# Golden ratio discovered in a quantum world

Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB, Germany), 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.

The research team is publishing these findings in *Science* on the 8 January.

On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study these nanoscale quantum effects the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on the nanoscale in solid state matter.

When applying a magnetic field at right angles to an aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains "The system reaches a quantum uncertain - or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."

By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains: "Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture." Radu Coldea is convinced that this is no coincidence. "It reflects a beautiful property of the quantum system - a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material", he explains.

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."

The researchers achieved these results by using a special probe - neutron scattering. It allows physicists to see the actual atomic scale vibrations of a system. Dr. Elisa Wheeler, who has worked at both Oxford University and Berlin on the project, explains "using neutron scattering gives us unrivalled insight into how different the quantum world can be from the every day". However, "the conflicting difficulties of a highly complex neutron experiment integrated with low temperature equipment and precision high field apparatus make this a very challenging undertaking indeed." In order to achieve success "in such challenging experiments under extreme conditions" the HZB in Berlin has brought together world leaders in this field. By combining the special expertise in Berlin whilst taking advantage of the pulsed neutrons at ISIS, near Oxford, permitted a perfect combination of measurements to be made.

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**More information:**Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Article in

*Science*, DOI:RE1180085/JEC/PHYSICS

**Citation**: Golden ratio discovered in a quantum world (2010, January 7) retrieved 21 September 2019 from https://phys.org/news/2010-01-golden-ratio-quantum-world.html

## User comments

gmurphyCalibanMy guess/intuition is that this harmonic symmetry is a Fundamental Property governing the relationship between matter and energy.

I hope that these scientists, and plenty of others, pursue this area of research aggressively.

shockrVibrational state... frequency.. harminic symmetry isn't this somewhere along the lines of string theory? (scientific layman here)

skand1nskyrgwCalibanMy personal(and also non-professional) opinion is that various theories(including string theory)are describing a part of the whole- eventually it is to be hoped that some kind of single theory will describe reality in an absolutely universal, fundamental way. of course, in order to do that may require(metaphorically speaking) god-like intelligence and insight- see skand1sky's comment- above.

Quantum and Classical physics also use spin, wavelength, vibrational state, et c to describe the properties of matter/energy- but so far, no one has developed a single theory that explains all. My hope is that this is the kind of result of research that will point the way. Can physical reality be understood as Feedback?

flaredoneKBKThus there is zero surprise over here that the expected and utilized system of mechanistic pattering at the gross level does occur at the quantum levels.

This all goes back to the idea of infinitely huge 2-d stress fields oscillating and interacting creates matter as a roiling and rolling spin interactive (vectoral resultant of that given interactive) we like to call an atomic structure. thus we get unidirectional time with the open future and the closed past. This also explains zeeman, lamor frequencies, etc, the whole kit and caboodle. Recall or know for the first time that this is explained in Maxwell's full original equations of 20 equations in 20 unknowns, and it is asymmetrical and explains the quanta of time. Asymmetrical considerations are required for time and energy, etc to even exist. Yet Lorentz and Heaviside removed the fundamentals and broke Maxwell's work. Golden ratio!

flaredonehttp://tinyurl.com/yd379mv

I can see nothing intelligent on the fact, some random arrangement of particles is more compact, then another one, so it spreads energy more slowly (so the universe appears larger in it).

After then it's logical to expect, certain particular arrangement remains the most effective possible - and this geometry corresponds just the largest observable space, i.e. the cosmic space. Don't look for mystery, where none exists.

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