Abstract:
We show that it is not possible to smooth out the metric on the Deutsch-Politzer time machine to obtain an everywhere non-singular asymptotically flat Lorentzian metric.

Abstract:
It has been proposed that wormholes can be made to function as time-machines. This opens up the question of whether this can be accomodated within a self-consistent physics or not. In this contribution we present some quantum mechanical considerations in this respect.

Abstract:
We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. The resulting computability theory leads to a notion of computation on the reals and concepts of decidability and semi-decidability for sets of reals as well as individual reals. Every Pi^1_1 set, for example, is decidable by such machines, and the semi-decidable sets form a portion of the Delta^1_2 sets. Our oracle concept leads to a notion of relative computability for reals and sets of reals and a rich degree structure, stratified by two natural jump operators.

Abstract:
We present a generic way of thinking about time machines from the view of a far away observer. In this model the universe consists of three (or more) regions: One containing the entrance of the time machine, another the exit and the remaining one(s) the rest of the universe. In the latter we know ordinary quantum mechanics to be valid and thus are able to write down a Hamiltonian describing this generic time machine. We prove the time-evolution operator to be non-symmetric. Various interpretations of this irreversibility are given.

Abstract:
The existence of time machines, understood as spacetime constructions exhibiting physically realised closed timelike curves (CTCs), would raise fundamental problems with causality and challenge our current understanding of classical and quantum theories of gravity. In this paper, we investigate three proposals for time machines which share some common features: cosmic strings in relative motion, where the conical spacetime appears to allow CTCs; colliding gravitational shock waves, which in Aichelburg-Sexl coordinates imply discontinuous geodesics; and the superluminal propagation of light in gravitational radiation metrics in a modified electrodynamics featuring violations of the strong equivalence principle. While we show that ultimately none of these constructions creates a working time machine, their study illustrates the subtle levels at which causal self-consistency imposes itself, and we consider what intuition can be drawn from these examples for future theories.

Abstract:
Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Abstract:
Irrespective of local conditions imposed on the metric, any extendible spacetime U has a maximal extension containing no closed causal curves outside the chronological past of U. We prove this fact and interpret it as impossibility (in classical general relativity) of the time machines, insofar as the latter are defined to be causality-violating regions created by human beings (as opposed to those appearing spontaneously).

Abstract:
We present a scenario in $1 + 1$ and $3 + 1$ dimensional space time which is paradoxical in the presence of a time machine. We show that the paradox cannot be resolved and the scenario has {\em no} consistent classical solution. Since the system is macroscopic, quantisation is unlikely to resolve the paradox. Moreover, in the absence of a consistent classical solution to a macroscopic system, it is not obvious how to carry out the path integral quantisation. Ruling out, by fiat, the troublesome initial conditions will resolve the paradox, by not giving rise to it in the first place. However this implies that time machines have an influence on events, extending indefinitely into the past, and also tachyonic communication between physical events in an era when no time machine existed. If no resolution to the paradox can be found, the logical conclusion is that time machines of a certain, probably large, class cannot exist in $3 + 1$ and $1 + 1$ dimensional space time, maintaining the consistency of known physical laws.

Abstract:
There is a deep structural link between acausal spacetimes and quantum theory. As a consequence quantum theory may resolve some "paradoxes" of time travel. Conversely, non-time-orientable spacetimes naturally give rise to electric charges and spin half. If an explanation of quantum theory is possible, then general relativity with time travel could be it.