Measured responses to quantum Bayesianism
December 2012, page 8
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Quantum mechanics
David Mermin, in his commentary in the July 2012 issue of Physics Today (page 8),
put forth what he calls the QBist (quantum Bayesian) approach to
quantum foundations. He claims that replacing a frequentist approach to
quantum probabilities with a Bayesian approach solves the quantum
measurement problem and fixes the “shifty split” between classical and
quantum that John Bell complained about.1
I disagree. Mermin has not addressed the real issue that besets quantum
probabilities, he has not solved the measurement problem, and he has
put the shifty split in the wrong place.
The quantum measurement problem,
understanding an actual physical measurement in fully quantum terms, has
two parts. First, unitary time development (Schrödinger’s equation)
often results in a quantum superposition of different outcomes—different
positions of the apparatus pointer, in the quaint language of quantum
foundations. Various equivocations proposed to get rid of that
Schrödinger’s cat were among the main targets of Bell’s critique. When
this first part is solved the second task is to link the pointer
position to the microscopic property the apparatus was designed to
measure, at a time before the measurement
took place. Experimental physicists talk about detecting a gamma ray
emitted by a nucleus, or a neutrino emitted in a supernova explosion,
using apparatus that either destroys or violently alters the object
under study. They are not fools, though one might think so from reading
textbook discussions of measurement that only consider properties of a
microscopic system at a time after interacting with the apparatus—best
referred to as a preparation, not a measurement.
Mermin seems to think that the
measurement problem—presumably the first problem—is solved by using the
quantum wavefunction to calculate a probability, in a manner easily
taught to undergraduates. However, the main conceptual difficulty with
quantum probabilities is not in calculating them but in identifying
their referents, what it is they are about. When the weatherman assigns a
high probability to a severe thunderstorm on Thursday afternoon, both
frequentists and Bayesians will want to seek shelter. They will agree
that the probability refers to thunderstorms rather than stock-market
prices. The first task in constructing a probabilistic model, for the
weather or games of chance or radioactive decay, is to identify a sample
space of mutually exclusive possibilities, one and only one of which
can be correct or occur in a particular experiment or on a particular
occasion. Only when a sample space has been defined is it possible to
assign probabilities to suitable subsets, averages to random variables,
and so forth.
A classical phase space is easily
turned into a probabilistic sample space: The different points represent
distinct physical states of affairs. But a quantum Hilbert space is
very different if, following John von Neumann’s thinking, one associates
physical properties with (closed) subspaces and associates their
negations with orthogonal complements of the subspaces. That
classical–quantum difference was the origin of quantum logic,2 which, despite early hopes and much hard work, has not resolved the conceptual difficulties of quantum mechanics.3
But it does point to important issues that need to be considered when
discussing quantum probabilities. Mermin and his fellow QBists should
pay attention.
Quantum orthodoxy has no solution for
the fundamental problem of defining a quantum sample space. Instead, it
covers with a black box the mysterious whatever-it-is that the quantum
wavefunction might have something to do with. Talking about what is
under the box is more or less strictly forbidden, for it is well known
that physicists who attempt to do so will fall into the quantum swamp,
to be eaten by the Great Smoky Dragon or driven insane by the Paradoxes.
The black box is my term for Bell’s split between the macroscopic and
microscopic, a split forever shifting as experimentalists manage to
entangle larger and larger quantum systems. According to Mermin, the
QBists place the split “between the world in which an agent lives and
her experience of that world.” That is no improvement: The box would
then cover the physicist rather than the quantum mystery. Bell would not
have been pleased.
Bell was unaware of the consistent or decoherent histories approach to quantum mechanics,4
which, unlike QBism, solves both measurement problems in a way fully
consistent with the Hilbert space structure of quantum mechanics and
consistent with special relativity. It drives the shifty split off to
infinity where it belongs: Quantum physics applies at all scales, from
the quarks to the quasars. And it gets rid of the spooky nonlocal
influences that Einstein found so distasteful. It seems odd that Mermin
has thrown his lot in with the QBists rather than paying serious
attention to the histories approach which, unlike QBism, clearly
satisfies two desiderata for a good quantum interpretation that he
himself put forward 15 years ago:5
“The theory should describe an objective reality independent of
observers and their knowledge” and “objectively real internal properties
of an isolated individual system should not change when something is
done to another non-interacting system.”
Mermin says even undergraduates can
be taught enough quantum mechanics to update a quantum state assignment.
I remember when my undergraduate quantum mechanics teacher, Robert
Dicke of cosmic-background fame, was visibly uncomfortable as he
introduced us to wavefunction collapse. For those who share this
discomfort, I recommend that rather than telling students to “shut up
and calculate,” we
‣ Introduce them to the rudiments of
probability theory, including the conditional probabilities used by both
frequentists and Bayesians; one need not take sides.
‣ Explain how to construct quantum sample spaces and assign probabilities in a way that does not generate paradoxes.
‣ Explain wavefunction collapse as a
tool for calculating certain conditional probabilities that can also be
obtained using other methods; it is not a physical process.
Readers who want more details can contact me or consult the works cited in reference 4.
I think it is high time we abolished antiquated approaches to teaching
quantum theory along with the shifty split that confuses both students
and their instructors.
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