Logical independence and quantum randomness
Abstract
We propose a link between logical independence and quantum physics. We demonstrate that quantum systems in the eigenstates of Pauli group operators are capable of encoding mathematical axioms and show that Pauli group quantum measurements are capable of revealing whether or not a given proposition is logically dependent on the axiomatic system. Whenever a mathematical proposition is logically independent of the axioms encoded in the measured state, the measurement associated with the proposition gives random outcomes. This allows for an experimental test of logical independence. Conversely, it also allows for an explanation of the probabilities of random outcomes observed in Pauli group measurements from logical independence without invoking quantum theory. The axiomatic systems we study can be completed and are therefore not subject to Gödel's incompleteness theorem.
 Publication:

New Journal of Physics
 Pub Date:
 January 2010
 DOI:
 10.1088/13672630/12/1/013019
 arXiv:
 arXiv:0811.4542
 Bibcode:
 2010NJPh...12a3019P
 Keywords:

 Quantum Physics
 EPrint:
 9 pages, 4 figures, published version plus additional experimental appendix