Philosophy, Physics

Efimov’s exotic effect

Borromean rings

Most people have never heard of Vitaly Efimov or the exotic physics that he discovered as a young Russian scientist in 1970. I along with several colleagues got to meet Professor Efimov in 2014 at a dinner during a workshop in which I was participating at the Institute for Nuclear Theory of the University of Washington in Seattle. It was good to meet him. He reflected the kind of sanity and simple wisdom I associate with those deeply steeped in the ethos of science. Scientists have a natural affinity for and mutual understanding of one another when they get together, no matter where they come from. But what is so striking about Efimov physics?

Oddly enough, the physics of three bodies that mutually exert forces on one another is remarkably difficult. It was already known by Isaac Newton (1642-1727) that it is very challenging to get an exact mathematical solution for the mutual effect of three (or more) gravitating bodies, although Newton showed that two such bodies are remarkably simple to treat. In fact, it is only in the latter half of the 20th Century that conceptual advances in mathematical physics and technical advances with powerful digital computers enabled physicists to tackle the general three-body problem in practical ways.

If the bodies are very small ones like atoms instead of planets, we now know that Newton’s “classical” laws of motion must be replaced by new ones governed by discoveries in the early 20th Century known as “quantum mechanics.” Quantum physics explains how elementary entities like electrons, protons, or neutrons can bind together to form atoms, or how atoms can bind together to form molecules and build up the things in the world. I have spent my entire career studying such things. The “quantum world” is quite unlike that of Newton’s “classical world,” so much so that people still argue over what it means, although we are quite good at calculating real measurable effects involving atoms and other elementary entities.

Professor Efimov’s contribution in 1970 involved adding the laws of quantum physics to the three-body problem [1]. He discovered that three “quantum particles” that had just the right properties could bind together in a totally unexpected way that we now call “Efimov physics” [2]. In fact, one odd aspect of Efimov’s effect is that even if two of the particles could not bind to one another at all, adding a third could make the three stick together. This is just like the Borromean rings shown in the above image: you can not pull the three rings apart, but remove any one, and the remaining two fall apart easily.

It took a long time for Professor Efimov’s work to be appreciated. The first really definitive evidence of such states was demonstrated by my colleague, Rudolf Grimm, at the University of Innsbruck, Austria, in 2006 [3]. Rudi’s experimental physics group there could make three very cold cesium atoms stick together in the way expected for an Efimov state of the Borromean type. I had been studying the physics of cold cesium atoms where a special “resonance” effect could be produced by tuning a magnetic field to give the conditions required for the Efimov effect. I later contributed to 6 physics articles on Efimov physics, including one with Rudi’s group. It was due to my work in this area that I was attending the 2014 workshop in Seattle where I met Professor Efimov.

Beyond the physics

The truly odd thing is the oblique connection Professor Efimov’s work has with my pair of essays entitled Word and Fire for BioLogos, which I had written in 2014. These essays explore the fundamental unity of physics across vast ranges of space and time, from the cosmological to the everyday. While the essays have to do with the special chemistry of carbon atoms that is the basis of life, they ranged far beyond that to the philosophical and religious dimension of life, given the scope of the human mind to take in all of reality and its remarkable intelligibility.

All life in the universe, including the scientists who now study cosmology and Efimov states, depends on there being carbon and the other heavier elements like oxygen to build up the molecules on which life is based. The carbon is only synthesized from three alpha particles (helium nuclei) that were generated in the early universe and come together in the very hot interior of dying stars to make a carbon nucleus. This fusion of alpha particles is only possible because a special quantum state, known as the Hoyle state, exists in just the right way. Without this alpha-fusion enabled by the Hoyle state, no carbon-based life (as ours is) could exist anywhere in the universe. My essay Fire looks at this special physics of carbon formation in ancient stars of the early universe, whereas the Word essay looks at our contemporary situation

Professor Efimov’s original 1970 article, interestingly enough, raised the question as to whether the special quantum state of the carbon nucleus involved in alpha particle fusion might be one of these new kinds of three-body quantum states that he was proposing. It turns out that the Hoyle state is not an Efimov state, but that could not be known in 1970, as Professor Efimov noted in his paper, since the needed calculations could not be done then; they have only been carried out recently [4]. However, the other three-body system that Professor Efimov discussed in 1970, the triton made up of one proton and two neutrons (heavy hydrogen), does indeed turn out to involve one of his special states. His paper was remarkably insightful.

One thing that I have come to appreciate very much after a life in science is that all things are interconnected. Ordinary human life today is connected to events in the universe long, long ago and far, far away. The entire universe is fine-tuned to be just right so that we can be here to participate in it as the kind of beings that we find ourselves to be. Physics on all times scales, from the billions of years since the Big Bang to the unimaginably short time scale of the collision of three alpha particles to make a carbon nucleus (much less than a billionth of a billionth of a second), all work together to make a “universe.” where everything hangs together and our living human minds comprehend it all, even if imperfectly [5].

Our word “universe” comes from the fusion of two Latin words meaning “one” and “to turn.” Thus, to be a universe means to be turned or combined into one, into a whole. The human mind takes in all the scattered bits of knowledge that come to it and integrates it into a picture of the whole of reality, the universe in which we live. This relates to the ancient questions of being and becoming, of the one and the many, of the universal and the particular: what remains stable in a world of flux and change? The integration is a life-long process–of all of us together, not just the work of any one individual–and we then live our lives within the scope of this collectively generated picture. It is something we do naturally. We can not avoid it. Whether we think of it in terms of “mythos” or in terms of “science,” we all do it nevertheless. Otherwise, we would not be human.

To be human is to have a worldview, a picture of the whole in which we fit, a sense of “what is” and “what is not.” And not only a sense of what is true, but a sense of what is good and what is not good. This is inescapably “beyond physics,” that is, what has traditionally been called metaphysics. It is not possible to engage with science or life without it, without a sense of the meaning, or lack of meaning, of the whole. But as Richard Feynman tells us, science as we normally conceive it can not and does not give us a sense of the meaning of the whole. We have to look elsewhere for that. And that takes me back to my Word essay of the Word and Fire pair: science is only possible because of the order, the Logos, in reality that enables it to be an intelligible universe ordered to its source of unity. That order transcends us, given to us from a source beyond us. “In the beginning was the Logos…” Everything follows from that: we participate in an order we have been given and to which we are responsible. Professor Efimov’s physics is true and good and beautiful as it opens up for us a tiny glimpse of the order that encompasses all things and enables them to be what they are.


1. Vitaly Efimov, then at the A. F. Ioffe Physico-Technical Institute, Leningrad, USSR, published his paper in English in Physics Letters, Volume 33B, pages 563-564 (21 December 1970), entitled “Energy levels arising from resonant two-body forces in a three-body system.”

2. A nice and clear review of Efimov physics, sticking close to Efimov’s original formation, has been written (with co-author Shimpei Endo) by Pascal Naidon, a former postdoc of mine at NIST who is now a senior research scientist at RIKEN in Japan, in Reports on Progress in Physics, Volume 80, Article 056001 (78 pages) (2017), entitled “Efimov physics: a review.”

3. The paper was published in Nature, Volume 440, pages 315–318 (2006) by Kraemer et al, entitled “Evidence for Efimov quantum states in an ultracold gas of cesium atoms.” 

4. Section of the review article in [2] above explains how more recent studies have conclusively shown that the Hoyle state of the carbon nucleus is not an Efimov state. Section of the same review article shows that the triton can be interpreted as a true Efimov state.

5. I discuss the enormous range of time scales involved in life in another essay for BioLogos, entitled Time and Eternity.