The many worlds interpretation (MWI) of quantum mechanics, proposed by Hugh Everett in 1957, suggests that all possible outcomes of quantum measurements become real in some ‘world’ or universe. This interpretation has captivated physicists and philosophers alike, but it also presents a significant challenge: the role of probability in this framework.
Since the MWI’s inception, physicists have been puzzled about the role of probability in it. The interpretation posits that every quantum event branches the universe into multiple, equally real worlds. But if all outcomes occur, how can we meaningfully assign probabilities to them? This question has sparked intense debate and led to various proposed solutions, each with its own set of criticisms.
The incoherence problem: why probability at all?
The incoherence problem lies at the heart of the MWI’s struggle with probability. In a deterministic theory where all outcomes occur, the concept of probability seems incoherent. If an observer exists in every possible outcome across different branches, what does it mean to ask, ‘What is the probability of outcome A?’
Proponents of the incoherence problem, such as David Albert and Adrian Kent, argue that probability requires genuine uncertainty about outcomes. In the MWI, however, all outcomes are realized, making the notion of probability unclear. Some defenders of the MWI, like David Wallace, have attempted to redefine probability as a measure of an agent’s ‘caring’ about different branches. However, critics contend that this approach changes the subject, focusing on betting behavior rather than explaining why we observe Born-rule frequencies in our world.
The decision-theoretic program: rational agents in a multiverse
The decision-theoretic program championed by David Deutsch and David Wallace, aims to derive the Born rule from principles of rational decision-making. According to this approach, rational agents in an Everettian multiverse should weight outcomes by the Born rule when making decisions. The program posits that certain axioms of rational preference constrain how agents should bet on quantum experiments, leading to the Born rule as the only consistent weighting.
However, this approach has faced significant criticism. Critics like Adrian Kent and Huw Price argue that the decision-theoretic axioms are not constitutive of rationality but rather substantive claims. Moreover, the program has been accused of circularity, as it relies on the Born rule to define branches and assign probabilities, which is what it aims to derive in the first place.
The circularity objection: a vicious circle
The circularity objection highlights a fundamental issue in attempts to derive the Born rule within the MWI. Decoherence, the process that defines branches in the multiverse, depends on the Born rule. Without decoherence, there is no preferred basis and no well-defined branches, making it impossible to assign probabilities to outcomes. This creates a vicious circle: the Born rule is needed to establish decoherence, which in turn is needed to define branches and assign probabilities.
Critics like Harvey R. Brown and Jeffrey A. Barrett have pointed out that this circularity undermines the MWI’s ability to provide a non-circular derivation of the Born rule. Defenders of the MWI, such as David Wallace and Wojciech Zurek, have attempted to break this circle by arguing that decoherence is a structural feature of the formalism, not probabilistic. However, these responses have not convinced all critics, and the circularity charge remains a significant challenge.
The branch-counting problem: a natural but flawed measure
The branch-counting problem arises from the most natural probability measure in the MWI: branch counting. This approach assigns equal weight to each branch, regardless of amplitude. However, this measure contradicts the Born rule, as it leads to incorrect predictions for quantum probabilities.
Proponents of the branch-counting problem, such as Paul Teller and Simon Saunders, argue that the most natural probability measure in the MWI is branch counting. However, this measure generically contradicts the Born rule, as it assigns equal weight to each branch, regardless of amplitude. Defenders of the MWI must explain why amplitude-weighted measure is preferred over branch counting, a task that has proven challenging.
The self-locating uncertainty approach: grounding probability in uncertainty
The self-locating uncertainty approach proposes that between decoherence and observation, an observer genuinely doesn’t know which branch they occupy. This uncertainty is thought to ground probability as rational credence about self-location. Proponents of this approach, such as Lev Vaidman and Sean Carroll, argue that the ‘sleeping pill’ thought experiment demonstrates that an observer can rationally assign probabilities to being in each branch.
However, this approach has faced criticism from philosophers like David Lewis and Richard Dawid. Lewis argues that the uncertainty is either spurious or wrongly placed, making it unable to yield probabilistic predictions. Dawid and Simon Friederich have criticized the central principle of the self-locating uncertainty approach, arguing that it is implausible given its own motivating assumptions.
The debate surrounding the many worlds interpretation and its struggle with probability continues to captivate physicists and philosophers alike. As new arguments and criticisms emerge, the quest for a satisfactory understanding of probability in the MWI remains an ongoing challenge.
