Dear Colleagues,Science & Ultimate Reality
A few days ago, I posted the summary of Freeman Dyson's paper titled
"Thought Experiments in Honor of John Wheeler." In it, Dyson made the claim
"statements about the past cannot in general be made in quantum-mechanical
language." Dyson's comments provoked a vigorous debate on this website about
the nature of quantum mechanics in general, and more specifically whether
the theory is lopsided in its treatment of past and future events. Today's
summary paper, by Aephraim Steinberg, tackles a similar theme. What exactly
can we know about a world described by quantum mechanics? Can we retrodict
as much about past events as we can predict about future events? Steinberg
is even prepared to question whether the standard probabilistic foundations
of quantum mechanics are sacrosanct.
What is exciting about Steinberg's paper is that it describes a new
experiment which might be called "quantum retrodiction." It is based on an
exotic optical switch he has been developing. The experiment promises to
expose a new dimension of quantum weirdness and focus attention on the
foundational assumptions of quantum mechanics, especially its time symmetry
(or otherwise). It seems that the subject of time and quantum mechanics is
shaping up as a major theme for the symposium.
Paul Davies
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Title: What can be known: past and future
Author: Aephraim M. Steinberg
Summary:
If the title of this summary is triply ambiguous, it is only in part
because I don't know exactly what I want to say. It is also in part
because I want to say some things about exactly what we can know--
and this is a subject rife with ambiguity.
While the evolution of our knowledge about the universe with the
advent of new physical theories is nothing surprising, perhaps
the most striking feature of the scientific revolutions of the
20th century is the evolution of our beliefs about the limitations
of that knowledge. G\"odel shows us that not all truths are provable;
relativity shows us that different observers may have different but
equally valid perspectives on questions as fundamental as the direction
of time; and quantum mechanics shows us that uncertainty is intrinsic
to the universe, even leading many to divide physical questions into
"allowed" and "forbidden." John Wheeler has not only made remarkable
contributions to what is known, and not only contributed fascinating
thought experiments to address the issues of what may be asked in a
quantum world, but has also speculated about the primacy of information
in the universe, and about the ultimate fate of our quest to know
the "laws" which govern this world.
What can be known? It appears that our answer to this question is still
evolving, in response not only to theory but also to experiment, perhaps
for the first time in the history of natural philosophy. Some would even
say that there is no immutable answer to the question, for what can
be known is a function of the theoretical framework within which one
works, and these frameworks are transient, human constructions. One
of the things I would like to discuss during this symposium is how
(or whether) quantum-mechanical experiment can help us refine our
answers to such epistemological questions. Will we be led to new
formulations of quantum mechanics which "allow" us to know more than
we have been taught was permitted?
At a more down-to-earth level, "what can be known?" breaks up into some
rather distinct sub-questions. Sciences like archaeology and cosmology
use present observation coupled with theory to know the past. While
their practitioners are familiar with the practical difficulty of
establishing certainty about the distant past, most of us innately
assume that in principle all questions about the past have definite
answers we could potentially possess; in the light of general relativity,
this may not be the case for cosmology, and in the light of quantum
mechanics, it could conceivably fail even for archaeology! Sciences
like mechanics are generally cast in terms of using present conditions
coupled with theory to predict the future, although the time-reverse
is of course also possible. It is well known that quantum uncertainty
makes this prediction impossible, at least given the most common
assumptions about what prediction means.
The orthodox view of quantum mechanics holds that what has been measured
can be known, and what has not ought not to be discussed. If a particle
is prepared in a certain wave packet, that function is to be considered
a complete description, and any additional questions about where the
particle "is" are deemed uncouth, at least until such a measurement is
made. The absence of trajectories in quantum mechanics means that one
supposedly has no right to discuss where the particle "was" prior to
that measurement. Yet the fundamental laws of quantum mechanics are
as time-reversible as those of Newton, and one quite reasonably wonders
why it is any less valid to use a measurement to draw inferences about
a particle's history than to make predictions as to its future behaviour.
Such considerations led Yakir Aharonov and his coworkers to a formalism
of "weak measurements" which allows one to discuss the state of evolving
quantum systems in a fundamentally time-symmetric way. I plan to discuss
some of these ideas, and show how they can be applied to the problem
of a tunneling particle. What can we know about where a particle was
before it appeared on the far side of a forbidden barrier?
These new ideas about measurement naturally lead one to think about
epistemology. Is the wave function the fullest description of what
we can know about a system? Or can we sometimes have more information
than is encoded in a single wave function? Or is it impossible ever
to know as much as a wave function, and are we limited to knowing the
outcomes of the specific measurements we have performed? Can we have
anything more than statistical knowledge about the outcomes of future
measurements? I will discuss some planned experiments that touch on
these issues. In addition, they make one question whether even our
probabilistic description of reality is complete, or whether exotic
entities such as negative or complex probabilites may actually be
meaningful.
The explosive growth of the field of quantum information, with its
potential applications and headline-making buzzwords, has surprised
many by turning "philosophical" research programmes into timely,
relevant, and some suspect even lucrative projects. These questions about
past and future are no exception. I plan to describe some of our recent
work on a quantum "switch," in which a single photon may be transmitted
or not, depending on whether or not a single other photon is present.
The thorn is that it is impossible to know whether either photon
was ever present in the first place... as in many quantum optics
experiments, the outcome depends on conditions which can only be
measured after the fact. On this new work, I have no philosophical
conclusions to draw: only a cautionary tale about how tricky these
quantum conundra remain even for those building the experiments, and
a hope that the other participants will help us learn how to think
about our own experiments in new ways.
To come full circle, let me remark that our first planned application
of this "switch" is to carry out an experimental investigation of quantum
reality first proposed by Lucien Hardy, extending ideas due to Elitzur
and Vaidman. This experiment allows one to demonstrate that what at
first glance appears to be perfectly airtight reasoning about the history
of particles once they have been detected can lead to a seeming
contradiction. More recently, it has been recognized that this
contradiction can be eliminated if one applies the formalism of weak
measurements and accepts these "exotic" probabilities as a correct
description of reality. We believe that most if not all of these
ideas are now accessible in the laboratory.
In conclusion, the question of how to describe reality is a deeply
troubling one, but questions as to whether the future is predictable,
or the past reconstructable, hinge directly on what type of description
we are trying to predict or reconstruct. My suspicion is that if we can
settle on the right description of the present, we will find that the
answer to what can be known is straightforward: both the future and
the past.
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