To view contributed talk abstracts, click here. 

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Yakir Aharonov, Tel Aviv University
On the 2-vector re-formulation of quantum mechanics
I will discuss properties of pre- and post-selected ensembles in quantum mechanics.  I will also discuss the proper way to observe these properties through the use of a new type of non-disturbing measurement which I call 'weak measurement'.  A number of these new experiments have already been successfully performed and others are in the planning stage. These experiments have confirmed the unique property of pre- and post-selected ensembles that I call 'weak values.' Theoretical analysis of the outcomes of these experiments have produced several very rich results. First, it has shed new light on the most puzzling features of quantum mechanics, such as interference, entanglement, etc. Secondly, it has uncovered a host of new quantum phenomena, which were previously hidden."

Leslie Ballentine, Simon Fraser University
The Statistical Interpretation of Quantum Mechanics and its Relation to Probability Theory
I shall review the evidence for an Ensemble, rather than an Individual, interpretation of the quantum state.  The evidence comes from several sources, some old (Schroedinger's cat, Measurement problem) and some new (emergence of classicality).
It supports the conclusion that the quantum state function is not itself an "element of reality", but rather it should be interpreted as a generator of probabilities for an ensemble of similarly prepared systems.  But this leads to further questions, since there are many different kinds of probability (often, but less appropriately called "interpretations of probability").  I shall discuss how quantum probabilities fit into the array of probabilities.

Stephen Bartlett, University of Sydney
Epistemic vs ontic interpretations of the state of quantum systems in the presence of closed timelike curves

Gian Paolo Beretta, Università di Brescia, Italy
Mechanics and Thermodynamics can be fundamentally united by density operators with an ontic status obeying a locally maximum entropy production dynamics. But at what price?
Perhaps the earliest explicit ansatz of a truly ontic status for the density operator has been proposed in [G.N. Hatsopoulos and E.P. Gyftopoulos, Found. Phys., Vol.6, 15, 127, 439, 561 (1976)]. Their self-consistent, unified quantum theory of Mechanics and Thermodynamics hinges on: (1) modifyng the ‘state postulate’ so that the full set of ontic individual states of a (strictly isolated and uncorrelated) quantum system is one-to-one with the full set of density operators (pure and mixed); and (2) complementing the remaining usual postulates of quantum theory with an ‘additional postulate’ which effectively seeks to incorporate the Second Law into the fundamental level of description. In contrast with the epistemic framework, where the linearity of the dynamical law is a requirement, the assumed ontic status of the density operator emancipates its dynamical law from the restrictive requirement of linearity. Indeed, when the ‘additional postulate’ is replaced by the dynamical ansatz of a (locally) steepest entropy ascent, nonlinear evolution equation for the density operator proposed in [G.P. Beretta, Sc.D. thesis, M.I.T., 1981, e-print quant-ph/0509116; and follow-up papers], the (Hatsopoulos-Keenan statement of the) Second Law emerges as a general theorem of the dynamics (about the Lyapunov stability of the equilibrium states). As a result, the ontic status is acquired not only by the density operator, but also by the entropy (which emerges as a microscopic property of matter, at the same level as energy), and by irreversibility (which emerges as a microscopic dynamical effect). This “adventurous scheme ... may end arguments about the arrow of time -- but only if it works” [J. Maddox, Nature, Vol.316, 11 (1985)]. Indeed, the scheme resolves both the Loschmidt paradox and the Schroedinger-Park paradox about the concept of ‘individual quantum state’. However, nonlinearity imposes a high price: the maximum entropy production (MEP) dynamical law does not have a universal structure like that of the Liouville-von Neumann equation obeyed by the density operator within the epistemic (statistical mechanics) view. Instead, much in the same way as the implications of the Second Law depend on the assumed model of a given physical reality, the MEP dynamical law for a composite system is model dependent: its structure depends on which constituent particles or subsystems are assumed as elementary and separable, i.e., incapable of no-signaling violations. See www.quantumthermodynamics.org for references.

Robin Blume-Kohout, Perimeter Institute
Quantum Knowledge
It's been suggested that "decoherence explains the emergence of a classical world".  That is, if we believe our world is quantum, then decoherence can explain why it LOOKS classical. Logically, this implies that without decoherence, the world would not look classical.  But... what on earth WOULD it look like?  Human beings seem incapable of directly observing anything "nonclassical". I'll show you how a hypothetical quantum critter could interact with, and learn about, its world.  A quantum agent can use coherent measurements to gain quantum knowledge about its surroundings.  They can use that quantum knowledge to accomplish tasks.  Moreover, clumsy classical critters (like me!) could identify quantum agents (and prove that they are using quantum knowledge), because they outperform all classical agents.  I'll explain the remarkable new perspective on quantum states that comes from thinking about quantum knowledge, and I'll argue that it's a useful perspective by showing you two concrete applications derived from it.

