Insolubility from No-Signalling
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This paper improves on the result in my (Bacciagaluppi in Eur. J. Philos. Sci. 3: 87–100, 2013), 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 result follows directly from the no-signalling theorem applied to the entangled state of measured system and ancilla. As opposed to many other ‘insolubility theorems’ for the measurement problem of quantum mechanics, it focuses on the impossibility of reproducing the phenomenological collapse of the state of the measured system.
KeywordsMeasurement problem Insolubility No-Signalling Von Neumann
I wish to thank audiences at Aberdeen, Berlin, Cagliari and Oxford, as well as Arthur Fine and Max Schlosshauer, who heard or read and commented on previous versions of this and connected material. I am particularly indebted to Alex Blum, Martin Jähnert and especially Christoph Lehner for discussions of Einstein’s argument and of how it might relate (or not) to von Neumann’s. These discussions also helped me redirect my use of the no-signalling theorem to the general case of measurements with ancillas, whether or not there is spatial separation. Finally, I wish to thank Elise Crull, my collaborator on the Leverhulme Trust Project Grant ‘The Einstein Paradox’: The Debate on Nonlocality and Incompleteness in 1935 (project grant nr. F/00 152/AN), during the tenure of which this paper was written.
- 8.Albert, D.Z.: Quantum Mechanics and Experience. Harvard University Press, Cambridge (1992) Google Scholar
- 14.Bub, J.: Quantum correlations and the measurement problem (2012). arXiv:1210.6371. Accessed 9 January 2013
- 15.Bub, J., Bananaworld: Quantum mechanics for primates (2012). arXiv:1211.3062. Accessed 9 January 2013
- 16.Fine, A.: Einstein’s critique of quantum theory: the roots and significance of EPR. In: Barker, P., Shugart, C.G. (eds.) After Einstein: proceedings of the Einstein Centennial Celebration at Memphis State University, 14–16 March 1979, pp. 147–158. Memphis State University Press, Memphis (1981). Reprinted in: Fine, A. The shaky game: Einstein, realism and the quantum theory, pp. 26–39. University of Chicago Press, Chicago (1986) Google Scholar
- 19.von Meyenn, K. (ed.): Eine Entdeckung von ganz außerordentlicher Tragweite: Schrödingers Briefwechsel zur Wellenmechanik und zum Katzenparadoxon. 2 vols. Springer, Berlin (2011) Google Scholar