Transcript Everett and Evidence

Everett and Evidence
Wayne C. Myrvold
Department of Philosophy
University of Western Ontario
Quantum Mechanics
Principle of Superposition
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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–.
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.
Quantum Superpositions of
Macroscopically Distinct
States?
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.
“Interpretations” of QM
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Anti-realist
Realist
Supplement QM state description (de
Broglie-Bohm, modal interpretations)
Modify quantum dynamics (dynamic
collapse)
Everett/many worlds
The Everettian
picture
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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.
All of these outcomes have the same
claim to reality.
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.
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.
Theory and Evidence:
a common picture
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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.
All theories that are compatible with
the observations are equally well
supported by them.
Tossing a coin, I
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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 can get very good evidence this
way about the bias (or lack thereof) in
the toss.
Tossing a coin, II
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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.
What counts, for confirming a
hypothesis, is how likely the observed
result is, if the hypothesis is true.
QM and probability
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From QM we calculate probabilities of results of
experiments.
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.
One can imagine other theories that yielded
very different probabilities.
We say (correctly) that the evidence we have
supports QM over those theories.
A side comment
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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).
Probability in an
Everettian Universe?
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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?
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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.
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.
Danger!
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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.
The decision-theoretic
approach
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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.
Example:
Nuclear power plant design
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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.
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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.
Everettian branch weights
as “caring measures”
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One way to think of this: an Everettian
agent, making a decision, should care
more about consequences on highweight branches.
These caring measures act as
surrogates for probabilities.
Danger averted?
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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.
The evidential problem remains.
The challenge addressed
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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.
Both available on PhilSci archive
http://philsci-archive.pitt.edu/
Shimony’s dictum
Discussion of
the Everett
interpretation
(like a gas)
expands to fill
the space
allowed to it.