Time-reversed information flow through a wormhole in scalar-tensor gravity

This Letter aims to advance unexplored properties of a new class of Closed Timelike Curves recently discovered in scalar-tensor gravity, reported in Universe 9, 467 (2023) and Eur.$\,$Phys.$\,$J.$\,$C 83, 626 (2023). Therein, it was shown that when the Weak Energy Condition is violated, the topology of spacetime in scalar-tensor gravity is altered, enabling the formation of two-way traversable wormholes. Furthermore, each of these wormholes acts a gateway between two $\textit{time-mirrored}$ worlds, where the two asymptotically flat sheets in the Kruskal-Szekeres diagram are glued antipodally along $\textit{three}$ directions -- time $t$ and the polar and azimuth angles $(\theta,\,\varphi)$ of the 2-sphere -- to form a wormhole throat. This contrasts with the standard embedding diagram which typically glues the sheets only along the $\theta$ and $\varphi$ directions. Crucially, due to the `gluing' along the $t$ direction, the wormhole becomes a portal connecting the two spacetime sheets with $\textit{opposite}$ physical time flows, enabling the emergence of closed timelike loops which straddle the throat. We shall point out that this portal $\textit{mathematically}$ permits the possibility of backward propagation of information $\textit{against}$ time. This feature is ubiquitous for wormholes in scalar-tensor theories. In addition, we formulate the Feynman sum for transition amplitudes of microscopic particles in the proximity of a wormhole throat in which we account for timelike paths that experience time reversal.