At the 1927 Como conference Bohr spoke the famous words “It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature.” However, if the Copenhagen interpretation really adheres to this motto, why then is there this nagging feeling of conflict when comparing it with realist interpretations? Surely what one can say about nature should in a certain sense be interpretation independent. In this paper I take Bohr’s motto seriously and develop a quantum logic that avoids assuming any form of realism as much as possible. To illustrate the non-triviality of this motto, a similar result is first derived for classical mechanics. It turns out that the logic for classical mechanics is a special case of the quantum logic thus derived. Some hints are provided as to how these logics are to be used in practical situations and finally, I discuss how some realist interpretations relate to these logics.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Baltag A., Smets S. (2011) Quantum logic as a dynamic logic. Synthese 179: 285–306
Bell, J. S. 1964. On the Einstein Podolsky Rosen paradox. Physics1(3), 195–200. Reprinted in Bell J. S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.
Bell, J. S. (1982). On the impossible pilot wave. Foundations of Physics 12, 989–999. Reprinted in Bell J. S. (1987). Speakable and unspeakable in quantum mechanics. Cambridge: Cambridge University Press.
Bell J. S. (1990) Against measurement. Physics World 3: 33–40
Birkhoff, G., von Neumann J. (1936). The logic of quantum mechanics. Annals of Mathematics 37(4), 823–843. (Reprinted in Hooker, C. A. (1975). The logico-algebraic approach to quantum mechanics, Vol. I, Boston: D. Reidel.)
Bohm D. (1952) A suggested interpretation of the quantum theory in terms of “Hidden” variables I & II. Physical Review 85(2): 166–193
Caspers M., Heunen C., Landsman N. P., Spitters B. (2009) Intuitionistic quantum logic of an n-level system. Foundations of Physics 39: 731–759
Clauser J. F., Horne M. A., Shimony A., Holt R. A. (1969) Proposed experiment to test local hidden-variable theories. Physical Review Letters 23(15): 880–884
Clifton R., Kent A. (2001) Simulating quantum mechanics by non-contextual hidden variables. Proceedings: Mathematical, Physical and Engineering Sciences 456(2001): 2101–2114
Corbett J. V., Durt T. (2009) Collimation processes in quantum mechanics interpreted in quantum real numbers. Studies in History and Philosophy of Modern Physics 40(1): 68–83
Döring A., Isham C. (2011) “What is a thing?”: Topos theory in the foundations of physics. In: Coecke B. (ed.) New structures for physics, Vol. 813 of Lecture Notes in Physics. Springer, Berlin, pp 753–937
Dummett M. (1976) Is logic empirical?. In: Lewis H. D. (ed.) Contemporary british philosophy, Vol. IV. George Allen and Unwin, London, pp 45–68
Feynman R. P., Leighton R. B., Sands M. (1963) The Feynman lectures on physics, Vol. 1. Addison-Wesley, Reading
Folse H. J. (1981) Complementarity, Bell’s theorem, and the framework of process metaphysics. Process Studies 11(4): 259–273
Griffiths R. B. (2011) EPR, Bell, and quantum locality. American Journal of Physics 79(9): 954–965
Hermens R. (2011) The problem of contextuality and the impossibility of experimental metaphysics thereof. Studies in History and Philosophy of Modern Physics 42(4): 214–225
Heunen, C., Landsman, N. P., Spitters, B. (2011). Bohrification of operator algebras and quantum logic Synthese pp. 1–34. doi:10.1007/s11229-011-9918-4.
Isham C. J. (1995) Lectures on quantum theory. Imperial College Press, London
Kent A. (1999) Noncontextual hidden variables and physical measurements. Physical Review Letters 83(19): 3755–3757
Kochen, S., & Specker, E. P. (1967). The problem of hidden variables in quantum mechanics. Journal of Mathematics and Mechanics 17, 59–67. (Reprinted in Hooker, C. A. (1975). The logico-algebraic approach to quantum mechanics, Vol. I, Boston: D. Reidel.)
Maudlin T. (2005) The tale of quantum logic. In: Ben-Menahem Y. (ed.) Hilary Putnam (Contemporary philosophy in focus). Cambridge University Press, Cambridge, pp 156–187
Meyer D. A. (1999) Finitie precision measurement nullifies the Kochen–Specker theorem. Physical Review Letters 83(19): 3751–3754
Peres A. (1978) Unperformed experiments have no results. American Journal of Physics 46(7): 745–747
Peres A. (1984) The classic paradoxes of quantum theory. Foundations of Physics 14(11): 1131–1145
Peres A. (2002) Quantum theory: Concepts and methods. Kluwer Academic, Dordrecht
Popper K. R. (1968) Birkhoff and von Neumann’s interpretation of quantum mechanics. Nature 219: 682–685
Putnam, H. (1969). Is logic empirical?. Boston studies in the philosophy of science V. (Reprinted in Hooker, C. A. (1975). The logico-algebraic approach to quantum mechanics, Vol. II, Boston: D. Reidel.)
Stairs A. (1983) Quantum logic, realism, and value definiteness. Philosophy of Science 50: 578–602
von Neumann, J. (1955) Mathematical foundations of quantum mechanics (R. T. Beyer, Trans). Princeton: Princeton University Press. (Original title: Mathematische Grundlagen der Quantenmechanik, Berlin 1932).
About this article
Cite this article
Hermens, R. Speakable in quantum mechanics. Synthese 190, 3265–3286 (2013). https://doi.org/10.1007/s11229-012-0158-z
- Quantum logic
- Intuitionistic logic