*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 point in opposite horizontal directions the
thumb points down. In short: thumbs UP for agreement, thumbs DOWN for
disagreement.
This configuration displays classical correlations, reminiscent
of two bar magnets which, when in contact, align north pole to south pole.
If the magnets are then separated without rotation, their orientations
remain correlated throughout their subsequent histories. Observing one
instantly reveals the direction of the other, regardless of their distance
of separation.
The horizontal and vertical spin directions of particles in a
GHZ state could conceivably assume their values during preparation, and
retain them as they are separated. GHZ states have, in fact, been
assembled, and their properties have been confirmed experimentally. They
are robust. Once two horizontal spins have been measured, the third,
vertical spin can be predicted with certainty. Einstein would have
considered it to be a “real” property of the third particle, pre-existing
any observation.
Quantum mechanics throws a spanner into the works. Suppose that
the experimenter assembles a GHZ state, but measures the first two spins
along the z axis, obtaining UU. What is the prediction for the third
vertical spin? In any triangular relationship, if two pairs agree, the
third pair must agree also (transitivity). Since all three horizontal
spins (*if they were measured*) would point in the same direction, the
third spin should point UP, so the classical, logical prediction for the
allowed state is UUU. Quantum mechanics, however, decrees that UUU is
forbidden, and that the result is UUD instead. Experiments confirm this
seemingly bizarre prediction.
GHZ presents a choice between realism and locality, defined as
the absence of spooky action-at-a-distance. The paradox can be resolved in
one of two ways. Many physicists insist on realism – believing that theory
should describe nature as it really is. This implies that properties
predictable with certainty pre-exist the measurement – that they are
carried along by the particle. Some realistic interpretations of quantum
mechanics require that the Schrödinger wavefunction is nonlocal. In the
case of GHZ this means that the first two measurements yielding UU, even
though they take place far from the third particle, instantaneously
influence its spin and constrain it to point down.
The second option for GHZ is to give up realism in favor of
locality – the QBist approach. The wavefunction becomes a purely abstract
mathematical object designed to predict measurement outcomes. The
unmeasured horizontal spins cannot be invoked to make logical inferences:
they have no values at all unless they enter an agent’s experience. Once
the first two vertical spins are measured, they co-exist at one location –
the agent’s mind – where they become input information for the (correct)
quantum mechanical calculation.
Quoting from the second reference below: “[B]ecause everything
any of us knows about the world is constructed out of his or her individual
private experience, it can be unwise to rely on a picture of the physical
world from which personal experience is explicitly excluded, as it has been
from physical science. Schrödinger traces this exclusion back more than
two thousand years to the ancient Greeks. It worked for over two millennia
and played an important role in the construction of classical science.
But when we attempted to understand phenomena not directly
accessible to our senses, our ingrained practice of divorcing the objects
of our investigations from the subjective experiences they induce in us got
us into trouble. While our efforts at dealing with phenomena at these new
scales were spectacularly successful, we have just as spectacularly failed
for almost a century to reach agreement about the nature or meaning of that
success.”
QBism, by placing human experience at the center of a new
worldview, suggests a way of “restoring the subject-object balance” to
science.
My popular exposition of QBism was published in the June 2013
issue of SCIENTIFIC AMERICAN and some of its translations. A more
sophisticated but non-mathematical primer dated 20 November 2013, by
Christopher Fuchs, David Mermin, and Rüdiger Schack, is available gratis at
www.arxiv.org with the ID number 1311.5253v1.
HAPPY NEW YEAR 2014!
_______________________________________________
fis mailing list
fis@listas.unizar.es
https://webmail.unizar.es/cgi-bin/mailman/listinfo/fis
