Piero Scaruffi(Copyright © 2013 Piero Scaruffi | Legal restrictions )
These are excerpts and elaborations from my book "The Nature of Consciousness"
Quantum Mechanics as Pure Math
There is a school of thought that is trying to derive Quantum Mechanics as a purely abstract mathematical theory from a handful of axioms. In 2001 the British physicist Lucien Hardy showed that quantum mechanics is actually the simplest theory that can describe a physical system if one wants to express the probability of observing each of the system's possible states in a measurement, given five simple and reasonable axioms ("Quantum Theory from Five Reasonable Axioms", 2001). Another derivation based on axioms, but in this case axioms about information, was proposed in 2010 by Giulio Chiribella, Giacomo Mauro D'Ariano and Paolo Perinotti: information should be localized in space and time, systems should be able to encode information about each other, and every process should in principle be reversible, i.e. information must be conserved ("Informational Derivation of Quantum Theory", 2011). In the so-called "standard model", elementary particles are manifestations of three "symmetry groups": SU(3), SU(2) and U(1), correspond to the strong, weak and electromagnetic forces. In 1973 the Turkish mathematicians Feza Gursey and Murat Gunaydin discovered that one can build a model of the quarks (of the strong force, of the symmetry group SU(3)) based on octonionic algebra (octonions are numbers with eight degrees of freedom). In 2014 the Canadian mathematician Cohl Furey constructed an octonionic model of both the strong and electromagnetic forces, a model that also explains why the electric charge comes in discrete units. The model consists in ten matrices called "generators." Nine of the generators act like spatial dimensions, and the tenh behaves like time. String theory too predicts ten dimensions.
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