Order in de Broglie - Bohm quantum mechanics

A usual assumption in the so-called {\it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding' wavefunctions turn to be quite irregular, i.e. {\it chaotic} (in the dynamical systems' sense). In the present paper, we consider mainly cases in which the quantum trajectories are {\it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H\'{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {\it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.Comment: 25 pages, 12 figure

Geometrical view of quantum entanglement

Although a precise description of microscopic physical problems requires a full quantum mechanical treatment, physical quantities are generally discussed in terms of classical variables. One exception is quantum entanglement which apparently has no classical counterpart. We demonstrate here how quantum entanglement may be within the de Broglie-Bohm interpretation of quantum mechanics visualized in geometrical terms, giving new insight into this mysterious phenomenon and a language to describe it. On the basis of our analysis of the dynamics of a pair of qubits, quantum entanglement is linked to concurrent motion of angular momenta in the Bohmian space of hidden variables and to the average angle between these momenta

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio

The nature of dark energy

According to a variety of cosmological observations at small and large redshifts, the universe is composed by a large fraction of a weakly clustered component with negative pressure, called dark energy. The nature of the dark energy, i.e. its interaction and self-interaction properties, is still largely unknown. In this contribution we review the properties of dark energy as inferred from observations, with particular emphasis on the cosmic microwave background. We argue that the current dataset imposes strong constraints on the coupling of dark energy to dark matter, while it is still insufficient to constrain the equation of state or potential. Future data will dramatically improve the prospects

Inflationary Cosmology as a Probe of Primordial Quantum Mechanics

We show that inflationary cosmology may be used to test the statistical predictions of quantum theory at very short distances and at very early times. Hidden-variables theories, such as the pilot-wave theory of de Broglie and Bohm, allow the existence of vacuum states with non-standard field fluctuations ('quantum nonequilibrium'). We show that inflationary expansion can transfer microscopic nonequilibrium to macroscopic scales, resulting in anomalous power spectra for the cosmic microwave background. The conclusions depend only weakly on the details of the de Broglie-Bohm dynamics. We discuss, in particular, the nonequilibrium breaking of scale invariance for the primordial (scalar) power spectrum. We also show how nonequilibrium can generate primordial perturbations with non-random phases and inter-mode correlations (primordial non-Gaussianity). We address the possibility of a low-power anomaly at large angular scales, and show how it might arise from a nonequilibrium suppression of quantum noise. Recent observations are used to set an approximate bound on violations of quantum theory in the early universe.Comment: 44 pages. Minor changes in v

A non-local, Lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories

We demonstrate how to construct a lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. The covariant theory that we propose employs a multi-time formalism and a lorentz-invariant rule for the coordination of the space-time points on the individual particle trajectories. In this way we show that there is no contradiction between nonlocality and lorentz invariance in quantum mechanics. The approach is illustrated for relativistic bosons, using a simple model to discuss the individual non-locally correlated particle motion which ensues when the wavefunction is entangled. A simple example of measurement is described.Comment: 12 pages, 2 figure