## Abstract

Hugh Everett III proposed his relative-state formulation of pure wave mechanics as a solution to the quantum measurement problem. He sought to address the theory’s determinate record and probability problems by showing that, while counterintuitive, pure wave mechanics was nevertheless empirically faithful and hence empirical acceptable. We will consider what Everett meant by empirical faithfulness. The suggestion will be that empirical faithfulness is well understood as a weak variety of empirical adequacy. The thought is that the very idea of empirical adequacy might be renegotiated in the context of a new physical theory given the theory’s other virtues. Everett’s argument for pure wave mechanics provides a concrete example of such a renegotiation.

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## Notes

See Barrett (1999, 2010, 2011a, b, 2014) and Barrett and Byrne (2012) for recent discussions of Everett’s understanding of physical theories in general and pure wave mechanics in particular. Much of this work is based on documents that can now be found in Barrett and Byrne (2012) and at the UCIspace Hugh Everett III Manuscript Archive permanent url: http://hdl.handle.net/10575/1060.

See Everett (1956, pp. 74–78) and Wigner (1961) for the two versions of the story. Wigner was a member of the physics faculty at Princeton while Everett was a graduate student in the department. The stories are remarkably similar, but there is a salient difference in presentation. While Everett used his story to argue that the standard collapse theory was inconsistent, Wigner used his to argue that in order for the standard theory to be consistent and for observers get determinate measurement results, observers, unlike ordinary physical systems, must cause collapses. Wigner thought that a sort of mind–body dualism was required to provide a complete, consistent, and principled formulation of the standard theory. In particular, he took the nonlinear dynamics to apply if and only if a conscious entity apprehends the state of a physical system.

Wigner believed that \(O\)-type measurements would allow one to tell whether \(A\) caused a collapse of \(S\). If the result was always \(+1\), then it did not cause collapses; if the result was ever \(-1\), then it did. For his part, Everett held that there were no collapses and, hence, a measurement of \(O\) would always reveal that \(A+S\) was in the entangled superposition predicted by pure wave mechanics.

On his account, as we will see, \(B\) is describing the absolute state of \(A+S\) and \(A\) is describing relative states of \(A\) and \(S\). In contrast to proponents of strongly splitting worlds, Everett did not believe that decoherence rendered interference effects between relative measurement records in principle unobservable.

See, for example, Everett (1956, p. 119) and the

*Deductions*section following that page.This sometimes appears as the curious claim that the mathematical formalism of pure wave mechanics somehow interprets itself. This was DeWitt’s (1970) explicit view when he came to accept the theory and serve as its principle apologist. See Saunders et al. (2010) for more recent expressions of this view. Wallace (2010a, pp. 69–70) provides a particularly salient example.

One needs something like a notion of typicality here to defend the theory against explaining too much, but we do not have this yet. It is in this sense that solving the surplus structure problem requires one to also solve the probability problem.

This is also true for approximate measurements (as Everett points out) or if one only relatively, rather than absolutely, makes the sequence of observations.

Indeed, given what it means for a physical theory to be empirically faithful, there is a sense in which the preferred-basis problem is simply irrelevant to his project. Or put another way, Everett solves the preferred basis problem not by choosing a preferred basis but by showing that no choice of preferred basis is required for empirical faithfulness. Rather, all one needs is to find an appropriate sequence of relative records appropriately associated with the modeled observer. That there are also relative states where the observer does not have any determinate relative records at all, indeed, where there is not even a determinate relative observer, doesn’t matter for the empirical faithfulness of the theory.

We will return to this point later.

See Everett’s discussions of this point (1955, p. 67, 1956, pp. 121–123 and 130–131, and 1957, pp. 186–188 and 194–195). See also Albert (1992) and Barrett (1999) for discussions of these and other suggestive properties of pure wave mechanics (the bare theory). We will discuss Everett’s

*deductions*further below.Ultimately, the explanation of the expected stability of relative measurement records depends on implicit thermodynamic assumptions. In particular, to argue that a particular relative record is likely to persist, one must suppose that it is unlikely that the physical state is such that the relative records will interfere in just such a way as to undo the correlation between the recording and object systems. The argument might go something like this. If a particular measurement record involves many degrees of freedom, then states where an erasing re-interference would occur are relatively rare in Hilbert space the Lebesgue measure induced by the inner product. So if one assumes that the absolute state of the world is typical in this measure, then one should expect that relative records involving many degrees of freedom are typically stable.

See Barrett and Byrne (eds) (2012, p. 68).

An early example is Zeh (1970). A more recent example is the Saunders–Wallace–Deutsch many-worlds interpretation of Everett, which appeals to decoherence considerations to characterize of the diachronic identity of worlds and the classical appearance of macroscopic objects in those worlds. See Deutsch (1997), Saunders et al. (2010), and Wallace (2012).

Since all Everett needed to explain determinate measurement outcomes was to find the outcomes as relative records in the model of pure wave mechanics, he did not need any mechanism to choose a physically preferred basis, so he did not need decoherence considerations for that purpose. He also required that a satisfactory formulation of quantum mechanics allow one to tell the Wigner’s Friend story coherently, a story where decoherence considerations by stipulation do not obtain.

