Everett and EvidenceEverett and Evidence

Wayne C. MyrvoldWayne C. Myrvold

Department of PhilosophyDepartment of Philosophy

University of Western OntarioUniversity of Western Ontario

Quantum MechanicsQuantum MechanicsPrinciple of Principle of SuperpositionSuperposition Quantum represents the state of a Quantum represents the state of a

physical system by a physical system by a state vectorstate vector.. These can be added: These can be added: e.g.e.g. a positive- a positive-

spin state in the spin state in the xx-direction is a sum of -direction is a sum of spin spin zz++ and spin and spin z–.z–.

This is:This is: Not Not a state in which the particle has both a state in which the particle has both

+ and – spins in the z-direction (what + and – spins in the z-direction (what would that mean?)would that mean?)

Not Not (unless QM is incomplete) a state in (unless QM is incomplete) a state in which it has one of these spin-z values, which it has one of these spin-z values, unknown to us.unknown to us.

Quantum Superpositions Quantum Superpositions of Macroscopically of Macroscopically Distinct States?Distinct States?

Usual quantum rule of Usual quantum rule of state evolution leads to state evolution leads to QSMDs.QSMDs.

Either the wavefunction, as given by the

Schrödinger equation, is not everything, or it is not

right.

““Interpretations” of Interpretations” of QMQM Anti-realistAnti-realist RealistRealist

Supplement QM state description Supplement QM state description (de Broglie-Bohm, modal (de Broglie-Bohm, modal interpretations)interpretations)

Modify quantum dynamics (dynamic Modify quantum dynamics (dynamic collapse)collapse)

Everett/many worldsEverett/many worlds

The Everettian The Everettian picturepicture

The quantum state description is The quantum state description is complete, and the usual, linear state complete, and the usual, linear state evolution is correct.evolution is correct.

At the end of a typical measurement, At the end of a typical measurement, state of system + apparatus + state of system + apparatus + observer is a superposition of different observer is a superposition of different outcomes.outcomes.

All of these outcomes have the same All of these outcomes have the same claim to reality.claim to reality.

Ockham’s razor trims Ockham’s razor trims the branches?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.

A guiding principleA guiding principle

We should be prepared to We should be prepared to accept that the world is very accept that the world is very

different from how we different from how we antecedently think it is, antecedently think it is,

given sufficient evidence.given sufficient evidence.

Theory and Evidence:Theory and Evidence:a common picturea common picture Theories are tested by their Theories are tested by their

observable consequences.observable consequences. If a theory makes a prediction If a theory makes a prediction

that is not borne out by that is not borne out by observation, we should reject the observation, we should reject the theory.theory.

All theories that are compatible All theories that are compatible with the observations are equally with the observations are equally well supported by them.well supported by them.

Tossing a coin, ITossing a coin, I

Compare various hypotheses Compare various hypotheses about bias in a coin toss.about bias in a coin toss.

We test these by flipping the coin We test these by flipping the coin a number of times, and analyzing a number of times, and analyzing the results.the results.

We can get very good evidence We can get very good evidence this way about the bias (or lack this way about the bias (or lack thereof) in the toss. thereof) in the toss.

Tossing a coin, IITossing a coin, II

Given any hypothesis about bias, Given any hypothesis about bias, everyevery conceivable sequence of conceivable sequence of outcomes gets outcomes gets somesome non-zero non-zero probability.probability.

Every sequence of outcomes is Every sequence of outcomes is compatiblecompatible with every hypothesis with every hypothesis about bias.about bias.

What counts, for confirming a What counts, for confirming a hypothesis, is how hypothesis, is how likelylikely the observed the observed result is, if the hypothesis is true.result is, if the hypothesis is true.

QM and probabilityQM and probability

From QM we calculate probabilities of From QM we calculate probabilities of results of experiments.results of experiments.

We test the correctness of these We test the correctness of these probabilities by repeated experiments probabilities by repeated experiments (much like the oin toss).(much like the oin toss).

Much of the evidence that QM is getting Much of the evidence that QM is getting something right consists of such tests.something right consists of such tests.

One can imagine other theories that One can imagine other theories that yielded very different probabilities.yielded very different probabilities.

We say (correctly) that the evidence we We say (correctly) that the evidence we have supports QM over those theories.have supports QM over those theories.

