The Golden Ratio and the Quantum World

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Looks like God is playing dice with the Universe.

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.

And the winning number is:

\varphi = \frac{1+\sqrt{5}}{2}\approx 1.61803\,39887\ldots\,

or

\varphi = [1; 1, 1, 1, \dots] = 1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \ddots}}}


The proper response to this should go something like "OMG!"

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A Slovenian scientist and mathematician following Mohamed El Naschie expand the idea of mechanical oscillators. Many papers have been published on this subject by L. Marek-Crnjac. Take a two degree of freedom oscillator. Two masses connected by two linear springs. Write the equation of motion. Set the value for the masses as well as the spring constants equal unity. The secular equation is then simply a quadratic equation. The Eigen values are golden mean related. The only positive real Eigen value is the golden mean. Imagine now that you have infinitely many such oscillators connected together. Consequently you can estimate the Eigen value using two well known theorems on Eigen values. These are the Southwell theorem and the Dunkerly theorem. They correspond to what we have studied in school about joining electrical resistance of Ome’s law. When they are successive you add the inverses and when they are parallel you add them. Eigen values are frequencies. Frequencies are energy and energy is mass. Extrapolating the whole thing to quantum mechanics as argued by El Naschie and Marek-Crnjac you have another plausibility explanation for why the golden mean will pop up in any accurate measurement in quantum mechanics phenomenon.

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This page contains a single entry by Christian Sarkar published on January 9, 2010 10:38 AM.

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