ÄŒaslav Brukner, University of Vienna
What are the costs of dealing with "states of reality" in quantum theory?
Bell and experimental tests of his inequality showed that it is impossible to explain all of the predictions of quantum mechanics using a theory which satisfies the basic concepts of locality and realism, but which (if not both) is violated is still an open question. As it seems impossible to resolve this question experimentally, one can ask how plausible realism -- the idea that external properties of systems exist prior to and independent of observations -- is, by considering the amount of resources consumed by itself and its non-local features. I will construct an explicit realistic model in which the number of hidden-variable states scales polynomially with the number of possible quantum measurements. In the limit of a large number of measurements, the model recovers the result of Montina, that no hidden-variable theory that agrees with quantum predictions could use less hidden-variable states than the straightforward model in which every quantum state is associated with one such hidden state. Thus, for any given system size, realistic theories cannot describe nature more efficiently than quantum theory itself. I will then turn to the problem of "non-locality" in realistic theories showing that every such theory that agrees with quantum predictions allows superluminal signaling at the level of hidden variable states.

Sheldon Goldstein, Rutgers University, United States
Reality and the Role of the Wave Function in Quantum Mechanics
The most puzzling issue in the foundations of quantum mechanics is perhaps that of the status of the wave function of a system in a quantum universe. Is the wave function objective or subjective? Does it represent the physical state of the system or merely our information about the system? And if the former, does it provide a complete description of the system or only a partial description? I shall address these questions here mainly from a Bohmian perspective, and shall argue that part of the difficulty in ascertaining the status of the wave function in quantum mechanics arises from the fact that there are two different sorts of wave functions involved. The most fundamental wave function is that of the universe, which, I argue, has a law-like character. From the wave function of the universe together with its configuration one can define the wave function of a subsystem of the universe. This, while objective, does indeed have a strong informational/subjective aspect.

Claus Kiefer, University of Cologne
Semiclassical Gravity and the Meaning of the Quantum State
It is widely believed that quantum theory and relativity have to be united in a theory of quantum gravity. In my talk, I shall elaborate on the meaning of the quantum states in such a theory. For simplicity, I restrict myself to the most conservative approach - quantum geometrodynamics. After a general introduction to the full approach, I shall devote the major part of my talk to semiclassical gravity and the recovery of standard quantum theory in an external spacetime as an approximation. I shall focus, in particular, on the meaning of time, Hilbert space, and the quantum-to-classical transition. I shall conclude that most of these concepts make sense only in the limit where gravity is semiclassical.

N. David Mermin, Cornell University
Confusing Ontic and Epistemic Causes Trouble in Classical Physics Too
The subject of this conference is the Quantum State --- what the hell it is. A central issue is whether quantum states describe reality (the ontic view) or an agent's knowledge of reality (the epistemic view). Advocates of the epistemic view maintain that many quantum puzzles and conundra are artifacts of an inappropriate reification of strictly epistemic concepts. To provide a broader context for such considerations, I argue that even in classical physics we have got into major trouble by inappropriately conferring physical reality on the abstractions we have used to organize what we know.

Alberto Montina, Università di Firenze
Does the wave-function concern information or reality? Further progress towards an answer
In the standard interpretation of quantum mechanics, the wave-function is not a real object, but is similar to the concept of a classical probability distribution, providing an ensemble description of physical systems. In spite of this similarity, in this interpretation no attempt is made to describing the state of single systems by means of well-defined quantities.
Ontological models, such as de Broglie-Bohm mechanics, are designed to reintroduce a realistic description of reality in the quantum phenomena. However, in any known realistic theory the wave-function is always promoted to the rank of a physical field.
As a consequence, the number of resourses required to define the single system state grows exponentially with the number of particles or modes.

In this talk, I will present a theorem establishing that this exponential growth is an intrinsic feature of any short memory ontological theory. More precisely, I have proved that these theories must contain an ontological state whose space coincides with the Hilbert space. Furthermore, by means of a counterexample, I show that the short memory hypothesis is necessary to prove the thesis. 

