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-

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

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

Signature Change on the Brane

We explore the possibility of having a good description of classical signature change in the brane scenario.Comment: RevTeX, 4 pages, 1 figure. Uses epsfig package. Slightly shorter version to match the published version. Reference adde

General solutions of Einstein's spherically symmetric gravitational equations with junction conditions

Einstein's spherically symmetric interior gravitational equations are investigated. Following Synge's procedure, the most general solution of the equations is furnished in case $T^{1}_{1}$ and $T^{4}_{4}$ are prescribed. The existence of a total mass function, $M(r,t)$, is rigorously proved. Under suitable restrictions on the total mass function, the Schwarzschild mass $M(r,t)=m$, implicitly defines the boundary of the spherical body as $r=B(t)$. Both Synge's junction conditions as well as the continuity of the second fundamental form are examined and solved in a general manner. The weak energy conditions for an \emph{arbitrary boost} are also considered. The most general solution of the spherically symmetric anisotropic fluid model satisfying both junction conditions is furnished. In the final section, various exotic solutions are explored using the developed scheme including gravitational instantons, interior $T$-domains and $D$-dimensional generalizations.Comment: 23 pages, 1 figure, uses AMS packages. Updated version has corrected typos as well as added comments and extension regarding ISLD junction conditions. Accepted for publication in Journal of Mathematical Physic

Spacetime Coarse Grainings in the Decoherent Histories Approach to Quantum Theory

We investigate the possibility of assigning consistent probabilities to sets of histories characterized by whether they enter a particular subspace of the Hilbert space of a closed system during a given time interval. In particular we investigate the case that this subspace is a region of the configuration space. This corresponds to a particular class of coarse grainings of spacetime regions. We consider the arrival time problem and the problem of time in reparametrization invariant theories as for example in canonical quantum gravity. Decoherence conditions and probabilities for those application are derived. The resulting decoherence condition does not depend on the explicit form of the restricted propagator that was problematic for generalizations such as application in quantum cosmology. Closely related is the problem of tunnelling time as well as the quantum Zeno effect. Some interpretational comments conclude, and we discuss the applicability of this formalism to deal with the arrival time problem.Comment: 23 pages, Few changes and added references in v

Decoherent histories analysis of the relativistic particle

The Klein-Gordon equation is a useful test arena for quantum cosmological models described by the Wheeler-DeWitt equation. We use the decoherent histories approach to quantum theory to obtain the probability that a free relativistic particle crosses a section of spacelike surface. The decoherence functional is constructed using path integral methods with initial states attached using the (positive definite) ``induced'' inner product between solutions to the constraint equation. The notion of crossing a spacelike surface requires some attention, given that the paths in the path integral may cross such a surface many times, but we show that first and last crossings are in essence the only useful possibilities. Different possible results for the probabilities are obtained, depending on how the relativistic particle is quantized (using the Klein-Gordon equation, or its square root, with the associated Newton-Wigner states). In the Klein-Gordon quantization, the decoherence is only approximate, due to the fact that the paths in the path integral may go backwards and forwards in time. We compare with the results obtained using operators which commute with the constraint (the ``evolving constants'' method).Comment: 51 pages, plain Te

Probabilities in Quantum Cosmological Models: A Decoherent Histories Analysis Using a Complex Potential

In the quantization of simple cosmological models (minisuperspace models) described by the Wheeler-DeWitt equation, an important step is the construction, from the wave function, of a probability distribution answering various questions of physical interest, such as the probability of the system entering a given region of configuration space at any stage in its entire history. A standard but heuristic procedure is to use the flux of (components of) the wave function in a WKB approximation. This gives sensible semiclassical results but lacks an underlying operator formalism. In this paper, we address the issue of constructing probability distributions linked to the Wheeler-DeWitt equation using the decoherent histories approach to quantum theory. We show that the appropriate class operators (the generalization of strings of projectors) in quantum cosmology are readily constructed using a complex potential. We derive the class operator for entering or not entering one or more regions in configuration space. They commute with the Hamiltonian, have a sensible classical limit and are closely related to intersection number operators. We show that oscillatory WKB solutions to the Wheeler-DeWitt equation give approximate decoherence of histories, as do superpositions of WKB solutions, as long as the regions of configuration space are sufficiently large. The corresponding probabilities coincide, in a semiclassical approximation, with standard heuristic procedures. In brief, we exhibit the well-defined operator formalism underlying the usual heuristic interpretational methods in quantum cosmology.Comment: 49 pages, Latex, 8 figure

Demographic and clinical correlates of autism symptom domains and autism spectrum diagnosis

Demographic and clinical factors may influence assessment of autism symptoms. This study evaluated these correlates and also examined whether social communication and interaction and restricted/repetitive behavior provided unique prediction of autism spectrum disorder diagnosis. We analyzed data from 7352 siblings included in the Interactive Autism Network registry. Social communication and interaction and restricted/repetitive behavior symptoms were obtained using caregiver-reports on the Social Responsiveness Scale. Demographic and clinical correlates were covariates in regression models predicting social communication and interaction and restricted/repetitive behavior symptoms. Logistic regression and receiver operating characteristic curve analyses evaluated the incremental validity of social communication and interaction and restricted/repetitive behavior domains over and above global autism symptoms. Autism spectrum disorder diagnosis was the strongest correlate of caregiver-reported social communication and interaction and restricted/repetitive behavior symptoms. The presence of comorbid diagnoses also increased symptom levels. Social communication and interaction and restricted/repetitive behavior symptoms provided significant, but modest, incremental validity in predicting diagnosis beyond global autism symptoms. These findings suggest that autism spectrum disorder diagnosis is by far the largest determinant of quantitatively measured autism symptoms. Externalizing (attention deficit hyperactivity disorder) and internalizing (anxiety) behavior, low cognitive ability, and demographic factors may confound caregiver-report of autism symptoms, potentially necessitating a continuous norming approach to the revision of symptom measures. Social communication and interaction and restricted/repetitive behavior symptoms may provide incremental validity in the diagnosis of autism spectrum disorder

Trajectories for the Wave Function of the Universe from a Simple Detector Model

Inspired by Mott's (1929) analysis of particle tracks in a cloud chamber, we consider a simple model for quantum cosmology which includes, in the total Hamiltonian, model detectors registering whether or not the system, at any stage in its entire history, passes through a series of regions in configuration space. We thus derive a variety of well-defined formulas for the probabilities for trajectories associated with the solutions to the Wheeler-DeWitt equation. The probability distribution is peaked about classical trajectories in configuration space. The ``measured'' wave functions still satisfy the Wheeler-DeWitt equation, except for small corrections due to the disturbance of the measuring device. With modified boundary conditions, the measurement amplitudes essentially agree with an earlier result of Hartle derived on rather different grounds. In the special case where the system is a collection of harmonic oscillators, the interpretation of the results is aided by the introduction of ``timeless'' coherent states -- eigenstates of the Hamiltonian which are concentrated about entire classical trajectories.Comment: 37 pages, plain Tex. Second draft. Substantial revision