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Quantum Probability from Subjective Likelihood: improving on Deutsch’s proof of the probability rule
 STUDIES IN THE HISTORY AND PHILOSOPHY OF PHYSICS, FORTHCOMING
, 2005
"... I present a proof of the quantum probability rule from decisiontheoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch’s recent proof of the probability rule, but the proof is simpler and proceeds from weaker decisiontheor ..."
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I present a proof of the quantum probability rule from decisiontheoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch’s recent proof of the probability rule, but the proof is simpler and proceeds from weaker decisiontheoretic assumptions. This makes it easier to discuss the conceptual ideas involved in the proof, and to show that they are defensible.
Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability? ∗
"... Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing ..."
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Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing to an Everettian version of Savage’s rational decision theory. Deutsch argues not only that an analogue of classical decision under uncertainty makes sense in an Everett world; but also that under reasonable assumptions, the betting odds of a rational Everettian agent should be constrained by the Born rule. Deutsch’s proposal has been defended and developed by David Wallace, and in a different form by Hilary Greaves. In this paper I offer some objections to the DeutschWallaceGreaves argument, focussing in particular on the supposed analogy with classical decision under uncertainty. 1 Fabulous at fifty? Our forties are often a fortunate decade. Understanding ourselves better, resolving old problems, we celebrate our fiftieth year with new confidence, a new sense of purpose. So, too, for the Everett interpretation, at least according to one reading of its recent history. Its fifth decade has resolved a difficulty that has plagued it since youth, indeed since infancy, the socalled problem of probability. Critics
Two Dogmas About Quantum Mechanics
"... We argue that the intractable part of the measurement problem—the ‘big ’ measurement problem—is a pseudoproblem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell’s assertion that measurement should never be introduced as a primitive process in a fundament ..."
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We argue that the intractable part of the measurement problem—the ‘big ’ measurement problem—is a pseudoproblem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell’s assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the ‘truthmaker ’ for propositions about the occurrence and nonoccurrence of events, i.e., that the quantum state is a representation of physical reality. We show how both dogmas can be rejected in a realist informationtheoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the ∗Email address:
Probability in the ManyWorlds Interpretation of Quantum Mechanics
, 2011
"... It is argued that, although in the ManyWorlds Interpretation of quantum mechanics there is no \probability " for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: a). A \sleeping pill" gedanken exper ..."
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It is argued that, although in the ManyWorlds Interpretation of quantum mechanics there is no \probability " for an outcome of a quantum experiment in the usual sense, we can understand why we have an illusion of probability. The explanation involves: a). A \sleeping pill" gedanken experiment which makes correspondence between an illegitimate question: \What is the probability of an outcome of a quantum measurement? " with a legitimate question: \What is the probability that \I " am in the world corresponding to that outcome?"; b). A gedanken experiment which splits the world into several worlds which are identical according to some symmetry condition; and c). Relativistic causality, which together with (b) explain the Born rule of standard quantum mechanics. The Quantum Sleeping Beauty controversy and \caring measure " replacing probability measure are discussed. 1
ManyWorlds and Schrödinger’s First Quantum Theory
, 2009
"... Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the ca ..."
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Schrödinger’s first proposal for the interpretation of quantum mechanics was based on a postulate relating the wave function on configuration space to charge density in physical space. Schrödinger apparently later thought that his proposal was empirically wrong. We argue here that this is not the case, at least for a very similar proposal with charge density replaced by mass density. We argue that when analyzed carefully this theory is seen to be an empirically adequate manyworlds theory and not an empirically inadequate theory describing a single world. Moreover, this formulation—Schrödinger’s first quantum theory—can be regarded as a formulation of the manyworlds view of quantum mechanics that is ontologically clearer than Everett’s. PACS: 03.65.Ta. Key words: Everett’s manyworlds view of quantum theory; quantum theory without observers; primitive ontology; Bohmian mechanics; quantum nonlocality in the manyworlds view; nature of probability in the manyworlds view; typicality.
A formal proof of the Born rule from decisiontheoretic assumptions
, 2009
"... I develop the decisiontheoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everettinterpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ..."
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I develop the decisiontheoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everettinterpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed “counterexamples ” to show exactly which premises of the argument they violate. (This is a preliminary version of a chapter to appear — under the title “How to prove the Born Rule ” — in Saunders, Barrett, Kent and Wallace, Many worlds? Everett, quantum theory and reality, forthcoming
Everett and Evidence
, 2007
"... Much of the evidence for quantum mechanics is statistical in nature. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to reasoning on which statistical evidence in which observed relative frequencies that closely match calculated prob ..."
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Much of the evidence for quantum mechanics is statistical in nature. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to reasoning on which statistical evidence in which observed relative frequencies that closely match calculated probabilities counts as evidence in favour of a theory from which the probabilities are calculated. Since, on the Everett interpretation, all outcomes with nonzero amplitude are actualized on different branches, it is not obvious that sense can be made of ascribing probabilities to outcomes of experiments, and this poses a prima facie problem for statistical inference. It is incumbent on the Everettian either to make sense of ascribing probabilities to outcomes of experiments in the Everett interpretation, or to find a substitute on which the usual statistical analysis of experimental results continues to count as evidence for quantum mechanics, and, since it is the very evidence for quantum mechanics that is at stake, this must be done in a way that does not presuppose the correctness of Everettian quantum mechanics. This requires an account of theory confirmation that applies to branchinguniverse theories but does not presuppose the correctness of any such theory. In this paper, we supply and defend such an account. The account has the consequence that statistical evidence can confirm a branchinguniverse theory such as Everettian quantum mechanics in the same way in which it can confirm a probabilistic theory. 1 In the midst of this perplexity, I received from Oxford the manuscript you have examined. I lingered, naturally, on the sentence: I leave to the various futures (not to all) my garden of forking paths. Almost instantly, I understood: ‘the garden of forking paths ’ was the chaotic novel; the phrase ‘the various futures (not to all) ’ suggested to me the forking in time, not in space.
The Quantum Measurement Problem: State of Play
, 2007
"... This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physicsinformed philosophers, just where we have got to in the quest for a solu ..."
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This is a preliminary version of an article to appear in the forthcoming Ashgate Companion to the New Philosophy of Physics. In it, I aim to review, in a way accessible to foundationally interested physicists as well as physicsinformed philosophers, just where we have got to in the quest for a solution to the measurement problem. I don’t advocate any particular approach to the measurement problem (not here, at any rate!) but I do focus on the importance of decoherence theory to modern attempts to solve the measurement problem, and I am fairly sharply critical of some aspects of the “traditional ” formulation of the problem.
Probability in the Everett World: Comments on Wallace and
, 2006
"... 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 obje ..."
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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 DeutschWallace 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. 1