The discovery of pentagonal symmetry in crystals - even though rejected for decades - has “fundamentally altered how chemists conceive of solid matter.”
- Royal Swedish Academy of Sciences in awarding
$1.5 million 2011 Nobel Prize in Chemistry
Left: Optical micrograph of a large dodecahedral grain of Zinc 56.8,
Manganese 34.6 and Holmium 8.7 quasicrystal successfully grown from the
melt via a slow-cooling method by Ian Fisher, Ph.D., Stanford University,
and Paul Canfield, Ph.D., Ames Laboratory. Right: Electron
diffraction patterns taken along the 10-fold symmetry axis of the
Aluminum 72, Nickel 20 and Cobalt 8 decagonal quasicrystal. See: Nature.
Dan Shechtman, Ph.D., Technion-Israel Institute of Technology in Haifa, Israel, has received the 2011 Nobel Prize in Chemistry after three decades of ridicule by his science peers. “I was thrown out of my research group ( in 1982). They said I brought shame on them with what I was saying (about discovering quasicrystals). I never took it personally. I knew I was right and they were wrong.” Since Prof. Shechtman's 1982 discovery, quasicrystals have been produced in laboratories and a Swedish company found them in one of the most durable kinds of steel, which is now used in products such as razor blades and thin needles made specifically for eye surgery. Quasicrystals are also being studied for use in new materials that convert heat to electricity.
Roger Penrose was the first to conjecture that quasi-crystal growth is the product of collapsing a quantum mechanical wave in Hilbert Space. There is no other plausible explanation as to how indeterminate tiling systems grow. the alternative would be that the crystals know a priori, where they are going before they get there. For instance, you can tile a plane with squares with in a fix rectangular boundary quite easily. The resulting structure is invariant within the fix boundary. However, the fixed boundary for tiles with 5 fold symmetry will lead to numerous solutions given the same fixed boundaries. However to achieve these solutions, you would require a puzzle solving algorithm. These solutions are not arrived at by simplistic periodic crystal growth.
In lieu of an algorithm, all possible solutions exist as a wave function in Hilbert space. The collapse of the wave function in Event space leads to the correct assemblage in Event space, error free.
Quantum mechanical functions existing in Hilbert Space, has profound ramifications on the nature of reality.
The implication is that the Event space in which we move and exist has an antecedent of all possibilities existing at once and this antecedent is the higher reality from which Event space is derived. Thus when we observe electrons clouds in the vicinity of nuclei we are peering at reality in it's fullness.