Kastner, Ruth
(2019)
Unitary-Only Quantum Theory Cannot Consistently Describe the Use of Itself:
On the Frauchiger-Renner Paradox.
[Preprint]
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Abstract
The Frauchiger-Renner Paradox is an extension of paradoxes based on the “Problem of Measurement,” such as Schrodinger’s Cat and Wigner’s Friend. All these paradoxes stem from assuming that quantum theory has only purely unitary (linear) dynamics, and the attendant ambiguity about what counts as a ‘measurement’—i.e., the inability to account for the observation of determinate measurement outcomes from within the theory itself. It is generally forgotten that Schrodinger constructed his ‘Cat’ Paradox as a reductio ad absurdum of unitary-only quantum theory (i.e., quantum theory without a well-defined non-unitary process of collapse or reduction), and the FR paradox is an accentuation of that absurdity. This paper discusses a basic inconsistency arising in the FR scenario at a much earlier point than the derived contradiction: namely, the inconsistency inherent in treating an improper mixture (reduced density operator) as a proper, epistemic mixture. This is an illegitimate procedure that is nevertheless endemic if quantum theory is assumed to be always unitary. In contrast, under a non-unitary account of quantum state reduction yielding determinate outcomes, the use of a proper mixture for measurement results becomes legitimate, and this entire class of paradoxes cannot be mounted. The conclusion is that the real lesson of the FR paradox is that it is the unitary-only assumption that needs to be critically reassessed.
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