Simulations of Closed Timelike Curves

Proposed models of closed timelike curves (CTCs) have been shown to enable powerful information-processing protocols. We examine the simulation of models of CTCs both by other models of CTCs and by physical systems without access to CTCs. We prove that the recently proposed transition probability CTCs (T-CTCs) are physically equivalent to postselection CTCs (P-CTCs), in the sense that one model can simulate the other with reasonable overhead. As a consequence, their information-processing capabilities are equivalent. We also describe a method for quantum computers to simulate Deutschian CTCs (but with a reasonable overhead only in some cases). In cases for which the overhead is reasonable, it might be possible to perform the simulation in a table-top experiment. This approach has the benefit of resolving some ambiguities associated with the equivalent circuit model of Ralph et al. Furthermore, we provide an explicit form for the state of the CTC system such that it is a maximum-entropy state, as prescribed by Deutsch.     

Computers with Closed Timelike Curves Can Solve Hard Problems Efficiently

A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for the problem of factoring large numbers and argue that a similar approach can solve NP-complete and PSPACE-complete problems. I discuss the potential impact of quantum effects on this result.     

Perfect State Distinguishability and Computational Speedups with Postselected Closed Timelike Curves

Bennett and Schumacher’s postselected quantum teleportation is a model of closed timelike curves (CTCs) that leads to results physically different from Deutsch’s model. We show that even a single qubit passing through a postselected CTC (P-CTC) is sufficient to do any postselected quantum measurement with certainty, and we discuss an important difference between “Deutschian” CTCs (D-CTCs) and P-CTCs in which the future existence of a P-CTC might affect the present outcome of an experiment. Then, based on a suggestion of Bennett and Smith, we explicitly show how a party assisted by P-CTCs can distinguish a set of linearly independent quantum states, and we prove that it is not possible for such a party to distinguish a set of linearly dependent states. The power of P-CTCs is thus weaker than that of D-CTCs because the Holevo bound still applies to circuits using them, regardless of their ability to conspire in violating the uncertainty principle. We then discuss how different notions of a quantum mixture that are indistinguishable in linear quantum mechanics lead to dramatically differing conclusions in a nonlinear quantum mechanics involving P-CTCs. Finally, we give explicit circuit constructions that can efficiently factor integers, efficiently solve any decision problem in the intersection of NP and coNP, and probabilistically solve any decision problem in NP. These circuits accomplish these tasks with just one qubit traveling back in time, and they exploit the ability of postselected closed timelike curves to create grandfather paradoxes for invalid answers.     

Closed Timelike Curves and Time Travel: Dispelling the Myth

G?del’s contention that closed timelike curves (CTC’s) are a necessary consequence of the Einstein equations for his metric is challenged. It is seen that the imposition of periodicity in a timelike coordinate is the actual source of CTC’s rather than the physics of general relativity. This conclusion is supported by the creation of G?del-like CTC’s in flat space by the correct choice of coordinate system and identifications. Thus, the indications are that the notion of a time machine remains exclusively an aspect of science fiction fantasy. The element of the identification of spacetime points is also seen to be the essential factor in the modern creation of CTC’s in the Gott model of moving cosmic strings.     

Revisiting Consistency Conditions for Quantum States of Systems on Closed Timelike Curves: An Epistemic Perspective

There has been considerable recent interest in the consequences of closed timelike curves (CTCs) for the dynamics of quantum mechanical systems. A vast majority of research into this area makes use of the dynamical equations developed by Deutsch, which were developed from a consistency condition that assumes that mixed quantum states uniquely describe the physical state of a system. We criticize this choice of consistency condition from an epistemic perspective, i.e., a perspective in which the quantum state represents a state of knowledge about a system. We demonstrate that directly applying Deutsch’s condition when mixed states are treated as representing an observer’s knowledge of a system can conceal time travel paradoxes from the observer, rather than resolving them. To shed further light on the appropriate dynamics for quantum systems traversing CTCs, we make use of a toy epistemic theory with a strictly classical ontology due to Spekkens and show that, in contrast to the results of Deutsch, many of the traditional paradoxical effects of time travel are present.     

