There is probably nothing that makes mathematicians and physicists happier than discovering that untidy models resolve into harmonies and order. This may be especially true for the often described as ‘bizarre’ world of quantum physics.

Take a ‘chain’ of cobalt niobate atoms – like a magnetic bar one atom wide. Cool the chain to near absolute zero (zero degrees Kelvin). The atoms in the bar, which display the properties of having ferromagnetism (they magnetize like an iron bar), have a direction of spin. By introducing a magnetic force at right angles to that spin, the ‘spin’ of the atoms becomes…uncertain, erratic…a state that is characterized as quantum critical. Behavior of ‘normal’ atoms at the quantum level is already…unusual, but in a quantum critical state…. In this case, the cobalt niobate chain begins to act like a guitar string. It can be ‘tuned.’ The seemingly erratic spins begin to resonate. They vibrate at a specific frequency, as if making a note.

Using very sophisticated detection apparatus, an atomic probe of scattering neutrons, the researchers were able to measure the vibration frequency at each point in what became a scale (a series of frequencies). Then they noticed something both wonderful and unexpected: The first two ‘notes’ (frequencies) in this scale were exactly in the ratio of 1.618 to each other. This is the famous Golden Ratio, which has been studied for at least 2,400 years dating back to its supposed discovery by Pythagoras, the ancient Greek mathematician. The ratio, called Phi (after the Greek letter), has surfaced not only in geometry, but also in the arts (music, painting, architecture). It is considered the most astonishing number in the history of mathematics.

To find this number expressed by the vibrations of atoms under conditions of quantum criticality, well, it promises the possibility of something ordered and beautiful behind behaviors governed by the Heisenberg Uncertainty Principle.

Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture.
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The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology. Prof. Tennant remarks on the perfect harmony found in quantum uncertainty instead of disorder. “Such discoveries are leading physicists to speculate that the quantum, atomic scale world may have its own underlying order. Similar surprises may await researchers in other materials in the quantum critical state.”

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It’s predictable that some people will see the discovery of a Golden Ratio in a quantum behavior as a spiritual finding. For the specialists, it’s probably a stimulus and a clue that will lead to further research, no more, no less.