#### The Oxford Questions on the foundations of quantum physics

G. A. D. Briggs
J. N. Butterfield
A. Zeilinger
0
Faculty of Physics, University of Vienna
,
Vienna
,
Austria
1
Trinity College, University of Cambridge
,
Cambridge CB2 1TQ
,
UK
2
Department of Materials, University of Oxford
,
Oxford OX1 3PH
,
UK
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Perspective
The Oxford Questions on the foundations of quantum physics
G. A. D. Briggs1, J. N. Butterf ield2 and A. Zeilinger3
The twentieth century saw two fundamental
revolutions in physicsrelativity and quantum. Daily use of
these theories can numb the sense of wonder at their
immense empirical success. Does their instrumental
effectiveness stand on the rock of secure concepts or
the sand of unresolved fundamentals? Does
measuring a quantum system probe, or even create, reality
or merely change belief? Must relativity and quantum
theory just coexist or might we find a new theory
which unifies the two? To bring such questions into
sharper focus, we convened a conference on Quantum
Physics and the Nature of Reality. Some issues remain
as controversial as ever, but some are being nudged by
theorys secret weapon of experiment.
1. The achievements of twentieth century physics
Much of the history of twentieth century physics is the
story of the consolidation of the relativity and quantum
revolutions, with their basic postulates being applied
ever more widely. It is possible to forget how contingent,
indeed surprising, it is that the basic postulates of
relativity and quantum theory have proved to be so
successful in domains of application far beyond their
original ones. Why should the new chronogeometry,
introduced by Einsteins special relativity in 1905 [1]
for electromagnetism, be extendible to mechanics,
thermodynamics and other fields of physics? And why
should the quantum theory devised for systems of
atomic dimensions (1010 m) be good for scales both
much smaller (cf. high-energy experiments 1017 to
1020 m) and vastly larger (cf. superconductivity and
superfluidity, or even a neutron interferometer, involving
2013 The Authors. Published by the Royal Society under the terms of the
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source are credited.
scales of a fraction of a metre or more)? Is there an upper limit to the scale on which quantum
theory should be expected to work? There is a sense in which all properties of matter are quantum
mechanical. Topics as diverse as phase changes of alloys and conduction in semiconductors have
all yielded to quantum theory. New quantum mechanical models are being developed for a
growing range of superconductors, magnets, multiferroics and topological insulators.
The point applies equally well when we look beyond terrestrial physics. General relativity
makes a wonderful story: the theory was created principally by one person, motivated by
conceptual, in part genuinely philosophical, considerationsyet, it has proved experimentally
accurate in all kinds of astronomical situations. They range from weak gravitational fields such as
occur in the solar system, where it famously explains the minuscule precession of the perihelion
of Mercury (43 of arc per century) that was unaccounted for by Newtonian theory, to fields
10 000 times stronger in a distant binary pulsar, which in the last 30 years has given us compelling
evidence for a phenomenon (gravitational radiation) that was predicted by general relativity and
long searched for.
But general relativity is not the only success story in modern physics description of
nonterrestrial phenomena. Quantum theory has also been extraordinarily successful in application
to astronomy: the obvious example is the use of nuclear physics to develop a very accurate and
detailed theory of stellar structure and evolution.
Indeed, there is a more general point here, going beyond the successes of relativity and
quantum theory. We tend to get used to the various unities in Nature that science revealsand
thereby to forget how contingent and surprising they are. Of course, this is not just a tendency
of our own era. For example, nineteenth century physics confirmed Newtons law of gravitation
to apply outside the Solar System and discovered terrestrial elements to exist in the stars (by
spectroscopy): discoveries that were initially surprising, but soon taken for granted, incorporated
into the educated persons common sense. Similarly, nowadays: the many and varied successes
of physics in the last few decades, in modelling very accurately phenomena that are vastly distant
in space and time, and/or very different from our usual laboratory scales (in their characteristic
values of such quantities as energy, temperature or pressure, etc.), reveal an amazing unity in
Nature. For a modern, specific (and literally spectacular) example, consider the precision and
detail of our models of supernovaeas confirmed by the wonderful capacity of modern telescope
technology to see and analyse individual supernovae, even in other galaxies.
In some cases, a theoretical prediction came first, stimulating experimental confirmation;
sometimes, it has been the other way round. It was nearly half a century after the experimental
discovery of superconductivity that a satisfactory quantum theory was developed, but the
prediction of the Josephson junction preceded its experimental implementation. There had long
been a quest for higher temperature superconductors, but their remarkable discovery came as
rather astonishing.
