of rings that won't come undone unless any one rubber band or loop of string is cut, after which every piece comes apart from every other one.

Disclosure: IAAMathematician, but IANAKT (knot theorist)
posted by monkeymadness at 7:19 PM on January 8, 2011


Love this post, also love the user name.
posted by empath at 7:23 PM on January 8, 2011


Hilarious. Ok, so I'm far from original. Funny that rubber bands seem to be the way to think of these things!
posted by monkeymadness at 7:23 PM on January 8, 2011


Also seen in many public bathrooms in the US- Svenska Cellulosa Aktiebolaget uses a valknut as their logo.
posted by zamboni at 7:35 PM on January 8, 2011 [1 favorite]


I had to draw set of four rings, no two linked.

The Borromean rings and your example are both special cases of Brunnian links, which can have an arbitrary number of simple closed curves.
posted by twoleftfeet at 8:07 PM on January 8, 2011 [2 favorites]


If you connect vertices of an icosahedron to form mutually perpendicular golden rectangles, the boundaries of the rectangles form Borromean rings.
posted by twoleftfeet at 8:31 PM on January 8, 2011 [6 favorites]


Bathsheba Grossman's version is $24.
posted by spasm at 8:52 PM on January 8, 2011 [1 favorite]


Sigh, it makes me sad that I couldn't visualize the icosahedron set up, but that diagram is just wonderful.
posted by sammyo at 8:56 PM on January 8, 2011


Great, great post.
posted by ORthey at 9:13 PM on January 8, 2011


Fabulous, thought-provoking post. Thank you.
posted by ~Sushma~ at 9:23 PM on January 8, 2011 [1 favorite]


Not to be confused with Boromirian rings, which turn you invisible and lead to Shakespeare-worthy levels of family drama.
posted by Bromius at 9:25 PM on January 8, 2011 [2 favorites]


Needs more links.
posted by dougrayrankin at 12:47 AM on January 9, 2011


knotty.
posted by eeeeeez at 1:32 AM on January 9, 2011


So what do you call the configuration resulting after I drop a spherical coil shaker whisk into a standard wire dish drying rack (sans bunny) and the two shapes merge into a linked whole? Plainly, one one of the merged items, the whisk, can no longer perform its intended utility, and the second--the dish rack--is limited in its performance. Is there, perhaps, a third element that the merging of the two has created, which has far-reaching implications in the fields of manual drink blending, static-state culinary implement dehydrating processes, and (dare I say) quantum mechanics?
posted by eegphalanges at 3:18 AM on January 9, 2011 [2 favorites]


What an odd and thoroughly fascinating post!

As for your user name... just curious: you're not an old Phlogger are you? If you don't know what I mean by that then I guess the answer's no. :-)
posted by Decani at 3:23 AM on January 9, 2011


Fantastic post. Thanks!
posted by Ahab at 5:11 AM on January 9, 2011


Is there, perhaps, a third element that the merging of the two has created, which has far-reaching implications in the fields of manual drink blending, static-state culinary implement dehydrating processes, and (dare I say) quantum mechanics?

No.
posted by Xezlec at 8:51 AM on January 9, 2011


I ran into these at a math camp when we watched the video Not Knot (part one part two). Much later, I eventually got a tatoo with three ouroboroses in this structure. So fantastic post.
posted by Hactar at 10:30 AM on January 9, 2011


As for your user name... just curious: you're not an old Phlogger are you?

My user name is a reflection of my abiding hope that I cannot be set on fire.
posted by dephlogisticated at 12:39 PM on January 9, 2011 [1 favorite]


As for the historical meaning of these rings, they represented the three families which ruled Lombardy at that time, namely Sforza, Visconti and Borromeo. They made a pact of peace through marriage (see here) and that was the symbol the chose for this pact. If any of the families broke the pact, the other two would fell apart as well.
posted by volpe at 2:14 PM on January 9, 2011


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