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Chance in the Everett Interpretation

Simon W. Saunders

Published Jun 24, 2010• 73 citations
Publisher

Abstract

Abstract The concept of objective probability — chance — has three distinctive features: chances are measured by statistics, but only with high chance, increasing with the number of trials involved; when the chances of the outcomes of a chance process are known, even in the context of a single trial, then one's subjective probabilities — credences — in those outcomes should be set equal to those chances; and finally, chance processes involve uncertainty as to the outcomes of those processes. The second of these features is established for ratios in the squared norms of branches by the Born-rule theorem, proved in Chapter 8. This chapter shows that the first and third hold for those same quantities. All three characteristics of chance thus apply to branching in the Everett interpretation. In consequence, branching processes should be identified with chance processes, and ratios in the squared norms with chances.

DOI
10.1093/acprof:oso/9780199560561.003.0008

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Abstract The concept of objective probability — chance — has three distinctive features: chances are measured by statistics, but only with high chance, increasing with the number of trials involved; when the chances of the outcomes of a chance process are known, even in the context of a single trial, then one's subjective probabilities — credences — in those outcomes should be set equal to those chances; and finally, chance processes involve uncertainty as to the outcomes of those processes. The second of these features is established for ratios in the squared norms of branches by the Born-rule theorem, proved in Chapter 8. This chapter shows that the first and third hold for those same quantities. All three characteristics of chance thus apply to branching in the Everett interpretation. In consequence, branching processes should be identified with chance processes, and ratios in the squared norms with chances.
As we saw in the previous chapter, the Everett interpretation seems to dispense with probabilities in quantum mechanics. Instead of describing a world for which many things are possible, but only some of those possibilities are actualised, it suggests a world in which all possibilities actually happen . Moreover, this is something of which we can be absolutely certain . Obviously, this does not straightforwardly fit our experience. We do not see multiple possibilities becoming actual. Whenever we measure a superposed particle, we observe only one property or another. Moreover, we have a very useful probabilistic rule to help us to predict what we will see. How can the success of this probabilistic rule be explained, if an Everett world does not involve any uncertainty? There are two main moves that are employed in response to this challenge. The first – what I call Stage A – is to show that there is a relevant sort of uncertainty, even in a universe where we are certain that everything will happen. The second move – Stage B – is to try to vindicate the probability of the Born rule in particular. That is, to show that we should not merely be uncertain about the future, but that we have good reason to attach the particular probabilities dictated by the Born rule to the possible outcomes of a quantum experiment. We will consider these two stages in turn.
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance with statistics, but with degrees of belief, and more broadly the entire phenomenology of (seemingly) chance events and their measurement. Branching structure in the decoherence-based many worlds theory provides an account of what chance is that satisfies all these desiderata, including the requirement that chance involves uncertainty.
Abstract Those who criticize the Everett interpretation on the grounds that it makes no sense of probability apply a double-standard, for no other physical theory of probability does any better in explaining probability or in deriving its link with decision theory. In fact, others do worse, for in any one world theory it is a mystery as to why, given that only a single outcome of a chance process occurs, we should nevertheless act so as to maximize expected utilities, which involves all possible outcomes of a chance process. This difficulty does not apply to the Everett interpretation, in which all outcomes happen.
Abstract Many theories and models from physics are probabilistic. This observation raises several philosophical questions: What are probabilities in physics? Do they reflect objective chances which exist independently of the human mind? Or do they only express subjective credences and thus capture our own uncertainty about the world? Finally, which metaphysical lessons, if at all, can one draw from the largely probabilistic character of physics? The chapters collected in this volume address these questions and provide a detailed philosophical appraisal of the status of probabilities in all of physics. Particular emphasis is laid upon statistical physics and quantum mechanics. Many chapters reflect a desire to understand probabilities from physics as objective chances. These chances are characterized, e.g., as time-averages, as probabilities from a best system in the terms of David Lewis, or using the Boltzmannian typicality approach. Other chapters are sympathetic to a Bayesian view of probabilities in physics. The chapters about quantum mechanics elucidate the peculiar characteristics of quantum correlations and discuss strategies to justify the Born Rule. Finally, the chapters of this volume demonstrate how closely interpretive issues about probabilities are entangled with other foundational problems of physics such as the Reversibility Paradox, the ontology of the quantum world and the question whether the world is deterministic.
Everettian quantum mechanics tells us that the fundamental dynamics of the universe are deterministic. So what are the `probabilities' that the Born rule describes? One popular answer has been to treat these probabilities as rational credences. A recent alternative, Isaac Wilhelm's centered Everett Interpretation (CEI), takes the Born probabilities to be centered chances: the objective chances that some centered propositions are true. Thus, the CEI challenges the `orthodox assumption’ that fundamental physical laws concern only uncentered facts. I provide three arguments against the centered Everett Interpretation. First, I argue that the CEI is in apparent tension with a significant motivation for adopting Everettian quantum mechanics: rejecting the attribution of special significance to observers or agents in fundamental physics. I suggest the CEI can avoid this tension, but only at the cost of sacrificing its central claim that there are objective chances in an Everettian multiverse. My second argument concerns the CEI’s claim that the centered Born rule is a fundamental physical law. I provide two plausible notions of fundamentality for physical laws, and I argue that the centered Born rule satisfies neither. My final argument is that the CEI’s branch-relative laws cannot explain or constrain an agent’s rational credences in the way that the CEI claims.
The Everett interpretation of quantum mechanics is, inter alia, an interpretation of objective probability: an account of what probability really is. Everett called his work “wave mechanics without probability” for good reason: it provides a non-chancy base level of categorical properties and relations. The objection may concern justification rather than understanding, particularly if decoherence theory is used to derive the Born rule. The branch-counting rule makes nonsense of quantum mechanics but it appears to be suggested by the picture of branching. Branch counting is hardly a rival to the branch-weight rule as an interpretation of branching structure, if it brings that branching structure crashing down. Denizens of anomalous branches, or of anomalous stretches of history in one-world theories, will be misled by the observed statistics of measurements.