Abstract
This paper improves on the result in my [1], showing that within the framework of the unitary Schroedinger 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.
| Original language | English |
|---|---|
| Pages (from-to) | 3465-3474 |
| Number of pages | 10 |
| Journal | International Journal of Theoretical Physics |
| Volume | 53 |
| Issue number | 10 |
| Early online date | 21 Nov 2013 |
| DOIs | |
| Publication status | Published - Oct 2014 |
Bibliographical note
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.Keywords
- measurement problem
- insolubility
- no-signalling
- Von Neumann