Abstract Steeger (Synthese 200(2), 2022) has recently claimed that Bohmians are able to make use of the Deutsch-Wallace derivation of quantum-mechanical chance values. I argue that Steeger’s proposal does not succeed, but a close cousin of it—for de Broglie-Bohm epistemic probabilities—does. This clarifies the relationship between Born rule probabilities in Everettian quantum mechanics and de Broglie-Bohm theory, as well as the scope of the Deutsch-Wallace theorem.
Abstract Steeger (Synthese 200(2), 2022) has recently claimed that Bohmians are able to make use of the Deutsch-Wallace derivation of quantum-mechanical chance values. I argue that Steeger’s proposal does not succeed, but a close cousin of it—for de Broglie-Bohm epistemic probabilities—does. This clarifies the relationship between Born rule probabilities in Everettian quantum mechanics and de Broglie-Bohm theory, as well as the scope of the Deutsch-Wallace theorem.
Abstract The reality of the patterns in the wave-function representing different worlds is not like that of locality and the uncertainty relations, which hold only for the equilibrium distribution. Nor, in the light of the Deutsch–Wallace representation theorem for the Born rule, is the appeal to non-equilibrium probability distributions as the ground for the distinction between pilot-wave theory and many-worlds theory well-motivated. Finally, Valentini's counter-claim, that the latter is motivated by eigenvalue realism, ignores the need to give an account of macroscopic superpositions.
We reply to claims (by Deutsch, Zeh, Brown and Wallace) that the pilot-wave theory of de Broglie and Bohm is really a many-worlds theory with a superfluous configuration appended to one of the worlds. Assuming that pilot-wave theory does contain an ontological pilot wave (a complex-valued field in configuration space), we show that such claims arise from not interpreting pilot-wave theory on its own terms. Specifically, the theory has its own ('subquantum') theory of measurement, and in general describes a 'nonequilibrium' state that violates the Born rule. Furthermore, in realistic models of the classical limit, one does not obtain localised pieces of an ontological pilot wave following alternative macroscopic trajectories: from a de Broglie-Bohm viewpoint, alternative trajectories are merely mathematical and not ontological. Thus, from the perspective of pilot-wave theory itself, many worlds are an illusion. It is further argued that, even leaving pilot-wave theory aside, the theory of many worlds is rooted in the intrinsically unlikely assumption that quantum measurements should be modelled on classical measurements, and is therefore unlikely to be true.
It is often objected that the Everett interpretation of QM cannot make adequate sense of quantum probabilities, in one or both of two senses: either it cannot make sense of probability at all, or cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, and that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has recently developed and defended Deutsch's proposal, and greatly clarified its conceptual basis. In this note I outline some concerns about the Deutsch argument, as presented by Wallace, and about related proposals by Hilary Greaves. In particular, I argue that the argument is circular, at a crucial point.
It is often objected that the Everett interpretation of QM cannot make sense of quantum probabilities, in one or both of two ways: either it can't make sense of probability at all, or it can't explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections. He argues not only that rational decision under uncertainty makes sense in the Everett interpretation, but also that under reasonable assumptions, the credences of a rational agent in an Everett world should be constrained by the Born rule. David Wallace has developed and defended Deutsch's proposal, and greatly clarified its conceptual basis. In particular, he has stressed its reliance on the distinguishing symmetry of the Everett view, viz., that all possible outcomes of a quantum measurement are treated as equally real. The argument thus tries to make a virtue of what has usually been seen as the main obstacle to making sense of probability in the Everett world. In this note I outline some objections to the Deutsch-Wallace argument, and to related proposals by Hilary Greaves about the epistemology of Everettian QM. (In the latter case, my arguments include an appeal to an Everettian analogue of the Sleeping Beauty problem.) The common thread to these objections is that the symmetry in question remains a very significant obstacle to making sense of probability in the Everett interpretation.
The de Broglie-Bohm interpretation of quantum mechanics (BM) has been favored as the preferred alternative to standard quantum mechanics on the ground that it allows a realist construal of the quantum world. We examine in the present work whether BM is consistent with scientific realism. Indeed, Bohmian mechanics makes strong ontological claims but accepts in principle the impossibility of generating epistemic warrants in support of its assumptions. We will argue that such a situation gives rise, at best, to an unsolvable underdetermination dilemma. This leads in turn to the following paradox: although Bohmian mechanics has frequently been invoked to reconcile quantum mechanics with realism, its status as a valid interpretation of quantum mechanics hinges nonetheless on nonevidential epistemological arguments traditionally associated with antirealism.
I defend the Deutsch-Wallace (DW) theorem against a dilemma presented by Dawid and Thébault (2014), and endorsed in part by Read (2018), and Brown and Porath (2020), according to which the theorem is either redundant or in conflict with general frequency-to-chance inferences. I argue that neither horn of the dilemma is well-posed. On the one hand, the DW theorem is not in conflict with general frequency-to-chance inferences on the most natural way of stating the theorem. On the other hand, the DW theorem is crucial for establishing the Born rule as a prediction of Everettian quantum mechanics (EQM), and so cannot be redundant within the theory.