And yet: complacency, let alone triumphalism, is not in order! Not only is physics full of
unfinished business: that is always true in human enquiry. We think most physicists would also
agree that there are clouds on the horizon that may prove as great a threat to the extrapolated
success of twentieth century physics, in particular quantum physics, as were the anomalies
confronting classical physics at the end of the nineteenth century. But physicists might well
disagree about what these clouds are in broad terms as well as in their details.
In 2010, believing that the time was ripe for better defining these clouds, we organized a
conference entitled Quantum Physics and the Nature of Reality. In 2, we describe it, and how it
led to the formulation of a list of main open questions about the foundations of quantum physics.
In 3, we discuss progress on the questions; and in 4, we return to more general discussion of
the present situation in physics.
2. The Oxford conference on Quantum Physics and the Nature of Reality
The conference was a celebration of the 80th birthday of Reverend Dr John Polkinghorne, in
recognition of his wide-ranging enquiries into the deeper significance of quantum physics,
Box 1. The Oxford Questions.
(1) Time, irreversibility, entropy and information
(2) The quantumclassical relationships
(a) Is irreversibility fundamental for describing the classical world?
(b) How is irreversibility involved in quantum measurement?
(c) What can we learn about quantum physics by using the notion of information?
(a) Does the classical world emerge from the quantum, and if so which concepts
are needed to describe this emergence?
(b) How should we understand the transition from observation to informed action?
(c) How can a single-world realistic interpretation of quantum theory be
compatible with non-locality and special relativity?
(3) Experiments to probe the foundations of quantum physics
(a) What experiments can probe macroscopic superpositions, including tests of
LeggettGarg inequalities?
(b) What experiments are useful for large complex systems, including technological
and biological?
(c) How can the progressive collapse of the wave function be experimentally
monitored?
(4) Quantum physics in the landscape of theories
(5) Interaction with questions in philosophy
(a) What insights are to be gained from category-theoretic, informational,
geometric and operational approaches to formulating quantum theory?
(b) What are productive heuristics for revisions of quantum theory?
(c) How does quantum physics cohere with spacetime and with massenergy?
(a) How do different aspects of the notion of reality influence our assessment of the
different interpretations of quantum theory?
(b) How do different concepts of probability contribute to interpreting quantum
theory?
building on his distinguished career in mathematical quantum theory. The participants included,
in roughly equal proportions: experimentalists, theoreticians and philosophers of physics. The
conference was carefully planned to produce a set of questions, to be known as the Oxford
Questions, which would gather the collected wisdom of all three disciplines in a form which
would be both far-reaching and tractable.
From all three viewpointsexperimental, theoretical and philosophicalthe foundations of
quantum physics is a thriving, lively and even controversial field of research. Across the world,
many active groups of researchers are engaged in probing the nature of quantum theory
and the nature of reality, as described by quantum theory. This work drawsequally, and to a
considerable extent, synergisticallyon the expertise of the three communities. Accordingly, in
organizing the conference, we were keen to invite a broad range of speakers from the various
facets of the subject. But we also wanted to avoid re-hashing various aspects of the status quo
in debates about the foundations of quantum physics: we instead aspired to identify (albeit
contentiously!) a set of central open problems about the nature of quantum reality, to stimulate
and guide future research and scholarship. To this end, we
(i) invited some participants (again: including experimentalists, theoreticians and
philosophers) to write a short white paper which was circulated in advance;
(ii) asked speakers to zoom out from the details of their latest research and give very short
talks; and
(iii) asked speakers, in discussion periods and coffee-breaks, to meet with us to help formulate
the open problemswhich, by the end of the conference, we collectively settled on as the
Oxford Questions (see box 1).
3. The questions in play
For all three communities in quantum foundationsexperimentalists, theoreticians and
philosophersthe last 20 or so years have been especially rich, thanks to the rise of quantum
information science (taken as including quantum computation and quantum cryptography). This
has stimulated, and been stimulated by, extraordinary advances in experimental progress in a
range of implementations across many fields of physics: in optics, trapped ions and lattices of
atoms, in three different ways in superconductors (viz. phase, flux and Cooper-pair box), and in
nuclear and electron spins in molecules, semiconductors and diamond.
Another prominent theme for all three communities, throughout the last 20 years, has been
decoherence: that is, the extremely fast and ubiquitous process by which information about the
quantum system propagates into the environment, so that we lose the ability to show quantum
interference. The interaction between the system and the environment is normally such as to
leave the system in an improper mixture whose density matrix is nearly diagonal in a quantity;
for example, the position of the centre of mass that we intuitively wish to be definite in value.
