Hidden variable interpretation of spontaneous localization theory

The spontaneous localization theory of Ghirardi, Rimini, and Weber (GRW) is a theory in which wavepacket reduction is treated as a genuine physical process. Here it is shown that the mathematical formalism of GRW can be given an interpretation in terms of an evolving distribution of particles on configuration space similar to Bohmian mechanics (BM). The GRW wavefunction acts as a pilot wave for the set of particles. In addition, a continuous stream of noisy information concerning the precise whereabouts of the particles must be specified. Nonlinear filtering techniques are used to determine the dynamics of the distribution of particles conditional on this noisy information and consistency with the GRW wavefunction dynamics is demonstrated. Viewing this development as a hybrid BM-GRW theory, it is argued that, besides helping to clarify the relationship between the GRW theory and BM, its merits make it worth considering in its own right.Comment: 13 page

Non-parametric reconstruction of the primordial power spectrum at horizon scales from WMAP data

We extend to large scales a method proposed in previous work that reconstructs non-parametrically the primordial power spectrum from cosmic microwave background data at high resolution. The improvement is necessary to account for the non-gaussianity of the Wilkinson Microwave Anisotropy Probe (WMAP) likelihood due primarily to cosmic variance. We assume the concordance LambdaCDM cosmology, utilise a smoothing prior and perform Monte Carlo simulations around an initial power spectrum that is scale-free and with spectral index n_s=0.97, very close to the concordance spectrum. The horizon scale for the model we are considering corresponds to the wavenumber k_h=4.52X10^{-4} Mpc^{-1}. We find some evidence for the presence of features and we quantify the probabilities of exceeding the observed deviations in WMAP data with respect to the fiducial models. We detect the following marginal departures from a scale-free (spectral index n_s=0.97) initial spectrum: a cut-off at 0.0001<k<0.001 Mpc^{-1} at 79.5% (92%), a dip at 0.001<k<0.003 Mpc^{-1} at 87.2% (98%) and a bump at 0.003<k<0.004 Mpc^{-1} at 90.3% (55.5%) confidence level. These frequentist confidence levels are calculated by integrating over the distribution of the Monte Carlo reconstructions built around the fiducial models. The frequentist analysis finds the low k cutoff of the estimated power spectrum to be about 2.5 sigma away from the n_s=0.97 model, while in the Bayesian analysis the model is about 1.5 sigma away from the estimated spectrum. (The sigma's are different for the two different methods.)Comment: 9 pages, 8 figures. Revised version accepted for publication in MNRA

Response to Comment on `Undamped electrostatic plasma waves' [Phys. Plasmas 19, 092103 (2012)]

Numerical and experimental evidence is given for the occurrence of the plateau states and concomitant corner modes proposed in \cite{valentini12}. It is argued that these states provide a better description of reality for small amplitude off-dispersion disturbances than the conventional Bernstein-Greene-Kruskal or cnoidal states such as those proposed in \cite{comment

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 new search for features in the primordial power spectrum

We develop a new approach toward a high resolution non-parametric reconstruction of the primordial power spectrum using WMAP cosmic microwave background temperature anisotropies that we confront with SDSS large-scale structure data in the range k~0.01-0.1 h/Mpc. We utilise the standard LambdaCDM cosmological model but we allow the baryon fraction to vary. In particular, for the concordance baryon fraction, we compare indications of a possible feature at k~0.05 h/Mpc in WMAP data with suggestions of similar features in large scale structure surveys.Comment: revised version, conclusions unchanged, 7 figures, accepted for publication in MNRA

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

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

Are All Particles Identical?

We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same particle, just as spin-up and spin-down do. The implications of this viewpoint can be best appreciated within Bohmian mechanics, a precise formulation of quantum mechanics with particle trajectories. The implementation of this viewpoint in such a theory leads to trajectories different from those of the usual formulation, and thus to a version of Bohmian mechanics that is inequivalent to, though arguably empirically indistinguishable from, the usual one. The mathematical core of this viewpoint is however rather independent of the detailed dynamical scheme Bohmian mechanics provides, and it amounts to the assertion that the configuration space for N particles, even N ``distinguishable particles,'' is the set of all N-point subsets of physical 3-space.Comment: 12 pages LaTeX, no figure

Undamped electrostatic plasma waves

Electrostatic waves in a collision-free unmagnetized plasma of electrons with fixed ions are investigated for electron equilibrium velocity distribution functions that deviate slightly from Maxwellian. Of interest are undamped waves that are the small amplitude limit of nonlinear excitations, such as electron acoustic waves (EAWs). A deviation consisting of a small plateau, a region with zero velocity derivative over a width that is a very small fraction of the electron thermal speed, is shown to give rise to new undamped modes, which here are named {\it corner modes}. The presence of the plateau turns off Landau damping and allows oscillations with phase speeds within the plateau. These undamped waves are obtained in a wide region of the $(k,\omega_{_R})$ plane ($\omega_{_R}$ being the real part of the wave frequency and $k$ the wavenumber), away from the well-known `thumb curve' for Langmuir waves and EAWs based on the Maxwellian. Results of nonlinear Vlasov-Poisson simulations that corroborate the existence of these modes are described. It is also shown that deviations caused by fattening the tail of the distribution shift roots off of the thumb curve toward lower $k$-values and chopping the tail shifts them toward higher $k$-values. In addition, a rule of thumb is obtained for assessing how the existence of a plateau shifts roots off of the thumb curve. Suggestions are made for interpreting experimental observations of electrostatic waves, such as recent ones in nonneutral plasmas.Comment: 11 pages, 10 figure