Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.Comment: 25 pages, phyzzx, CALT-68-188

The Unruh-deWitt Detector and the Vacuum in the General Boundary formalism

We discuss how to formulate a condition for choosing the vacuum state of a quantum scalar field on a timelike hyperplane in the general boundary formulation (GBF) using the coupling to an Unruh-DeWitt detector. We explicitly study the response of an Unruh-DeWitt detector for evanescent modes which occur naturally in quantum field theory in the presence of the equivalent of a dielectric boundary. We find that the physically correct vacuum state has to depend on the physical situation outside of the boundaries of the spacetime region considered. Thus it cannot be determined by general principles pertaining only to a subset of spacetime.Comment: Version as published in CQ

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

The Quantum Propagator for a Nonrelativistic Particle in the Vicinity of a Time Machine

We study the propagator of a non-relativistic, non-interacting particle in any non-relativistic ``time-machine'' spacetime of the type shown in Fig.~1: an external, flat spacetime in which two spatial regions, $V_-$ at time $t_-$ and $V_+$ at time $t_+$, are connected by two temporal wormholes, one leading from the past side of $V_-$ to t the future side of $V_+$ and the other from the past side of $V_+$ to the future side of $V_-$. We express the propagator explicitly in terms of those for ordinary, flat spacetime and for the two wormholes; and from that expression we show that the propagator satisfies completeness and unitarity in the initial and final ``chronal regions'' (regions without closed timelike curves) and its propagation from the initial region to the final region is unitary. However, within the time machine it satisfies neither completeness nor unitarity. We also give an alternative proof of initial-region-to-final-region unitarity based on a conserved current and Gauss's theorem. This proof can be carried over without change to most any non-relativistic time-machine spacetime; it is the non-relativistic version of a theorem by Friedman, Papastamatiou and Simon, which says that for a free scalar field, quantum mechanical unitarity follows from the fact that the classical evolution preserves the Klein-Gordon inner product

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

Gravitational collapse to toroidal, cylindrical and planar black holes

Gravitational collapse of non-spherical symmetric matter leads inevitably to non-static external spacetimes. It is shown here that gravitational collapse of matter with toroidal topology in a toroidal anti-de Sitter background proceeds to form a toroidal black hole. According to the analytical model presented, the collapsing matter absorbs energy in the form of radiation (be it scalar, neutrinos, electromagnetic, or gravitational) from the exterior spacetime. Upon decompactification of one or two coordinates of the torus one gets collapsing solutions of cylindrical or planar matter onto black strings or black membranes, respectively. The results have implications on the hoop conjecture.Comment: 6 pages, Revtex, modifications in the title and in the interpretation of some results, to appear in Physical Review

Evolving Lorentzian Wormholes

Evolving Lorentzian wormholes with the required matter satisfying the Energy conditions are discussed. Several different scale factors are used and the corresponding consequences derived. The effect of extra, decaying (in time) compact dimensions present in the wormhole metric is also explored and certain interesting conclusions are derived for the cases of exponential and Kaluza--Klein inflation.Comment: 10 pages( RevTex, Twocolumn format), Two figures available on request from the first author. transmission errors corrected

Response of the Brazilian gravitational wave detector to signals from a black hole ringdown

It is assumed that a black hole can be disturbed in such a way that a ringdown gravitational wave would be generated. This ringdown waveform is well understood and is modelled as an exponentially damped sinusoid. In this work we use this kind of waveform to study the performance of the SCHENBERG gravitational wave detector. This first realistic simulation will help us to develop strategies for the signal analysis of this Brazilian detector. We calculated the signal-to-noise ratio as a function of frequency for the simulated signals and obtained results that show that SCHENBERG is expected to be sensitive enough to detect this kind of signal up to a distance of $\sim 20\mathrm{kpc}$.Comment: 5 pages, 4 figures, Amaldi 5 Conference Proceedings contribution. Submitted to Class. Quantum Gra

Fibre bundle formulation of nonrelativistic quantum mechanics: I. Introduction. The evolution transport

We propose a new systematic fibre bundle formulation of nonrelativistic quantum mechanics. The new form of the theory is equivalent to the usual one but it is in harmony with the modern trends in theoretical physics and potentially admits new generalizations in different directions. In it a pure state of some quantum system is described by a state section (along paths) of a (Hilbert) fibre bundle. Its evolution is determined through the bundle (analogue of the) Schr\"odinger equation. Now the dynamical variables and the density operator are described via bundle morphisms (along paths). The mentioned quantities are connected by a number of relations derived in this work. The present first part of this investigation is devoted to the introduction of basic concepts on which the fibre bundle approach to quantum mechanics rests. We show that the evolution of pure quantum-mechanical states can be described as a suitable linear transport along paths, called evolution transport, of the state sections in the Hilbert fibre bundle of states of a considered quantum system.Comment: 26 standard (11pt, A4) LaTeX 2e pages. The packages AMS-LaTeX and amsfonts are required. Revised: new material, references, and comments are added. Minor style chages. Continuation of quan-ph/9803083. For continuation of the this series see http://www.inrne.bas.bg/mathmod/bozhome

Unitarity Restoration in the Presence of Closed Timelike Curves

A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations, this proposal is causal, linear in the initial density matrix and preserves probability. It provides a physically reasonable interpretation of invertible nonunitary evolution by redefining the final Hilbert space so that the evolution is unitary or equivalently by removing the nonunitary part of the evolution operator using a polar decomposition.Comment: LaTeX, 17pp, Revisions: Title change, expanded and clarified presentation of original proposal, esp. with regard to Heisenberg picture and remaining in original Hilbert spac