Insolubility Theorems and EPR Argument
I present a very general and simple argument—based on the no-signalling theorem—showing that within the framework of the unitary Schrödinger equation it is impossible to reproduce the phenomenological description of quantum mechanical measurements (in particular the collapse of the state of the measured system) by assuming a suitable mixed initial state of the apparatus. The thrust of the argument is thus similar to that of the ‘insolubility theorems’ for the measurement problem of quantum mechanics (which, however, focus on the impossibility of reproducing the macroscopic measurement results). Although I believe this form of the argument is new, I argue it is essentially a variant of Einstein’s reasoning in the context of the EPR paradox—which is thereby illuminated from a new angle.
KeywordsQuantum mechanics Measurement problem Insolubility theorems EPR argument
I wish to thank in particular Arthur Fine for very perceptive comments on a previous draft of this paper. Many thanks also to Theo Nieuwenhuizen for inspiration, to Max Schlosshauer for correspondence, to two anonymous referees for shrewd observations, and to audiences at Aberdeen, Cagliari and Oxford (in particular to Harvey Brown, Elise Crull, Simon Saunders, Chris Timpson and David Wallace) for stimulating questions. This paper was written during my tenure of a Leverhulme Grant on ‘The Einstein Paradox’: The Debate on Nonlocality and Incompleteness in 1935 (Project Grant nr. F/00 152/AN), and it was revised for publication during my tenure of a Visiting Professorship in the Doctoral School of Philosophy and Epistemology, University of Cagliari (Contract nr. 268/21647).
- Allahverdyan, A. E., Balian, R., & Nieuwenhuizen, T. M. (2011). Understanding quantum measurement from the solution of dynamical models. arXiv:1107.2138v1.
- Bacciagaluppi, G., & Crull, E. M. (in preparation). ‘The Einstein Paradox’: The debate on nonlocality and incompleteness in 1935. Cambridge: Cambridge University Press, expected publication 2014 or 2015.Google Scholar
- Bell, J. S. (1964). On the Einstein-Podolsky-Rosen paradox. Physics, 1, 195–200 (Reprinted in Bell, J. S. (1987). Speakable and unspeakable in quantum mechanics (pp. 14–21). Cambridge: Cambridge University Press).Google Scholar
- Busch, P., Grabowski, M., & Lahti, P. (1995). Operational quantum physics (Vol. m31). Lecture Notes in Physics. Berlin: Springer; second, corrected printing, 1997.Google Scholar
- d’Espagnat, B. (1966). Two remarks on the theory of measurement. Supplemento al Nuovo Cimento, 4, 828–838.Google Scholar
- d’Espagnat, B. (1971). Conceptual foundations of quantum mechanics. Reading, Mass.: W. A. Benjamin.Google Scholar
- Fine, A. (1981). Einstein’s critique of quantum theory: The roots and significance of EPR. In P. Barker, & C. G. Shugart (Eds.), After Einstein: Proceedings of the Einstein centennial celebration at Memphis State University, 14–16 March 1979 (pp. 147–158). Memphis: Memphis State University Press (Reprinted in Fine, A. (1986). The shaky game: Einstein, realism and the quantum theory (pp. 26–39). Chicago: University of Chicago Press).Google Scholar
- Gisin, N. (1989). Stochastic quantum dynamics and relativity. Helvetica Physica Acta, 62(4), 363–371.Google Scholar
- Price, H. (1996). Time’s arrow and Archimedes’ point: New directions for the physics of time. New York: Oxford University Press.Google Scholar
- Stein, H. (1997). Maximal extension of an impossibility theorem concerning quantum measurement. In R. S. Cohen, M. Horne, & J. Stachel (Eds.), Potentiality, entanglement and passion-at-a-distance: Quantum mechanical studies for Abner Shimony, Vol. 2 (Vol. 194, pp. 231–243). Boston Studies in the Philosophy of Science, Dordrecht: Kluwer.Google Scholar
- von Meyenn, K. (Ed.) (2011). Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon, 2 vols. Berlin and Heidelberg: Springer.Google Scholar
- von Neumann, J. (1932). Mathematische Grundlagen der Quantenmechanik. Berlin: Springer 2nd ed. 1996. (Transl. by R. T. Beyer (1955). Mathematical foundations of quantum mechanics. Princeton: Princeton University Press).Google Scholar