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Everett and Evidence Wayne C. Myrvold Department of Philosophy University of Western Ontario

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Quantum Mechanics Principle of Superposition Quantum represents the state of a physical system by a state vector. Quantum represents the state of a physical system by a state vector. These can be added: e.g. a positive-spin state in the x-direction is a sum of spin z+ and spin z–. These can be added: e.g. a positive-spin state in the x-direction is a sum of spin z+ and spin z–. This is: This is: Not a state in which the particle has both + and – spins in the z-direction (what would that mean?) Not (unless QM is incomplete) a state in which it has one of these spin-z values, unknown to us.

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Quantum Superpositions of Macroscopically Distinct States?

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Usual quantum rule of state evolution leads to QSMDs. Either the wavefunction, as given by the Schrödinger equation, is not everything, or it is not right.

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“Interpretations” of QM Anti-realist Anti-realist Realist Realist Supplement QM state description (de Broglie-Bohm, modal interpretations) Modify quantum dynamics (dynamic collapse) Everett/many worlds

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The Everettian picture The quantum state description is complete, and the usual, linear state evolution is correct. The quantum state description is complete, and the usual, linear state evolution is correct. At the end of a typical measurement, state of system + apparatus + observer is a superposition of different outcomes. At the end of a typical measurement, state of system + apparatus + observer is a superposition of different outcomes. All of these outcomes have the same claim to reality. All of these outcomes have the same claim to reality.

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Ockham’s razor trims the branches? Nature does nothing in vain, and it is in vain to do with more what can be done with fewer. For nature is simple and does not indulge in the luxury of superfluous causes. There are many things that God does with more that He could do with fewer. Nor should any other explanation be sought. And it follows from the fact that He will it that it is fitting and not futile for it to be done.

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A guiding principle We should be prepared to accept that the world is very different from how we antecedently think it is, given sufficient evidence.

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Theory and Evidence: a common picture Theories are tested by their observable consequences. Theories are tested by their observable consequences. If a theory makes a prediction that is not borne out by observation, we should reject the theory. If a theory makes a prediction that is not borne out by observation, we should reject the theory. All theories that are compatible with the observations are equally well supported by them. All theories that are compatible with the observations are equally well supported by them.

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Tossing a coin, I Compare various hypotheses about bias in a coin toss. Compare various hypotheses about bias in a coin toss. We test these by flipping the coin a number of times, and analyzing the results. We test these by flipping the coin a number of times, and analyzing the results. We can get very good evidence this way about the bias (or lack thereof) in the toss. We can get very good evidence this way about the bias (or lack thereof) in the toss.

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Tossing a coin, II Given any hypothesis about bias, every conceivable sequence of outcomes gets some non-zero probability. Given any hypothesis about bias, every conceivable sequence of outcomes gets some non-zero probability. Every sequence of outcomes is compatible with every hypothesis about bias. Every sequence of outcomes is compatible with every hypothesis about bias. What counts, for confirming a hypothesis, is how likely the observed result is, if the hypothesis is true. What counts, for confirming a hypothesis, is how likely the observed result is, if the hypothesis is true.

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QM and probability From QM we calculate probabilities of results of experiments. From QM we calculate probabilities of results of experiments. We test the correctness of these probabilities by repeated experiments (much like the oin toss). We test the correctness of these probabilities by repeated experiments (much like the oin toss). Much of the evidence that QM is getting something right consists of such tests. Much of the evidence that QM is getting something right consists of such tests. One can imagine other theories that yielded very different probabilities. One can imagine other theories that yielded very different probabilities. We say (correctly) that the evidence we have supports QM over those theories. We say (correctly) that the evidence we have supports QM over those theories.

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A side comment Local Hidden-Variables theories, whose predictions violate the Bell Inequalities, are compatible with all experimental results so far: they just bestow an exceedingly small probability on those results (compared to the QM probability). Local Hidden-Variables theories, whose predictions violate the Bell Inequalities, are compatible with all experimental results so far: they just bestow an exceedingly small probability on those results (compared to the QM probability).

