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

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Massive scalar field in multiply connected flat spacetimes

The vacuum expectation value of the stress-energy tensor $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ is calculated in several multiply connected flat spacetimes for a massive scalar field with arbitrary curvature coupling. We find that a nonzero field mass always decreases the magnitude of the energy density in chronology-respecting manifolds such as $R^3 \times S^1$, $R^2 \times T^2$, $R^1 \times T^3$, the M\"{o}bius strip, and the Klein bottle. In Grant space, which contains nonchronal regions, whether $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ diverges on a chronology horizon or not depends on the field mass. For a sufficiently large mass $\left\langle 0\left| T_{\mu\nu} \right|0\right\rangle$ remains finite, and the metric backreaction caused by a massive quantized field may not be large enough to significantly change the Grant space geometry.Comment: 19 pages, REVTeX, 5 figures in separate uuencoded compressed fil

Chronology Protection in Generalized Godel Spacetime

The effective action of a free scalar field propagating in the generalized Godel spacetime is evaluated by the zeta-function regularization method. From the result we show that the renormalized stress energy tensor may be divergent at the chronology horizon. This gives a support to the chronology protection conjecture.Comment: Latex 6 pages, typos correcte

van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes

The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3) One loop approximations to functional integrals. (4) The theory of caustics in geometrical optics and ultrasonics. (5) The focussing and defocussing of geodesic flows in Riemannian manifolds. While all of these topics are interrelated, the present paper is particularly concerned with the last case and presents extensive theoretical developments that aid in the computation of the van Vleck determinant associated with geodesic flows in Lorentzian spacetimes. {\sl A fortiori} these developments have important implications for the entire array of topics indicated. PACS: 04.20.-q, 04.20.Cv, 04.60.+n. To appear in Physical Review D47 (1993) 15 March.Comment: plain LaTeX, 18 page

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

A Self-Consistent Vacuum for Misner Space and the Chronology Protection Conjecture

In this paper we find a self-consistent vacuum for Misner space. For this "adapted" Rindler vacuum the renormalized stress-energy tensor is zero throughout the Misner space. A point-like particle detector traveling on a timelike geodesic in a Misner space with this vacuum detects nothing. Misner space with this vacuum thus creates no problems for time travel in and of itself but a time traveler may pose a danger to himself and to the spacetime.Comment: 5 pages, received September 5, 1997, with a note added November 24, 199

Unitarity and Causality in Generalized Quantum Mechanics for Non-Chronal Spacetimes

Spacetime must be foliable by spacelike surfaces for the quantum mechanics of matter fields to be formulated in terms of a unitarily evolving state vector defined on spacelike surfaces. When a spacetime cannot be foliated by spacelike surfaces, as in the case of spacetimes with closed timelike curves, a more general formulation of quantum mechanics is required. In such generalizations the transition matrix between alternatives in regions of spacetime where states {\it can} be defined may be non-unitary. This paper describes a generalized quantum mechanics whose probabilities consistently obey the rules of probability theory even in the presence of such non-unitarity. The usual notion of state on a spacelike surface is lost in this generalization and familiar notions of causality are modified. There is no signaling outside the light cone, no non-conservation of energy, no ``Everett phones'', and probabilities of present events do not depend on particular alternatives of the future. However, the generalization is acausal in the sense that the existence of non-chronal regions of spacetime in the future can affect the probabilities of alternatives today. The detectability of non-unitary evolution and violations of causality in measurement situations are briefly considered. The evolution of information in non-chronal spacetimes is described.Comment: 40pages, UCSBTH92-0

No Time Machine Construction in Open 2+1 Gravity with Timelike Total Energy Momentum

It is shown that in 2+1 dimensional gravity an open spacetime with timelike sources and total energy momentum cannot have a stable compactly generated Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and shows, in particular, that not only a Gott pair cannot be formed from processes such as the decay of a single cosmic string as has been shown by Carroll et al., but that, in a precise sense, a time machine cannot be constructed at all.Comment: 7 pages. Several changes and 3 figures added. To appear in Phys. Rev.

Semi-Automatic Classification Of Histopathological Images: Dealing With Inter-Slide Variations

Introduction/ Background The large size and high resolution of histopathological whole slide images renders their manual annotation time-consuming and costly. State-of-the-art computer-based segmentation approaches are generally able to classify tissue reliably, but strong inter-slide variations between training and evaluation data can cause significant decreases in classification accuracy. Aims In this study, we focus on alpha-SMA stainings of the mouse kidney, and in particular on the classification of glomerular vs. non-glomerular regions. Even though all slides had been recorded using a common staining protocol, inter-slide variations could be observed. We investigate the impact of these variations as well as methods of resolution. Methods We propose an interactive, semi-automatic tissue classification approach [1] which adapts a pre-trained classification model to the new image on which classification should be performed. Image patches for which the class (glomerular/non-glomerular) is uncertain are automatically selected and presented to the user to determine the class label. The user interaction step is repeated several times to iteratively adjust the model to the characteristics of the new image. For image representation and classification, well known methods from the literature are utilized. Specifically, we combine Local Binary Patters with the support vector classifier. Results In case of 50 available labelled sample patches of a certain whole slide image, the overall classification rate increased from 92 % to 98 % through including the interactive labelling step. Even with only 20 labelled patches, accuracy already increased to 97 %. Without a pre-trained model, if training is performed on target domain data only, 88 % (20 labelled samples) and 95 % (50 labelled samples) accuracy, respectively, were obtained. If enough target domain data was available (about 20 images), the amount of source domain data was of minor relevance. The difference in outcome between a source domain training data set containing 100 patches from one whole slide image and a set containing 700 patches from seven images was lower than 1 %. Contrarily, without target domain data, the difference in accuracy was 10 % (82 % compared to 92 %) between these two settings. Execution runtime between two interaction steps is significantly below one second (0.23 s), which is an important usability criterion. It proved to be beneficial to select specific target domain data in an active learning sense based on the currently available trained model. While experimental evaluation provided strong empirical evidence for increased classification performance with the proposed method, the additional manual effort can be kept at a low level. The labelling of e.g. 20 images per slide is surely less time consuming than the validation of a complete whole slide image processed with a fully automatic, but less reliable, segmentation approach. Finally, it should be highlighted that the proposed interaction protocol could easily be adapted to other histopathological classification or segmentation tasks, also for implementation in a clinical system.