Travis Norsen, Marlboro College, United States
A Pilot Wave(s) Theory of Exclusively Local Beables
After reframing the question of the status of the quantum state in terms of J.S. Bell's "beables", I will sketch out a new theory which -- though nonlocal in the sense required by Bell's theorem -- posits exclusively local beables.  This is a theory, in particular, in which the quantum mechanical wave function plays no role whatsoever -- i.e., a theory according to which nothing corresponding to the wave function actually exists.  It provides, therefore, a concrete example of how the wave function might be regarded as (at best) "epistemic".

Philip Pearle, University of Hamilton, United States
Topics in dynamical wave function collapse
It will be shown how the CSL (continuous spontaneous localization) dynamical collapse equations work. A mathematically equivalent, non-collapse, Hamiltonian formulation will be described, with interpretative differences between it and CSL briefly discussed. A random field engenders collapse in CSL, and particle energies increase due to collapse.  Energy of the random field will be treated, such that energy of particles plus field is conserved. A conserved energy-momentum-stress density tensor for the random field will be presented, enabling gravitational applications. Finally, a possible role for collapse in the beginning of the universe is modeled.

Nelson Pinto-Neto, ICRA - Centro
Bohmian Quantum Cosmology
Quantum cosmology is the arena where the interpretations of quantum mechanics are pushed to their limits. For instance, the Copenhaguen interpretation cannot even be applied to this framework. With this in mind, I will describe the main results which emerge from the application of the Bohm-de Broglie interpretation to quantum cosmology, not only for an investigation of the later, but also to get a better understanding of the former in comparison with other interpretations. At first, without imposing any spacetime symmetry from the beginning, we show explicitly the breakdown of spacetime into space and time due to quantum effects, and an investigation of these latter structures within the Bohm-de Broglie picture. Afterwards, in the case of minisuperspace quantum cosmology, I will present how the notions of an evolution time parameter, cosmological singularities, and classical limit can be unambiguously defined. Cosmological non singular quantum bouncing solutions emerge, which are naturally led to th e standard cosmological model evolution before nucleosynthesis: large classical universes can be obtained without any traditional primordial inflationary expansion. A theory of quantum cosmological perturbations on these backgrounds is constructed, and almost scale invariant spectra are obtained. I argue about the possibility of testing these models against inflation. Use of the Bohm interpretation is crucial to obtain these results, which are otherwise unclear within other interpretations. Finally, I show potential discrepant results about the avoidance of cosmological singularities when different interpretations of quantum mechanics are used, and I speculate about constructing analog models where such differences could be tested.

Terry Rudolph, lmperial College
Does knowing my lambda mean knowing my psi?
All known hidden variable theories that completely reproduce all quantum predictions share the feature that they add some information to the quantum state "psi". That is, if one knew the "state of reality" given by the hidden variable(s) "lambda", then one could infer the quantum state - the hidden variables are additional to the quantum state. However, for the case of a single 2-dimensional quantum system Kochen and Specker gave a model which does not have this feature – the non-orthogonality of two quantum states is manifested as overlapping probability distributions on the hidden variables, and teh model could be termed “psi-epistemic”. A natural question arises whether a similar model is possible for higher dimensional systems. At the time of writing this abstract I have no clue. I will talk about various constraints on such theories (in particular on how they manifest contextuality) and I'll present some examples of failed attempts to construct such models for a 3-dimensional system. I will also discuss a very artificial tweaking of Bell’s original hidden variable model which renders it psi-epistemic for some (though not all) of the corresponding quantum states.

Ruediger Schack, University of London
The reflection principle and quantum Bayesian decoherence

Daniel Terno, Macquaire University
What does relativity tells us about quantum theory?
Spacelike separated classical interventions make us to rethink what is quantum and what is classical. Quantum Lorentz transformations show that identification of subsystems is a tricky business, ditto entropy, entanglement and thermodynamic quantities. Resolution of information loss problem in black hole physics is tied to a construction of a theory of quantized gravity.

Chris Timpson, University of Oxford
Ontology of the quantum state: wavefunction vs spacetime state realism
Realists about quantum mechanics may also want to be realists about the quantum state. But what does that mean? If one wants to think of the quantum state as representing a kind of thing, there is the question of what kind of thing that would be. I shall discuss some of the general issues surrounding the question of the ontology of the quantum state and will argue that what seems to be the predominant ontological view  (amongst those who’ve discussed it much) - wavefunction realism  (according to which the state describes a (separable) complex field on a high dimensional physical space) should be rejected in favour of spacetime state realism, according to which the state represents a non-separable field on ordinary spacetime. Joint work with David Wallace. arXiv:quant-ph/0907.5294

Antony Valentini, Imperial College, London
The nature of the wave function in de Broglie's pilot-wave theory