Absorption/Scattering of Massless Dirac Wave from Black Hole Spacetimes with Cosmic String

In this paper we investigate the scattering of massless Dirac wave from several different black hole spacetimes (i.e. the Schwarzschild black hole, the RN extremal black hole, the Schwarzschild de Sitter black hole, and the extremal Schwarzschild de Sitter black hole) which are influenced by the cosmic string, respectively. All these cases show us that the total absorption cross sections oscillate around the geometric-optical limit and decrease with linear mass density μ of the cosmic string. All of the total scattering cross sections exhibit that the main scattering angle becomes narrower for the high partial frequency wave. Due to the influence of cosmic string, the glory peak becomes wider for larger values of linear mass density μ of the cosmic string.     

Unified Free Quantum Fields for Massive and for Massless Particles

For any mass m ≧ 0 and arbitrary spin, free relativistic quantum fields are constructed using the same formulas for m > 0 and for m = 0. The transformation properties of these fields under P, C, T and some questions concerning super-selection rules are discussed.     

Deformations of Quantum Field Theories on Spacetimes with Killing Vector Fields

The recent construction and analysis of deformations of quantum field theories by warped convolutions is extended to a class of curved spacetimes. These spacetimes carry a family of wedge-like regions which share the essential causal properties of the Poincaré transforms of the Rindler wedge in Minkowski space. In the setting of deformed quantum field theories, they play the role of typical localization regions of quantum fields and observables. As a concrete example of such a procedure, the deformation of the free Dirac field is studied.     

Absorption/Scattering of Massless Dirac Wave from Black Hole Spacetimes with Cosmic String

In this paper we investigate the scattering of massless Dirac wave from several different black hole spacetimes(i.e. the Schwarzschild black hole, the RN extremal black hole, the Schwarzschild de Sitter black hole, and the extremal Schwarzschild de Sitter black hole) which are influenced by the cosmic string, respectively. All these cases show us that the total absorption cross sections oscillate around the geometric-optical limit and decrease with linear mass density μof the cosmic string. All of the total scattering cross sections exhibit that the main scattering angle becomes narrower for the high partial frequency wave. Due to the influence of cosmic string, the glory peak becomes wider for larger values of linear mass density μ of the cosmic string.     

Gauge Invariance of Sedeonic Equations for Massive and Massless Fields

In the present paper we discuss the gauge invariance of generalized second-order and first-order wave equations for massive and massless fields based on sedeonic space-time operators and sedeonic wave functions.     

Hertz Potentials and Asymptotic Properties of Massless Fields

In this paper we analyze Hertz potentials for free massless spin-s fields on the Minkowski spacetime, with data in weighted Sobolev spaces. We prove existence and pointwise estimates for the Hertz potentials using a weighted estimate for the wave equation. This is then applied to give weighted estimates for the solutions of the spin-s field equations, for arbitrary half-integer s. In particular, the peeling properties of the free massless spin-s fields are analyzed for initial data in weighted Sobolev spaces with arbitrary, non-integer weights.     

Global and Uniqueness Properties of Stationary and Static Spacetimes with Outer Trapped Surfaces

Global properties of maximal future Cauchy developments of stationary, m-dimensional asymptotically flat initial data with an outer trapped boundary are analyzed. We prove that, whenever the matter model is well posed and satisfies the null energy condition, the future Cauchy development of the data is a black hole spacetime. More specifically, we show that the future Killing development of the exterior of a sufficiently large sphere in the initial data set can be isometrically embedded in the maximal Cauchy development of the data. In the static setting we prove, by working directly on the initial data set, that all Killing prehorizons are embedded whenever the initial data set has an outer trapped boundary and satisfies the null energy condition. By combining both results we prove a uniqueness theorem for static initial data sets with outer trapped boundary.     

