*Quantum Bayesianism (QBism): An interpretation of quantum mechanics based
on quantum information theory*
Hans Christian von Baeyer, Professor of Physics, emeritus
College of William and Mary, Williamsburg, Virginia
January 2014
I am honored and proud to be asked by Pedro to inaugurate the
tradition of “New Year Lecture” to the FIS community, in the spirit of the
Royal Institution’s “Christmas Lectures”, which have been presented in
London almost every year since 1825. Those shows were originally intended
for a “juvenile audience”, but have always captivated young and old alike.
My electronic lecture is not for children, but like many of its famous
predecessors it features a mind-boggling experiment. In spite of the
scholarly nature my topic – the interpretation of quantum mechanics – my
principal message is simple, and I hope relevant to our quest for the
meaning of information. I look forward to a lively discussion after my
virtual lecture!
QBism (with a capital B) is a radical new interpretation of
quantum mechanics that resolves many of the paradoxes that have bedeviled
the theory since its invention. The technical successes of quantum theory
are unchanged and undisputed -- only the meaning of the formalism is
re-appraised. The revision has far-reaching implications for the
scientific worldview in general.
The crucial move for QBism, inspired by quantum information
theory, is very simple. It consists of revising the predominant
interpretation of probability. Most physicists accept the frequentist
interpretation of probability as “favorable outcomes/all possible
outcomes”. Even though this definition becomes rigorous only in the
unrealistic limit of an infinite number of trials, it is claimed to be
objective. QBism is based instead on the older Bayesian interpretation,
which defines probability as “degree of belief.” Specifically, the
probability that an event will occur is an agent’s personal assignment of
betting odds for the occurrence of the event. It is based on all the
information available to the agent, and is explicitly subjective. Bayesian
probability, unlike frequentist probability, is meaningful for a single,
unrepeatable event.
Bayesianism is more general than frequentism. In many cases,
such as normal laboratory practice, Bayesian probability can be *measured *by
conventional frequentist procedures, but the *meaning *of the result
remains Bayesian. (Similarly, temperature is measured by a thermometer, but
its meaning runs much deeper.) Bayesianism thus absorbs the successes of
frequentism.
By combining Bayesian probability with conventional quantum
mechanics, QBism locates the result of a calculation in the mind of the
agent who makes it. The Schrödinger wavefunction, which is a compendium of
information about a quantum system, and in turn yields probabilities for
the outcomes of future experiments, becomes subjective as well. Input for
assigning betting odds comes from the experiments the agent performs
herself, added to information she gathers from the written and oral records
of science, i.e. from the totality of her personal experiences. Since
wavefunctions are not real in this scheme, the problems associated with
such phenomena as the “collapse of the wavefunction” (when probability
snaps into certainty as a result of a measurement), Schrödinger’s cat,
nonlocality, and Bell inequalities, issues that were interminably debated
during the twentieth century, all dissolve.
The notorious problem of wavefunction collapse, for example,
which defies both mathematical description and the relativistic speed
limit, is interpreted as the modification of a probability assignment by a
measurement. It is a straightforward application of Bayes’ Law (also known
as Bayes’ Theorem or Rule) for updating a probability upon the acquisition
of new information. In this way QBism provides a natural and convincing
explanation of the mysterious collapse.
Apparent nonlocality is displayed most dramatically in an
experiment suggested in 1989 by Daniel Greenberger, Michael Horne, and
Anton Zeilinger (GHZ). The spin of a “spin 1/2 particle” (such as an
electron) can be measured along one axis at a time -- say pointing up or
down (U/D) along the z axis, or, alternatively, right or left (R/L) along
the x axis. Three identical particles are brought into close contact, and
prepared in the special GHZ configuration, in which they are said to be
“entangled.” They are then separated by large distances and it is found
that whenever two of them point in the same horizontal direction, the third
one points UP. (DOWN, if the first two point in opposite directions.) Thus
LLU, RRU, RLD and LRD are found among the measurement results, but LLD,
RRD, RLU and LRU never occur. A mnemonic: If your two index fingers point
in the same horizontal direction, one thumb (representing the third
particle,) points up. If they poi