The Pauli objection

Schroedinger's equation says that the Hamiltonian is the generator of time translations. This seems to imply that any reasonable definition of time operator must be conjugate to the Hamiltonian. Then both time and energy must have the same spectrum since conjugate operators are unitarily equivalent. Clearly this is not always true: normal Hamiltonians have lower bounded spectrum and often only have discrete eigenvalues, whereas we typically desire that time can take any real value. Pauli concluded that constructing a general a time operator is impossible (although clearly it can be done in specific cases). Here we show how the Pauli argument fails when one uses an external system (a "clock") to track time, so that time arises as correlations between the system and the clock (conditional probability amplitudes framework). In this case, the time operator is not conjugate to the system Hamiltonian, but its eigenvalues still satisfy the Schroedinger equation for arbitrary Hamiltonians.Comment: 6 page

Goal Driven Interaction (GDI) vs. Direct Manipulation (MD), an empirical comparison

Interacción'15, September 07-09, 2015, Vilanova i la Geltrú, Spain ACM 978-1-4503-3463-1/15/09. http://dx.doi.org/10.1145/2829875.2829892This paper presents a work in process about Goal Driven Interaction (GDI), a style of interaction intended for inexperienced, infrequent and occasional users, whose main priorities are to use a system and achieve their goals without cost in terms of time or effort. GDI basic philosophy is to guide the user about the "what" to do and the "how" to do it in each moment of the interaction process, without requiring from the user a previous knowledge to use the interface. This interaction style was introduced in previous work, where a description of its characteristics and the most appropriate user interface for it, were described. Those works included a methodology for the analysis and synthesis of the whole interactive process through a language of specification. This paper presents partial results we are collecting in real user testing, with the main aim of comparing GDI with direct manipulation interfaces (MD), nevertheless the most extended and commonly regarded as the most suitable for novice and experienced users.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The Fermi problem with artificial atoms in circuit QED

We propose a feasible experimental test of a 1-D version of the Fermi problem using superconducting qubits. We give an explicit non-perturbative proof of strict causality in this model, showing that the probability of excitation of a two-level artificial atom with a dipolar coupling to a quantum field is completely independent of the other qubit until signals from it may arrive. We explain why this is in perfect agreement with the existence of nonlocal correlations and previous results which were used to claim apparent causality problems for Fermi's two-atom system.Comment: 4 pages, 2 figures; typos corrected, introduction revised and experimental discussion extended, results unchange

The fate of non-trivial entanglement under gravitational collapse

We analyse the evolution of the entanglement of a non-trivial initial quantum field state (which, for simplicity, has been taken to be a bipartite state made out of vacuum and the first excited state) when it undergoes a gravitational collapse. We carry out this analysis by generalising the tools developed to study entanglement behaviour in stationary scenarios and making them suitable to deal with dynamical spacetimes. We also discuss what kind of problems can be tackled using the formalism spelled out here as well as single out future avenues of research.Comment: 9 pages, 2 figures. v2: Added Journal reference and small changes to match published versio

Falsifying cosmological models based on a non-linear electrodynamics

Recently, the nonlinear electrodynamics (NED) has been gaining attention to generate primordial magnetic fields in the Universe and also to resolve singularity problems. Moreover, recent works have shown the crucial role of the NED on the inflation. This paper provides a new approach based on a new model of NED as a source of gravitation to remove the cosmic singularity at the big bang and explain the cosmic acceleration during the inflation era on the background of stochastic magnetic field. Also, we found a realization of a cyclic Universe, free of initial singularity, due to the proposed NED energy density. In addition, we explore whether a NED field without or with matter can be the origin of the late-time acceleration. For this we obtain explicit equations for $H(z)$ and perform a MCMC analysis to constrain the NED parameters by using $31$ observational Hubble data (OHD) obtained from cosmic chronometers covering the redshift range $0 < z < 1.97$; and with the joint-light-analysis (JLA) SNIa compilation consisting in $740$ data points in the range $0.01<z<1.2$. All our constraints on the current magnetic field give $B_{0}\sim 10^{-31}\mathrm{cm^{-1}}$, which are larger than the upper limit $10^{-33}\mathrm{cm^{-1}}$ by the Planck satellite implying that NED cosmologies could not be suitable to explain the Universe late-time dynamics. However, the current data is able to falsify the scenario at late times. Indeed, one is able to reconstruct the deceleration parameter $q(z)$ using the best fit values of the parameters obtained from OHD and SNIa data sets. If the matter component is not included, the data sets predict an accelerated phase in the early Universe, but a non accelerated Universe is preferred in the current epoch...Comment: 20 pages, two-column, 14 figures. Accepted for publication in the European Physical Journal