PIAF 09' New Perspectives on the Quantum State

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.

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.

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.

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".

The classic debate between Einstein and Bohr over a realistic interpretation of quantum mechanics can be cast in terms of the measurement problem: Is there an underlying ontic state prior to measurement which maps deterministically to the measured outcome? According to the Kochen-Specker theorem, such a view is patently inconsistent with quantum theory, leading to the paradox of quantum contextuality. This result, however, relies upon the (arguably unwarranted) assumption that the ontic state remains unchanged through the process of measurement and attendant interaction with the measuring device. By relaxing this assumption, it will be shown that one is able to maintain a realistic view of a pre-existing ontic state, as Einstein insisted, while allowing for changes in that ontic state relative to the chosen measurement, in accordance with Bohr. In this view, the wavefunction respresents an epistemic ensemble of ontological states, corresponding to, say, a particular preparation procedure, and its collapse is a selection of and dynamical process on one member of that ensemble. The specific case of the Mermin-Peres square will be considered, both for its simplicity and its connection to recent experimental tests of quantum contextuality.

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.

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.