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Probability in an Everettian Universe? On the usual interpretation, it makes sense to ask: On the usual interpretation, it makes sense to ask: Which of the possible outcomes will actually occur? What is the probability that a given possibility will be the one that will actually occur? On the Everettian picture, such questions don’t seem to make sense. On the Everettian picture, such questions don’t seem to make sense. A typical experiment, with certainty, results in a splitting of states, with observations of different outcomes on different branches.

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So, who needs probabilities? Lev Vaidman, from online Stanford Encyclopedia of Philosophy: the advantage of the MWI is that it allows us to view quantum mechanics as a complete and consistent physical theory which agrees with all experimental results obtained to date.

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Danger! We’re at risk of constructing an “interpretation” QM that, though consistent with everything we observe, undermines much of the reason we have for taking QM seriously in the first place. We’re at risk of constructing an “interpretation” QM that, though consistent with everything we observe, undermines much of the reason we have for taking QM seriously in the first place.

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The decision-theoretic approach David Deutsch (1999) argued that an agent in an Everettian universe who knows that she is in an Everettian universe, and knows the quantum state, should behave (that is, make all decisions) in the same way as someone who had the standard, collapse interpretation of quantum probabilities. David Deutsch (1999) argued that an agent in an Everettian universe who knows that she is in an Everettian universe, and knows the quantum state, should behave (that is, make all decisions) in the same way as someone who had the standard, collapse interpretation of quantum probabilities. Defended and elaborated by David Wallace, Simon Saunders, Hilary Greaves. Defended and elaborated by David Wallace, Simon Saunders, Hilary Greaves.

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Example: Nuclear power plant design Which design is better? (non-Everettian) Which design is better? (non-Everettian) Design A has an equal probability of proper functioning and meltdown. Design B has a very high probability of proper functioning, and a very low probability of meltdown. Which design is better? (Everettian) Which design is better? (Everettian) Design A results in a branching, with equal weights for proper functioning and meltdown. Design B results in branching, with very high weight for the terms corresponding to proper functioning, and low weight for terms corresponding to meltdown.

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Everettian branch weights as “caring measures” One way to think of this: an Everettian agent, making a decision, should care more about consequences on high- weight branches. One way to think of this: an Everettian agent, making a decision, should care more about consequences on high- weight branches. These caring measures act as surrogates for probabilities. These caring measures act as surrogates for probabilities.

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Danger averted? The Deutsch-Wallace argument, even if it succeeds, presupposes the correctness of Everettian QM (and that the agent knows it) The Deutsch-Wallace argument, even if it succeeds, presupposes the correctness of Everettian QM (and that the agent knows it) Hence no good for answering why, on the Everettian account, those of us who are not born believing in QM should come to believe it on the basis of experimental evidence. Hence no good for answering why, on the Everettian account, those of us who are not born believing in QM should come to believe it on the basis of experimental evidence. The evidential problem remains. The evidential problem remains.

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The challenge addressed David Wallace, “Epistemology Quantised: circumstances in which we should come to believe in the Everett interpretation,” forthcoming in The British Journal for the Philosophy of Science. David Wallace, “Epistemology Quantised: circumstances in which we should come to believe in the Everett interpretation,” forthcoming in The British Journal for the Philosophy of Science. Hilary Greaves, “On the Everettian epistemic problem,” forthcoming in Studies in History and Philosophy of Modern Physics. Hilary Greaves, “On the Everettian epistemic problem,” forthcoming in Studies in History and Philosophy of Modern Physics. Both available on PhilSci archive Both available on PhilSci archivehttp://philsci-archive.pitt.edu/

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Shimony’s dictum Discussion of the Everett interpretation (like a gas) expands to fill the space allowed to it.

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