Noncanonical Quantization of Gravity. I. Foundations of Affine Quantum Gravity

The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel Hilbert space. Constraints are introduced following the projection operator method which involves no gauge fixing, no complicated moduli space, nor any auxiliary fields. The result, which is only qualitatively sketched in the present paper, involves another reproducing kernel with which inner products are defined for the physical Hilbert space and which is obtained through a reduction of the original reproducing kernel. Several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one-dimensional quantum mechanical models. These toy models help in motivating and understanding the analysis in the case of gravity.Comment: minor changes, LaTeX, 37 pages, no figure

A note on the cylindrical collapse of counter-rotating dust

We find analytical solutions describing the collapse of an infinitely long cylindrical shell of counter-rotating dust. We show that--for the classes of solutions discussed herein--from regular initial data a curvature singularity inevitably develops, and no apparent horizons form, thus in accord with the spirit of the hoop conjecture.Comment: 8 pages, LaTeX, ijmpd macros (included), 1 eps figure; accepted for publication in Int. J. Mod. Phys.

The time travel paradox

We define the time travel paradox in physical terms and prove its existence by constructing an explicit example. We argue further that in theories -- such as general relativity -- where the spacetime geometry is subject to nothing but differential equations and initial data no paradoxes arise.Comment: Minor changes + an explanatory note concerning the lions with the same world line

Simple Quantum Systems in Spacetimes with Closed Timelike Curves

Three simple examples illustrate properties of path integral amplitudes in fixed background spacetimes with closed timelike curves: non-relativistic potential scattering in the Born approximation is non-unitary, but both an example with hard spheres and the exact solution of a totally discrete model are unitary.Comment: 15 pages, CALT-68-180

Evaluation of genetic variability for Sclerotinia sclerotiorum Lib. de Bary resistance in a f2 population from a Cross between susceptible and resistant sunflower

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Time travel paradoxes, path integrals, and the many worlds interpretation of quantum mechanics

We consider two approaches to evading paradoxes in quantum mechanics with closed timelike curves (CTCs). In a model similar to Politzer's, assuming pure states and using path integrals, we show that the problems of paradoxes and of unitarity violation are related; preserving unitarity avoids paradoxes by modifying the time evolution so that improbable events bewcome certain. Deutsch has argued, using the density matrix, that paradoxes do not occur in the "many worlds interpretation". We find that in this approach account must be taken of the resolution time of the device that detects objects emerging from a wormhole or other time machine. When this is done one finds that this approach is viable only if macroscopic objects traversing a wormhole interact with it so strongly that they are broken into microscopic fragments.Comment: no figure

From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture

The recent interest in ``time machines'' has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings. This rather disturbing state of affairs has led Hawking to formulate his Chronology Protection Conjecture, whereby the formation of ``time machines'' is forbidden. This paper will use several simple examples to argue that the universe appears to exhibit a ``defense in depth'' strategy in this regard. For appropriate parameter regimes Casimir effects, wormhole disruption effects, and gravitational back reaction effects all contribute to the fight against time travel. Particular attention is paid to the role of the quantum gravity cutoff. For the class of model problems considered it is shown that the gravitational back reaction becomes large before the Planck scale quantum gravity cutoff is reached, thus supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision

Detection, Measurement and Gravitational Radiation

Here I examine how to determine the sensitivity of the LIGO, VIRGO, and LAGOS gravitational wave detectors to sources of gravitational radiation by considering the process by which data are analyzed in a noisy detector. By constructing the probability that the detector output is consistent with the presence of a signal, I show how to (1) quantify the uncertainty that the output contains a signal and is not simply noise, and (2) construct the probability distribution that the signal parameterization has a certain value. From the distribution and its mode I determine volumes $V(P)$ in parameter space such that actual signal parameters are in $V(P)$ with probability $P$. If we are {\em designing} a detector, or determining the suitability of an existing detector for observing a new source, then we don't have detector output to analyze but are interested in the ``most likely'' response of the detector to a signal. I exploit the techniques just described to determine the ``most likely'' volumes $V(P)$ for detector output corresponding to the source. Finally, as an example, I apply these techniques to anticipate the sensitivity of the LIGO and LAGOS detectors to the gravitational radiation from a perturbed Kerr black hole.Comment: 37 pages (plus 6 figures), LaTeX/REVTE

Ringholes and closed timelike curves

It is shown that in a classical spacetime with multiply connected space slices having the topology of a torus, closed timelike curves are also formed. We call these spacetime ringholes. Two regions on the torus surface can be distinguished which are separated by angular horizons. On one of such regions (that which surrounds the maximum circumference of the torus) everything happens like in spherical wormholes, but the other region (the rest of the torus surface), while still possessing a chronology horizon and non-chronal region, behaves like a coverging, rather than diverging, lens and corresponds to an energy density which is always positive for large speeds at or near the throat. It is speculated that a ringhole could be converted into a time machine to perform time travels by an observer who would never encounter any matter that violates the classical averaged weak energy condition. Based on a calculation of vacuum fluctuations, it is also seen that the angular horizons can prevent the emergence of quantum instabilities near the throat.Comment: 11 pages, RevTex, 4 figures available upon reques