Abstract
Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, within this axiomatic system. I will show that certain mathematical propositions can be encoded in quantum states and truth values of the propositions can be tested in quantum measurements. I will then show that whenever a proposition is undecidable within the system of axioms encoded in the state, the measurement associated with the proposition gives random outcomes. This suggests a view according to which randomness in quantum mechanics is of irreducible nature.
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References
Barrow, J.D.: Gödel and Physics. In: Horizons of Truth, Kurt Gödel Centenary Meeting, Vienna, April 27-29 (2006) arXiv:physics/0612253
Calude, C.S., Stay, M.A.: Int. J. Theor. Phys. 44, 1053–1065 (2005)
Svozil, K.: Phys. Lett. A 143, 433–437 (1990)
Calude, C.S., Svozil, K. (2006) arXiv:quant-ph/0611029
Chaitin, G.J.: Int. J. Theor. Phys. 21, 941–954 (1982)
Calude, C.S., Jürgensen, H.: Appl. Math. 35, 1–15 (2005)
Paterek, T., Dakić, B., Brukner, Č. (2008) arXiv:0804.2193
Bandyopadhyay, S., et al.: Algorithmica 34, 512 (2002)
Kochen, S., Specker, E.P.: J. Math. Mech. 17, 59 (1967)
Bell, J.: Physics 1, 195 (1964)
Zeilinger, A.: Found. Phys. 29, 631–643 (1999)
Paterek, T., Prevedel, R., Kofler, J., Klimek, P., Aspelmeyer, M., Zeilinger, A., Brukner, Č. (submitted)
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Brukner, Č. (2008). Quantum Experiments Can Test Mathematical Undecidability. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds) Unconventional Computing. UC 2008. Lecture Notes in Computer Science, vol 5204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85194-3_1
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DOI: https://doi.org/10.1007/978-3-540-85194-3_1
Publisher Name: Springer, Berlin, Heidelberg
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