Phi in Quantum Solid State Matter

Golden Ratio Discovered in Quantum World: Hidden Symmetry Observed for the First Time in Solid State Matter

In January 2010 Science Daily and Physics World announced the discovery of a hidden Phi symmetry in solid state matter.  As explained in the Science Daily article:

"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 E8 structure itself has relationships to Phi (1.618)

Symmetry plays a fundamental role in our understanding of the physical world. Perhaps the most intriguing of all is E8 – essentially a fantastically beautiful 8D diamond-like lattice of spheres in which each sphere is surrounded by 240 others.

E8 is a complex form of mathematical symmetry linked to string theory, glimpsed in the real world for the first time as described above in laboratory experiments on exotic crystals.

Mathematicians discovered this complex 248-dimensional symmetry called E8 in the late 1800s. The dimensions in the structure are not necessarily spatial, like the three dimensions we live in, but they correspond to mathematical degrees of freedom, where each dimension represents a different variable.  In the 1970s, the symmetrical form turned up in calculations related to string theory, a candidate for the "theory of everything" that might explain all the forces in the universe.  E8 shot to fame in 2007 when the US freelance physicist Garrett Lisi posted a paper on the arXiv preprint server suggesting that E8 could underpin a theory of everything by mapping out all known particles and how they interact with each other.

The two-dimensional view above of one plane the E8 structure reveals some interesting relationships to phi.  Note the light red concentric circles overlaying the illustration of E8.  The red lines were added to the E8 illustratation by using PhiMatrix software, where each red line is in a phi relationship, that is 1.618 of the diameter of the one before it.