A side commentA side comment

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

Probability in an Probability in an Everettian Universe?Everettian Universe? On the usual interpretation, it makes On the usual interpretation, it makes

sense to ask:sense to ask: Which of the possible outcomes will actually Which of the possible outcomes will actually

occur?occur? What is the probability that a given possibility What is the probability that a given possibility

will be the one that will actually occur?will be the one that will actually occur? On the Everettian picture, such questions On the Everettian picture, such questions

don’t seem to make sense.don’t seem to make sense. A typical experiment, with certainty, results in A typical experiment, with certainty, results in

a splitting of states, with observations of a splitting of states, with observations of different outcomes on different branches. different outcomes on different branches.

So, who needs So, who needs probabilities?probabilities?

Lev Vaidman, from online Lev Vaidman, from online Stanford Stanford Encyclopedia of PhilosophyEncyclopedia of Philosophy::

the advantage of the MWI is that it the advantage of the MWI is that it allows us to view quantum mechanics allows us to view quantum mechanics as a complete and consistent physical as a complete and consistent physical

theory which agrees with all theory which agrees with all experimental results obtained to experimental results obtained to

date. date.

Danger!Danger!

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

The decision-theoretic The decision-theoretic approachapproach David Deutsch (1999) argued that an agent David Deutsch (1999) argued that an agent

in an Everettian universe who in an Everettian universe who knowsknows that that she is in an Everettian universe, and knows she is in an Everettian universe, and knows the quantum state, should behave (that is, the quantum state, should behave (that is, make all decisions) in the same way as make all decisions) in the same way as someone who had the standard, collapse someone who had the standard, collapse interpretation of quantum probabilities.interpretation of quantum probabilities.

Defended and elaborated by David Defended and elaborated by David Wallace, Simon Saunders, Hilary Greaves.Wallace, Simon Saunders, Hilary Greaves.

Example:Example:Nuclear power plant Nuclear power plant designdesign Which design is better? (non-Everettian)Which design is better? (non-Everettian)

Design Design AA has an equal probability of proper has an equal probability of proper functioning and meltdown.functioning and meltdown.

Design Design BB has a very high probability of has a very high probability of proper functioning, and a very low proper functioning, and a very low probability of meltdown.probability of meltdown.

Which design is better? (Everettian)Which design is better? (Everettian) Design Design AA results in a branching, with equal results in a branching, with equal

weights for proper functioning and weights for proper functioning and meltdown.meltdown.

Design Design BB results in branching, with very results in branching, with very high weight for the terms corresponding to high weight for the terms corresponding to proper functioning, and low weight for terms proper functioning, and low weight for terms corresponding to meltdown.corresponding to meltdown.

Everettian branch Everettian branch weights as “caring weights as “caring measures”measures” One way to think of this: an One way to think of this: an

Everettian agent, making a Everettian agent, making a decision, should care more about decision, should care more about consequences on high-weight consequences on high-weight branches. branches.

These caring measures act as These caring measures act as surrogates for probabilities.surrogates for probabilities.

Danger averted?Danger averted?

The Deutsch-Wallace argument, even if it The Deutsch-Wallace argument, even if it succeeds, presupposes the correctness of succeeds, presupposes the correctness of Everettian QM (and that the agent knows Everettian QM (and that the agent knows it)it)

Hence no good for answering why, on the Hence no good for answering why, on the Everettian account, those of us who are Everettian account, those of us who are not born believing in QM should come to not born believing in QM should come to believe it on the basis of experimental believe it on the basis of experimental evidence.evidence.

The The evidentialevidential problem remains. problem remains.

The challenge The challenge addressedaddressed David Wallace, “Epistemology Quantised: David Wallace, “Epistemology Quantised:

circumstances in which we should come to circumstances in which we should come to believe in the Everett interpretation,” believe in the Everett interpretation,” forthcoming in forthcoming in The British Journal for the The British Journal for the Philosophy of SciencePhilosophy of Science..

Hilary Greaves, “On the Everettian epistemic Hilary Greaves, “On the Everettian epistemic problem,” forthcoming in problem,” forthcoming in Studies in History Studies in History and Philosophy of Modern Physicsand Philosophy of Modern Physics..

Both available on PhilSci archiveBoth available on PhilSci archivehttp://philsci-archive.pitt.edu/http://philsci-archive.pitt.edu/

Shimony’s dictumShimony’s dictum

Discussion of Discussion of the Everett the Everett

interpretatiointerpretation (like a gas) n (like a gas) expands to expands to

fill the space fill the space allowed to it.allowed to it.