Here follows a brief general description of activities over recent decades for each of the
three communities.
Ever since the inception of quantum theory, theoreticians have successively deepened our
understanding of its conceptual and mathematical structure. Confining ourselves to the growth
in foundational studies since the 1960s, any list of highlights must surely include
(i) the discovery of the various Bell inequalities, the BellKochenSpecker theorem, the
LeggettGarg inequality;
(ii) various deeper analyses, e.g. of quantization, of uncertainty relations, of the convex set
structure of quantum state spaces, of positive operator valued measures (also known as:
operational quantum physics);
(iii) the development of alternatives to quantum theory, such as the dynamical reduction
models of such authors as Ghirardi, Pearle, Penrose and Adler, whose differences from
quantum theory may in the foreseeable future be subjected to experimental test; and
(iv) with the rise of quantum information theory: analyses using ideas from such diverse
fields as information theory, complexity theory (applied to communication, computation
and cryptography) and category theory.
Experimentalists have in the last 30 or so years performed in their laboratories many of
the Gedanken experiments on single quantum systems which were first proposed by the
founding fathers of quantum theory. These experiments, together with many other foundational
experiments, for example, on multiphoton entanglement, or those that test Bell, BellKochen
Specker or Leggett-type inequalities, have served to make the interpretative issues about the
theory more vivid [2]. All the more so, with the rise of quantum information theory.
(i) The Bell inequality has been experimentally violated in a number of implementations
[3], thus experimentally demonstrating entanglement and thus showing that quantum
mechanics is not incomplete in the sense envisaged by Einstein et al. [4] in 1935.
Various delayed-choice experiments have been carried out, successively ruling out any
reconciliation of Bohrs complementarity with Einsteins local conception of physical
reality [5], and the experiments have been extended with increasing degrees of
sophistication to multi-particle situations [6].
(ii) Quantum interference has been demonstrated in diffraction experiments with molecules
of increasing size, most recently with molecules containing up to 430 atoms [7]. This is
not yet large enough to test continuous spontaneous localization models, but it does show
that no deviation from quantum predictions is found up to this scale.
(iii) The LeggettGarg inequality has been tested in various photonic, superconducting and
spin implementations. Some of these require weak measurements or an assumption
of stationarity, but it is possible to violate the inequality with true negative-result
measurements, with allowance made for possible venality due to imperfect initialization
[8]. The test has been extended to higher dimensional Hilbert space, with projective
measurements that are always undetectable within the protocol [9].
(iv) The KochenSpecker theorem has been directly tested in an experiment with single
photonic qutrits to show that no non-contextual theory can exist [10]. Quantum
teleportation has been demonstrated over 143 km [11]. This uses entanglement and
illustrates how the techniques required for quantum foundations and for quantum
technologies coincide to a remarkable degree. Perhaps this is not surprising: for
these very different motivations both require the degree of quantumness to be
experimentally extended.
Philosophy of quantum physics came of age with the growth in foundational studies since the
1960s. Naturally, it has focused on the paradoxes of non-locality and measurement. Apart from
re-evaluating, and deepening, some existing interpretations, in particular the Copenhagen and
Everett interpretations, it has also assessed, from a conceptual perspective: the heterodox theories,
such as the pilot-wave theory and dynamical reduction models; and the various developments in
quantum information science.
(i) Over the past decade, there has been progress in constraining hidden-variable
interpretations of quantum theory, i.e. interpretations that postulate physical states
underlying the quantum states. Such psi-epistemic theories aim to account for
randomness in measurement outcomes in terms of underlying statistical distributions
of these postulated states, whereas a psi-ontic theory would allow each physical state to
correspond to only one quantum state. Within LeggettGarg concepts of macrorealism,
a distinction can be made between measurements which are non-disturbing of the
quantum state and measurements which are non-invasive of the physical states. The
psiepistemic models have become subject to growing constraints. It has been suggested that
under certain assumptions psi-epistemic models may be ruled out or restricted [12].
(ii) There has also been progress in developing and in assessing the Everettian interpretation
of quantum mechanics. In particular, Everettians have sharpened: (a) their appeal to
decoherence to describe the splitting of worlds as an effective process which does not
conflict with relativity; (b) their appeal to decision theory to justify their applying the idea
of probability, indeed the Born rule, in a multiverse in which everything happens [13].
As regards assessment of the Everettian interpretation (including (a) and (b)), the state of
the art can be found in a recent anthology based on another Oxford conference [14].
