Tuesday, July 29, 2014

Quantum Mechanics Reconstruction 

I want to announce the paper: http://arxiv.org/abs/1407.7610:  

Quantum Mechanics reconstruction from invariance of the laws of nature under tensor composition

Quantum and classical mechanics are derived from 4 physical principles:
  • the laws of nature are invariant under time evolution, 
  • the laws of nature are invariant under tensor composition, 
  • the laws of nature are relational, 
  • positivity (the ability to define a physical state). 

Quantum mechanics is singled out by a fifth experimentally justified postulate: nature violates Bell's inequalities.

I will put the Standard Model math explanation series on hold for a bit and in subsequent posts I'll explain this result. ALL of quantum mechanics formalism follows from those 4+1 physical principles in a rigorous, constructive, step by step argument. Both the Hilbert space and the state space realizations are derived. 

The axioms are minimal: 

- Composition (tensorial, categorical) arguments are needed because there are classical physics models for quantum mechanics for a single particle. Correlations between systems are the essential quantum characteristic.
- Information theoretical arguments (positivity) are used because composition arguments produce a third unphysical solution. However there is no "it from bit", but: "it is what can generate a bit".

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