Golden ratio discovered in a quantum world

Golden ratio discovered in a quantum world
The magnetic field is used to tune the chains of spins to a quantum critical state. The resonant modes (“notes”) are detected by scattering neutrons. These scatter with the characteristic frequencies of the spin chains. Credit: Tennant/HZB

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 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 the researchers have focused on the 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 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
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Jan 07, 2010
This wiki article gives more detail about the quantum phase transitions which account for the fractal properties of the process http://en.wikiped...al_point What I don't understand is how interaction between the spins leads to resonance, how do spins interact?

Jan 07, 2010
I always understood "spin" to equate to a vibrational state, which would imply frequency/amplitude. So various "spins" will interact either constructively or destructively.

My 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.

Jan 08, 2010

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

Jan 08, 2010
This is the probably THE biggest discovery to come out of quantum weirdness. I've been espousing the idea for ages that the whole universe is one colossal fractal (including us humans), and this encoding of spins at the quantum level shows that this underlying Phi symmetry is scale invariant. That is, the golden ratio is universal and can be observed at all levels of reality. Intelligent design, anybody?

Jan 08, 2010
What good is intelligent design if we are all terminally stupid as a result thereof?

Jan 08, 2010
My 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?

Jan 10, 2010
Root system of E8 Lie group solves trivial question: "Which structure should have the tightest lattice of particles, exchanged/formed by another particles?". And such question has perfect meaning even from classical physics point of view! Such question has a perfect meaning in theory, describing the most dense structure of inertial particles formed by energy exchange between another particles. Another systems, which could exhibit E8 geometry are nested density fluctuations, which occurs inside of condensing supercritical vapor temporarily or so called Wigner crystals inside of cold plasma crystals.

Jan 13, 2010
As above- so below. You were told that, at least a few thousand years back. Get with the program. :)
Thus 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!

Jan 14, 2010
..the golden ratio is universal and can be observed at all levels of reality. Intelligent design, anybody?
Of course not - golden mean ratio is closely related to densest particle packing in similar way, like the E8 group geometry. Try to have look at this animation:

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.

Jan 14, 2010
In natural systems golden mean minimizes the surface/volume ratio, i.e. it defines most effective object packing in situations, where many particles are involved. In such objects energy spreads in slowest possible way (because they're so compact), which means, these objects are most stable and atemporal, i.e. they're of highest fitness and they can survive easier. Human brain is just an engine for particularly slow but atemporal energy spreading (i.e. without dispersion). Solitons (not just those in human brain) consist of waves, where frequency and energy of components follows golden mean ratio, too. Evolution is analogous to travel in dispersion environment, so we can imagine particles and planets as a most compact solitons, which survived the travel through CMB noise in most succesfull way.

Jan 14, 2010
..I hope that these scientists, and plenty of others, pursue this area of research aggressively..
We can apply the above principles too. Research follows both information spreading along well defined gradients/surfaces of knowledge, i.e. formal theories, both intuitive holistic thinking through bulk of knowledge independently to existing theories (so called "crackpottery", but I rather call it a "mutations"). After then the most effective strategy is just the approach, where the formal and intuitive approaches are ballanced in golden mean ratio. So we shouldn't expect, only blind combinations of equations will lead to some TOE fast - intuitive insights and ideas are important here, too.

Feb 23, 2010
This is an excellent, open minded overview on the subject. We hope the author will expand this site. We also sincerely hope this will remain a clean, scientific site with purely scientific arguments using scientific language and refraining from the usual blog language. Could we point out in this connection that an Elsevier journal published a considerable amount of papers on the subject of the golden mean, E8 and high energy physics. A concise overview may be found in the following review article: The theory of Cantorian spacetime and high energy particle physics (an informal review), Chaos, Solitons & Fractals, 41, 2009, p. 2635.

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