Abstract
We claim that, as it stands, the Deutsch–Wallace–Everett approach to quantum theory is conceptually incoherent. This charge is based upon the approach’s reliance upon decoherence arguments that conflict with its own fundamental precepts regarding probabilistic reasoning in two respects. This conceptual conflict obtains even if the decoherence arguments deployed are aimed merely towards the establishment of certain ‘emergent’ or ‘robust’ structures within the wave function: To be relevant to physical science notions such as robustness must be empirically grounded, and, on our analysis, this grounding can only plausibly be done in precisely the probabilistic terms that lead to conceptual conflict. Thus, the incoherence problems presented necessitate either the provision of a new, non-probabilistic empirical grounding for the notions of robustness and emergence in the context of decoherence, or the abandonment of the Deutsch–Wallace–Everett programme for quantum theory.
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Notes
Here the use of ‘epistemic’ rather than ‘subjective’ would perhaps be more consistent with the terminology in use within the philosophy of science. However, we will retain the original terminology to avoid confusion. The more recent argument from Wallace (see in particular p. 249 of Wallace 2012) that within his program the probabilities are actually objective, over and above the decision theoretic basis given to the Born rule, will be considered in Sect. 3.2
Once more we note the existence of the more recent argument from (Wallace (2012), p. 249) relating to ‘objective’ quantum probability and refer to the reader forward to §3.2 for detailed consideration of this point.
See Saunders (1998) for detailed philosophical consideration of this idea and Wallace (2012, p. 10.4) for consideration of its changing role within Wallace’s arguments. An alternative ‘objective determinism’ understanding of personal identity in this context has also been considered, see Wallace (2007) and references therein for details. This distinction is not important for the purposes of the arguments given here.
They would, in this respect, then be at the disadvantage of their Bohmian rivals who’s own derivation would not seem to be susceptible to the same objections on the grounds of circularity (Valentini and Westman 2005).
This crucial feature can be seen explicitly within the ‘Wilsonian EFT’ scheme where the irrelevant terms are neglected on precisely the basis of scaling in powers of \(E/\varLambda \) (where \(E\) is the energy scale and \(\varLambda \) is the cutoff). It is also implicit within the ‘continuum EFT’ scheme since a similar discarding of terms due to scaling behaviour is needed to calculate the matching correction. See Bain (2012).
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Dawid, R., Thébault, K.P.Y. Many worlds: decoherent or incoherent?. Synthese 192, 1559–1580 (2015). https://doi.org/10.1007/s11229-014-0650-8
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DOI: https://doi.org/10.1007/s11229-014-0650-8