Interferometers as Probes of Planckian Quantum Geometry

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, $t_P$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting operators for position in different directions, as defined by interactions with null waves. The resulting evolution of position wavefunctions in two dimensions displays a new kind of directionally-coherent quantum noise of transverse position. The amplitude of the effect in physical units is predicted with no parameters, by equating the number of degrees of freedom of position wavefunctions on a 2D spacelike surface with the entropy density of a black hole event horizon of the same area. In a region of size $L$, the effect resembles spatially and directionally coherent random transverse shear deformations on timescale $\approx L/c$ with typical amplitude $\approx \sqrt{ct_PL}$. This quantum-geometrical "holographic noise" in position is not describable as fluctuations of a quantized metric, or as any kind of fluctuation, dispersion or propagation effect in quantum fields. In a Michelson interferometer the effect appears as noise that resembles a random Planckian walk of the beamsplitter for durations up to the light crossing time. Signal spectra and correlation functions in interferometers are derived, and predicted to be comparable with the sensitivities of current and planned experiments. It is proposed that nearly co-located Michelson interferometers of laboratory scale, cross-correlated at high frequency, can test the Planckian noise prediction with current technology.Comment: 23 pages, 6 figures, Latex. To appear in Physical Review

Numerical simulations of gravitational collapse in Einstein-aether theory

We study gravitational collapse of a spherically symmetric scalar field in Einstein-aether theory (general relativity coupled to a dynamical unit timelike vector field). The initial value formulation is developed, and numerical simulations are performed. The collapse produces regular, stationary black holes, as long as the aether coupling constants are not too large. For larger couplings a finite area singularity occurs. These results are shown to be consistent with the stationary solutions found previously.Comment: 9 pages, 7 figures; v2: corrected typos, added minor clarifying remarks, improved discussion of results in conclusio

Non-local on-shell field redefinition for the SME

This work instigates a study of non-local field mappings within the Lorentz- and CPT-violating Standard-Model Extension (SME). An example of such a mapping is constructed explicitly, and the conditions for the existence of its inverse are investigated. It is demonstrated that the associated field redefinition can remove b-type Lorentz violation from free SME fermions in certain situations. These results are employed to obtain explicit expressions for the corresponding Lorentz-breaking momentum-space eigenspinors and their orthogonality relations.Comment: 12 pages, REVTeX

Tests of Lorentz and CPT symmetry with hadrons and nuclei

We apply chiral-perturbation-theory techniques to the QCD sector of the Lorentz and CPT violating standard-model extension. We derive the effective Lagrangian in terms of pions and nucleons for a selected set of dimension-five operators involving quarks and gluons. This derivation is based on chiral-symmetry properties of the operators, as well as on their behaviour under C,P, and T transformations. We consider the power counting rules and apply the heavy-baryon approach to account for the large nucleon mass. Having obtained the relevant Lorentz-violating contributions to the pion-nucleon Lagrangian, we proceed to derive the particle and anti-particle Hamiltonian, from which we obtain the Lorentz-violating contribution to comagnetometer experiments. This allows us to place stringent limits on some of the parameters. For some other parameters we find that the best bounds will come from nucleon nucleon interactions, and we derive the relevant nucleon-nucleon potential. These considerations imply possible new opportunities for spin-precession experiments involving for example the deuteron.Portuguese Foundation for Science and Technology (FCT) [SFRH/BPD/101403/2014]; program POPH/FS

Past and future blurring at fundamental length scale

We obtain the $\kappa$-deformed versions of the retarded and advanced Green functions and show that their causality properties are blurred in a time interval of the order of a length parameter $q=1/(2\kappa)$. The functions also indicate a smearing of the light cone. These results favor the interpretation of $q$ as a fundamental length scale below which the concept of a point in spacetime should be substituted by the concept of a fuzzy region of radius $q$, as proposed long ago by Heisenberg.Comment: Essentially, this is the version published in the Phys. Rev. Lett. 105, 211601 (2010). It has 4 pages and contains 2 figure

The Casimir Force in a Lorentz Violating Theory

We study the effects of the minimal extension of the standard model including Lorentz violation on the Casimir force between two parallel conducting plates in vacuum. We provide explicit solutions for the electromagnetic field using scalar field analogy, for both the cases in which the Lorentz violating terms come from the CPT-even or CPT-odd terms. We also calculate the effects of the Lorentz violating terms for a fermion field between two parallel conducting plates and analyze the modifications of the Casimir force due to the modifications of the Dirac equation. In all cases under consideration, the standard formulas for the Casimir force are modified by either multiplicative or additive correction factors, the latter case exhibiting different dependence on the distance between the plates.Comment: 20 pages, no figures, references added, accepted for publication in Phys. Rev.

An Investigation of the KFK_{F}-type Lorentz-Symmetry Breaking Gauge Models in N=1N=1-Supersymmetric Scenario

In this work, we present two possible venues to accomodate the $K_{F}$-type Lorentz-symmetry violating Electrodynamics in an $N=1$-supersymmetric framework. A chiral and a vector superfield are chosen to describe the background that signals Lorentz-symmetry breaking. In each case, the $\ K_{\mu \nu \kappa \lambda }$-tensor is expressed in terms of the components of the background superfield that we choose to describe the breaking. We also present in detail the actions with all fermionic partners of the background that determine $\ K_{\mu \nu \kappa \lambda }$.Comment: 10 page

A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.

Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and thereby to reinfect previously infected hosts. However, the ways in which these viruses evolve antigenically are highly diverse. Some have only limited diversity in the long-run, with every emergence of a new antigenic variant coupled with a replacement of the older variant. Other viruses rapidly accumulate antigenic diversity over time. Others still exhibit dynamics that can be considered evolutionary intermediates between these two extremes. Here, we present a theoretical framework that aims to understand these differences in evolutionary patterns by considering a virus's epidemiological dynamics in a given host population. Our framework, based on a dimensionless number, probabilistically anticipates patterns of viral antigenic diversification and thereby quantifies a virus's evolutionary potential. It is therefore similar in spirit to the basic reproduction number, the well-known dimensionless number which quantifies a pathogen's reproductive potential. We further outline how our theoretical framework can be applied to empirical viral systems, using influenza A/H3N2 as a case study. We end with predictions of our framework and work that remains to be done to further integrate viral evolutionary dynamics with disease ecology

Synchrotron Radiation in the Standard Model Extension

We obtain a system of exact solutions of the Dirac equation for an electron moving in a constant homogeneous external magnetic field with account of its vacuum magnetic moment and assumed Lorentz invariance violation in the minimal CPT-odd form in the framework of the Standard Model Extension. Using these solutions, characteristics of the particle synchrotron radiation are calculated, and possible observable effects caused by the Lorentz non-invariant interaction are described. We demonstrate that the angular distribution of the radiation has specific asymmetry, which can be explained as a consequence of non-conservation of transversal electron polarization in the presence of a background Lorentz non-invariant condensate field.Comment: 14 pages, 2 figure

Modified dispersion relations and the response of the rotating Unruh-DeWitt detector

We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a non-linear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed {\it exactly}\vee (albeit, numerically) even when it is coupled to a field that is governed by a non-linear dispersion relation. We also discuss the response of the rotating detector in the presence of a cylindrical boundary on which the scalar field is constrained to vanish. While super-luminal dispersion relations hardly affect the standard results, we find that sub-luminal dispersion relations can lead to relatively large modifications.Comment: V1: 11 pages, 3 figures; V2: 12 pages, 3 figures, considerably revised, we now calculate the detector response exactly; V3: 14 pages, 3 figures, minor changes, to appear in Phys. Rev.