Mathematical undecidability and quantum randomness Export

@article{citeulike:3731424, abstract = {We propose a new link between mathematical undecidability and quantum physics. We demonstrate that the states of elementary quantum systems are capable of encoding mathematical axioms and show that quantum measurements are capable of revealing whether a given proposition is decidable or not within the axiomatic system. Whenever a mathematical proposition is undecidable within the axioms encoded in the state, the measurement associated with the proposition gives random outcomes. Our results support the view that quantum randomness is irreducible and a manifestation of mathematical undecidability.}, archivePrefix = {arXiv}, author = {Paterek, Tomasz and Kofler, Johannes and Prevedel, Robert and Klimek, Peter and Aspelmeyer, Markus and Zeilinger, Anton and Brukner, Caslav}, citeulike-article-id = {3731424}, citeulike-linkout-0 = {http://arxiv.org/abs/0811.4542}, citeulike-linkout-1 = {http://arxiv.org/pdf/0811.4542}, day = {27}, eprint = {0811.4542}, keywords = {hierarchy-of-abstract-machines, hierarchy-of-complexity-classes, hierarchy-of-decision-problems, hierarchy-of-languages, hypercomputability, physicalized-mathematics, undecidability}, month = {Nov}, posted-at = {2008-12-06 12:46:22}, priority = {2}, title = {Mathematical undecidability and quantum randomness}, url = {http://arxiv.org/abs/0811.4542}, year = {2008} }

TY - JOUR ID - citeulike:3731424 L3 - citeulike-article-id:3731424 N2 - We propose a new link between mathematical undecidability and quantum physics. We demonstrate that the states of elementary quantum systems are capable of encoding mathematical axioms and show that quantum measurements are capable of revealing whether a given proposition is decidable or not within the axiomatic system. Whenever a mathematical proposition is undecidable within the axioms encoded in the state, the measurement associated with the proposition gives random outcomes. Our results support the view that quantum randomness is irreducible and a manifestation of mathematical undecidability. TI - Mathematical undecidability and quantum randomness KW - hierarchy-of-abstract-machines KW - hierarchy-of-complexity-classes KW - hierarchy-of-decision-problems KW - hierarchy-of-languages KW - hypercomputability KW - physicalized-mathematics KW - undecidability AU - Paterek, Tomasz AU - Kofler, Johannes AU - Prevedel, Robert AU - Klimek, Peter AU - Aspelmeyer, Markus AU - Zeilinger, Anton AU - Brukner, Caslav PY - 2008/Nov/27/ UR - http://arxiv.org/abs/0811.4542 ER -