See Barrett (2011b).

See, for example, Everett (1957, pp. 186–189).

See Everett’s letter in Barrett and Byrne (eds) (2012, pp. 254–255) for this part of his reply to DeWitt.

For proponents of the decohering-worlds interpretation, decoherence is a process by which branches on a decohering decomposition of the quantum state come to evolve independently of each other. And it is this independence, at some level of description, that justifies treating each component as a real, emergent physical world. See, for example, Wallace (2010a, pp. 62–65). Everett himself, however, argued the other direction. Since the linear dynamics requires that all branches are at least in principle detectable, pure wave mechanics requires that all branches are equal real. And again, this does not mean that only branches in some physically preferred basis are real. There is no preferred basis. Rather, it means that every branch in every decomposition of a composite system is real in the only sense of real that he understood.

Note that Everett assumes that the decomposition of the absolute state is in terms of

*orthogonal*elements. Note further that the third condition only makes sense if there is*no canonical decomposition*of the absolute state of the composite system. The general scheme then allows one to assign a measure over any orthogonal decomposition of the state whatsoever, not just a scheme for assigning a measure to the relative states of macroscopic systems or to decohering relative states or to the relative states of a rational observer.The original version of the long version of Everett’s thesis reads more modestly “We choose for this measure the square amplitude of the coefficients of the superposition, a choice which we shall subsequently see is not as arbitrary as it appears”. Of course, this is enough, since all he needs for the faithfulness of the theory is to find a suitable measure of typicality that is determined by the model of pure wave mechanics.

See, for example, the 1962 exchange between Everett and Podolski at the Xavier conference (Barrett and Byrne (eds) (2012, pp. 274–275).

See Barrett (1999) for a full reconstruction of the argument.

See Barrett (1999) for a discussion of the range of criteria of randomness for which this is true.

As discussed below, Everett’s strategy for finding the standard quantum statistics in the theory was quite different from the one employed by the Saunders–Wallace–Deutsch many-worlds interpretation. Following a suggestion by Deutsch (1999), probabilities on the Saunders–Wallace–Deutsch many-worlds view are taken to be recovered by arguing that in a universe described by pure wave mechanics a rational agent would act as if the Born rule (rule 4b) obtained. See Saunders et al. (2010) and Wallace (2012). While Everett was always looking for applications of game theory and decision theory, a lifelong passion, he never argued for this.

More specifically, Wallace has explained in correspondence that he takes the quantum state to be descriptive of the “microreality” and that he takes what the microreality actually is, physically, to be “very theory-dependent.”

Consider, for example, his application of his formulation of quantum mechanics to field theories that he characterizes as including general relativity as a special case (2012, p. 298), to black-hole dynamics (2012, pp. 400–401), and to closed timeline worlds trajectories in spacetimes with nontrivial global topologies (2012, pp. 401–419).

One of the reasons that Wallace’s hunch is particularly puzzling is that alternative geometries, at least as represented by alternative spacetime manifolds, do not form a linear space where one might represent linear superpositions.

In terms of Everett’s model of pure wave mechanics, some relative observers, in particular those with typical measurement records, would have evidence for the empirical faithfulness of pure wave mechanics. Of course, a relative observer whose experience does not exhibit the standard quantum statistics would not have evidence for the empirical faithfulness of pure wave mechanics. And the model provides no good reason to imagine that the first sort of observer is in any standard sense more likely than the second among real physical observers.

Note that contrary to what DeWitt and Graham once argued (see for example, DeWitt and Neill Graham 1973), the problem is not that one would be better off with a notion of typical that involves counting up relative states. Everett himself took DeWitt and Graham’s argument to be “bullshit.” See Barrett and Byrne (2012, pp. 364–366) for scans of Everett’s handwritten marginal notes. The central problem with understanding Everett’s measure as providing an expectation, rather, is that there is no sense whatsoever in which the theory selects a typical relative state, expected or not.

When many-worlds proponents argue that Everettian quantum mechanics requires one to modify one’s notion of

*probability*or to consider a*caring measure*or*quasicredences*associated with alternative branches, they are, on this view, suggesting that one give up or modify at least some of one’s pre-theoretic assumptions for evaluating physical theories when on comes to evaluate this particular theory. See Saunders (2010) for a description of these particular proposals for modifying our basic evaluative notions. Of course, an ardent proponent of a theory may very quick in suggesting that we give up evaluative assumptions that do not favor the theory.The same holds for other reverse-engineered proposals like those described in footnote 43.

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## Acknowledgments

I would like to thank Carl Hoefer, Albert Solé, and Jim Weatherall for discussions and comments. I would also like to thank David Wallace for helpful correspondence and the anonymous reviewers for their insightful comments.

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Barrett, J.A. Pure wave mechanics and the very idea of empirical adequacy.
*Synthese* **192**, 3071–3104 (2015). https://doi.org/10.1007/s11229-015-0698-0

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DOI: https://doi.org/10.1007/s11229-015-0698-0