(iii) The idea that quantum physics involves novel logical and algebraic structures goes back
to the 1930s, especially Birkhoffs and von Neumanns seminal 1936 paper The logic
of quantum mechanics [15]. But in recent years, new structures have been discovered
and explored, often making use of category theory and its sub-field, topos theory (which
mathematicians developed only after 1950). One main line of research has used category
theory to provide a new graphical formalism for quantum physics, especially quantum
information protocols such as teleportation. This is now sufficiently developed to yield
a good comparison with the Birkhoff and von Neumann proposal [16]. Another main
development has been the use of toposes to give yet a third quasi-logical formulation of
quantum theory [17].
4. Physics today and tomorrow
We will end by setting the Oxford Questions in the context of the discussion in 1. First, we will
relate them to two clouds (4a). Finally, in 4b, we will take an even broader view, by comparing
the present situation in physics with the sixteenth century scientific revolution.
(a) Two clouds on the horizon
Our first cloud is the quantum measurement problem: that is, the difficulty of explaining
completely, in terms of quantum theory, the emergence of a classical world, i.e. a world so
accurately described by classical physics with its definite valuesa world free of superposition
and entanglement.
This cloud gets better defined by several of the Oxford Questions, as follows:
the issue whether or not the collapse of the wave packet is a physical process bears upon
several Oxford Questions: in particular, 1b, 2a, 2c, 3a, 3c and 5a;
the issue whether ideas from information theory can illuminate our concept of reality
bears upon the questions: 1c, 4a, 5a and 5b; and
the consideration of heterodox alternatives to quantum theory bears upon the questions:
1a, 2a, 3a and 4b.
Our second cloud is the search for a quantum theory of gravity. In discussions of quantum
foundations, this is of course the proverbial elephant in the room (with an equally proverbial cat
representing the first cloud!). It is articulated by Oxford Question 4c: how does quantum physics
cohere with spacetime and with massenergy?
That is, general relativity and quantum theory are yet to be reconciled. While we
have developed successful quantum theories of the other fundamental forces of Nature
(electromagnetic, weak and strong), we have no analogously successful quantum theory
of gravity. Accordingly, finding such a reconciliation, perhaps unification, has become an
outstanding goal of theoretical physics.
There are conceptual reasons why this goal is so elusive. The contrasting conceptual structures
of the ingredient theories, and the ongoing controversies about interpreting them, make for
conflicting basic approaches to quantum gravity. Whereas relativity theory is grounded on
principles which are reasonable from a physical point of view, such as the principles of relativity
and of equivalence, it remains an open question whether quantum theory could be based on
comparable principles. More specifically, our first cloud, the quantum measurement problem,
or the collapse of the wave packet, appears here in a cosmological context. How do quantum
fluctuations in the early Universe, thought to be the source of gravitational perturbations that
seed large-scale structures, become classical?
But we want here to emphasize another reason: namely, a dire lack of experimental data! For
there are general reasons to expect data characteristic of quantum gravity to arise only in a regime
of energies so high (correspondingly, distances and times so short) as to be completely inaccessible
to us. To put the point in terms of length, the value of the Planck length which we expect to be
characteristic of quantum gravity is around 1035 m. This is truly minuscule: the diameters of an
atom, nucleus, proton and quark are, respectively, about 1010, 1014, 1015 and 1018 m. So the
Planck length is as many orders of magnitude from (the upper limit for) the diameter of a quark
as that diameter is from our familiar scale of a centimetre!
(b) Halfway through the woods
To complete this snapshot of the present state of physics, we would like to endorse an analogy of
Rovellis [18]. He suggests that our present situation is like that of the mechanical philosophers,
such as Galileo and Kepler of the early seventeenth century. Just as they struggled with the
clues given by Copernicus and Brahe, en route to the synthesis given by Newton, so also we
are halfway through the woods. Of course, we should be wary of too grossly simplifying
and periodizing the scientific revolution, and a fortiori of facile analogies between different
historical situations. Nevertheless, it is striking what a mixed bag the doctrines of figures such
as Galileo and Kepler turn out to have been, from the perspective of the later synthesis. For all
their genius, they appear to us (endowed with the anachronistic benefits of hindsight) to have
been transitional figures. One cannot help speculating that to some future reader of twentieth
century physics, enlightened by some future synthesis of general relativity and quantum theory,
the efforts of the last few decades in quantum gravity will seem strange: worthy and sensible
from the authors perspective (one hopes), but a hodge-podge of insight and error from
the readers!