Can a Circulating Light Beam Produce a Time Machine

Abstract

In a recent paper, Mallett found a solution of the Einstein equations in which closed tiimelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of hght; moving in circular paths around an axis. Here we show that, for physically realistic energy densities, the CTC's occur at distances from the axis greater than the radius of the visible universe by an immense factor. We then show that Mallett's solution has a curvature singularity on the axis, even in the case where the intensity of the light vanishes. Thus it is not the solution one would get by starting with Minkowski space and establishing a cylinder of light.

Formation of closed timelike curves in a composite vacuum/dust asymptotically flat spacetime

“…Thus, Godel's rotating-dust cosmological model [1] violates conditions (i,ii), as does Tipler's rotating-string solution [2]; the wormhole model by Moris, Thorne and Yurtsever [3] violates condition (iii). Gott's solution [4] of two infinitely long cosmic strings violates condition (ii) [10], and Mallett's solution [8] violates condition (i) (see [11]). …”

Frame dragging with optical vortices

“…These calculations demonstrated a phenomenon known as inertial frame dragging. Of further interest, in a later controversial publication, Mallet found exact solutions of the Einstein field equations and showed that the exterior metric contained closed timelike curves (CTCs) [10,11]. These light-induced CTCs are conjectured by Mallett to be the foundation for a time machine.…”

Geodesics in the static Mallett spacetime

“…Rather, as shown in Ref. [2], the light rays travel along geodesics orbiting a central line singularity.…”

“…However, Ref. [2] argues that this means that the spacetime of Ref. [1] is unlike the spacetime one would get by introducing circulating light into a flat background.…”