Massless Fields on Dirac Six-Cone and De Sitter Ambient Space

We have proceeded to obtain manifestly conformally invariant (CI) equations for thinkable graviton fields in de Sitter (dS) space-time. The tensor fields are originally considered in 4+2 dimensional conformal space or Dirac’s six-cone and then project to dS space which is embedded in 4+1 dimensional ambient space. It will be shown that, by projecting these tensor fields there exists a correspondence between the massless fields on the cone and dS space. Also, we have shown that for rank-2 tensor field the divergenceless condition, which is necessary when we attempt to correspond the tensor field with the unitary irreducible representations (UIRs) of dS group, is not really a condition at all, it is a consequence of ambient space property. Due to the combined occurrences of corresponding fields and divergenceless property, the appropriate CI field equations have obtained in a fairly simple way and without imposing any extra condition.     

Moving Branes with Background Massless and Tachyon Fields in the Compact Spacetime

In this article, we shall obtain the boundary state associated with a moving Dp-brane in the presence of the Kalb–Ramond field B _μν , an internal U(1) gauge field A _α and a tachyon field, in the compact spacetime. According to this state, properties of the brane and a closed string, with mixed boundary conditions emitted from it, will be obtained. Using this boundary state, we calculate the interaction amplitude of two moving Dp ₁ and Dp ₂-branes with above background fields in a partially compact spacetime. They are parallel or perpendicular to each other. Properties of the interaction amplitude will be analyzed, and contribution of the massless states to the interaction will be extracted.     

On some Closed Magnetic Curves on a 3-torus

We consider two magnetic fields on the 3-torus obtained from two different contact forms on the Euclidean 3-space and we study when their corresponding normal magnetic curves are closed. We obtain periodicity conditions analogues to those for the closed geodesics on the torus.     

Wave Equations for Classical Two-Component Proca Fields in Curved Spacetimes with Torsionless Affinities

The world formulation of the full theory of classical Proca fields in generally relativistic spacetimes is reviewed. Subsequently, the entire set of field equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the fields allowed for. It appears that no interaction couplings between such fields and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in effect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca fields and wave functions for gravitons.     

Tri-Hamiltonian Toda Lattice and a Canonical Bracket for Closed Discrete Curves

Flows on (or variations of) discrete curves in give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierarchy. Here it is shown that the canonical symplectic structure on , which can be interpreted as the phase space of closed discrete curves in with length N, induces Poisson commutation relations on the above-mentioned subalgebra which yield the tri-Hamiltonian poisson structure of the Toda lattice hierarchy.     

Asymptotic Completeness in a Class of Massless Relativistic Quantum Field Theories

This paper presents the first examples of massless relativistic quantum field theories which are interacting and asymptotically complete. These two-dimensional theories are obtained by an application of a deformation procedure, introduced recently by Grosse and Lechner, to chiral conformal quantum field theories. The resulting models may not be strictly local, but they contain observables localized in spacelike wedges. It is shown that the scattering theory for waves in two dimensions, due to Buchholz, is still valid under these weaker assumptions. The concepts of interaction and asymptotic completeness, provided by this theory, are adopted in the present investigation.     

Transformation Laws for Decomposable World-Spin Affinities in a Class of Conformally Flat Spacetimes

A class of conformally flat spacetimes that admit certain decomposable world-spin affine patterns is considered. New coordinate-derivative relations are particularly utilized to demonstrate that the procedures involved in a well-known spinor translation of the corresponding Riemann and Ricci tensors bear world invariance. The establishment of this invariance property will presumably shed some light upon the overall spacetime situation taken up by the underlying works.     

Pattern Theorems,Ratio Limit Theorems and Gumbel Maximal Clusters for Random Fields

We study occurrences of patterns on clusters of size n in random fields on ℤ ^d . We prove that for a given pattern, there is a constant a>0 such that the probability that this pattern occurs at most na times on a cluster of size n is exponentially small. Moreover, for random fields obeying a certain Markov property, we show that the ratio between the numbers of occurrences of two distinct patterns on a cluster is concentrated around a constant value. This leads to an elegant and simple proof of the ratio limit theorem for these random fields, which states that the ratio of the probabilities that the cluster of the origin has sizes n+1 and n converges as n→∞. Implications for the maximal cluster in a finite box are discussed.