Complex lapse, complex action and path integrals

Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the ``3+1'' action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and in particular allows a change of signature between the two. The action and variational equations are manifestly well defined in the Hamiltonian representation, with the momentum fields consequently being complex. The complex action interpolates between the Lorentzian and Riemannian actions as they appear formally in the respective path integrals. Thus the complex-lapse theory provides a unified basis for a path-integral quantum theory of gravity involving both Lorentzian and Riemannian aspects. A major motivation is the quantum-tunnelling scenario for the origin of the universe. Taken as an explanation for the observed quantum tunnelling of particles, the complex-lapse theory determines that the argument of the lapse for the universe now is extremely small but negative.Comment: 12 pages, Te

High performance software framework for the calculation of satellite-to-satellite data matchups (MMS version 1.2)

We present a Multisensor Matchup System (MMS) that allows systematic detection of satellite based sensor-to- sensor matchups and the extraction of local subsets of satellite data around matchup locations. The software system implements a generic matchup-detection approach and is currently being used for validation and sensor harmonisation purposes. An overview of the flexible and highly configurable software architecture and the target processing environments is given. We discuss improvements implemented with respect to heritage systems, and present some performance comparisons. A detailed description of the intersection algorithm is given which allows a fast matchup detection in geometry and time

The trace left by signature-change-induced compactification

Recently, it has been shown that an infinite succession of classical signature changes (''signature oscillations'') can compactify and stabilize internal dimensions, and simultaneously leads, after a coarse graining type of average procedure, to an effective (''physical'') space-time geometry displaying the usual Lorentzian metric signature. Here, we consider a minimally coupled scalar field on such an oscillating background and study its effective dynamics. It turns out that the resulting field equation in four dimensions contains a coupling to some non-metric structure, the imprint of the ''microscopic'' signature oscillations on the effective properties of matter. In a multidimensional FRW model, this structure is identical to a massive scalar field evolving in its homogeneous mode.Comment: 15 pages, LaTeX, no figure

BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE

We show that, contrary to recent criticism, our previous work yields a reasonable class of solutions for the massless scalar field in the presence of signature change.Comment: 11 pages, Plain Tex, no figure

Actions for signature change

This is a contribution on the controversy about junction conditions for classical signature change. The central issue in this debate is whether the extrinsic curvature on slices near the hypersurface of signature change has to be continuous ({\it weak} signature change) or to vanish ({\it strong} signature change). Led by a Lagrangian point of view, we write down eight candidate action functionals $S_1$,\dots $S_8$ as possible generalizations of general relativity and investigate to what extent each of these defines a sensible variational problem, and which junction condition is implied. Four of the actions involve an integration over the total manifold. A particular subtlety arises from the precise definition of the Einstein-Hilbert Lagrangian density $|g|^{1/2} R[g]$. The other four actions are constructed as sums of integrals over singe-signature domains. The result is that {\it both} types of junction conditions occur in different models, i.e. are based on different first principles, none of which can be claimed to represent the ''correct'' one, unless physical predictions are taken into account. From a point of view of naturality dictated by the variational formalism, {\it weak} signature change is slightly favoured over {\it strong} one, because it requires less {\it \`a priori} restrictions for the class of off-shell metrics. In addition, a proposal for the use of the Lagrangian framework in cosmology is made.Comment: 36 pages, LaTeX, no figures; some corrections have been made, several Comments and further references are included and a note has been added

Gravity and Signature Change

The use of proper ``time'' to describe classical ``spacetimes'' which contain both Euclidean and Lorentzian regions permits the introduction of smooth (generalized) orthonormal frames. This remarkable fact permits one to describe both a variational treatment of Einstein's equations and distribution theory using straightforward generalizations of the standard treatments for constant signature.Comment: Plain TeX, 6 pages; to appear in GR

Bohmian arrival time without trajectories

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wave function and its spatial derivative, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction, published versio

Closed Strings with Low Harmonics and Kinks

Low-harmonic formulas for closed relativistic strings are given. General parametrizations are presented for the addition of second- and third-harmonic waves to the fundamental wave. The method of determination of the parametrizations is based upon a product representation found for the finite Fourier series of string motion in which the constraints are automatically satisfied. The construction of strings with kinks is discussed, including examples. A procedure is laid out for the representation of kinks that arise from self-intersection, and subsequent intercommutation, for harmonically parametrized cosmic strings.Comment: 39, CWRUTH-93-

Evolution of cosmic string configurations

We extend and develop our previous work on the evolution of a network of cosmic strings. The new treatment is based on an analysis of the probability distribution of the end-to-end distance of a randomly chosen segment of left-moving string of given length. The description involves three distinct length scales: $\xi$, related to the overall string density, $\bar\xi$, the persistence length along the string, and $\zeta$, describing the small-scale structure, which is an important feature of the numerical simulations that have been done of this problem. An evolution equation is derived describing how the distribution develops in time due to the combined effects of the universal expansion, of intercommuting and loop formation, and of gravitational radiation. With plausible assumptions about the unknown parameters in the model, we confirm the conclusions of our previous study, that if gravitational radiation and small-scale structure effects are neglected, the two dominant length scales both scale in proportion to the horizon size. When the extra effects are included, we find that while $\xi$ and $\bar\xi$ grow, $\zeta$ initially does not. Eventually, however, it does appear to scale, at a much lower level, due to the effects of gravitational back-reaction.Comment: 61 pages, requires RevTex v3.0, SUSSEX-TH-93/3-4, IMPERIAL/TP/92-93/4

On Accelerated Inertial Frames in Gravity and Electromagnetism

When a charged insulating spherical shell is uniformly accelerated, an oppositely directed electric field is produced inside. Outside the field is the Born field of a uniformly accelerated charge, modified by a dipole. Radiation is produced. When the acceleration is annulled by the nearly uniform gravity field of an external shell with a 1 + beta cos theta surface distribution of mass, the differently viewed Born field is static and joins a static field outside the external shell; no radiation is produced. We discuss gravitational analogues of these phenomena. When a massive spherical shell is accelerated, an untouched test mass inside experiences a uniform gravity field and accelerates parallelly to the surrounding shell. In the strong gravity regime we illustrate these effects using exact conformastatic solutions of the Einstein-Maxwell equations with charged dust. We consider a massive charged shell on which the forces due to nearly uniform electrical and gravitational fields balance. Both fields are reduced inside by the ratio of the g_00 inside the shell to that away from it. The acceleration of a free test particle, relative to a static observer, is reduced correspondingly. We give physical explanations of these effects.Comment: 25 pages, LaTeX with 6 encapsulated postscript figures included. To appear in Annals of Physic