Twin-paradox and Entanglement

TL;DR

This work analyzes a quantum version of the twin paradox using two Unruh-DeWitt detectors coupled to a scalar field, where one detector undergoes non-uniform acceleration while the other remains inertial. By constructing the reduced detector-density matrix and evaluating entanglement measures such as negativity and mutual information, the authors show that changes in acceleration direction imprint distinctive features on detector responses and inter-detector correlations. The study finds that entanglement can be degraded during acceleration but partially retrieved after acceleration ends, with the geodesic separation and lines of simultaneity playing a crucial role in shaping the correlations. These results illuminate how non-inertial motion affects quantum correlations and have potential implications for information processing in curved spacetimes and black hole contexts, including connections to entanglement harvesting and spacetime structure.

Abstract

We study the quantum version of the classical twin paradox in special relativity by replacing the twins with quantum detectors, and studying the transitions and entanglement induced by coupling them to a quantum field. We show that the \textit{changes} in direction of acceleration leave imprints on detector responses and entanglement, inducing novel features which might have relevance in black hole spacetimes.

Figures (6)

• Figure 1: In the above figure we have depicted the trajectories followed by the two twins Alice $(A)$ and Bob $(B)$. Initially both observers are separated by a spatial distance $X_0$. At time $T=0$, Alice undergoes a sequence of accelerated motions and at $T=T_{\star}$ returns to her inertial state at distance $x_0$ from Bob. The clocks of Alice and Bob are synced at $T=0$. The peculiarities of time dilation are highlighted in the structure of geodesics connecting instants of same values of proper times on the two trajectories. These geodesics turn from spacelike to timelike, becoming null in between; see Fig. \ref{['fig:Sigma2-sync']}.
• Figure 2: The geodesic separation syncing the clocks of the twins Alice $A$ and $B$, which is $\sigma^2_{A,B}(\tau,\tau)$ is plotted as the proper time $\tau$ progresses. One can notice that this quantity changes sign and becomes negative from positive as $\tau$ increases. Here $\mathcal{X}_{\text{A}}=X^{A}(\tau)$.
• Figure 3: Single detector transition probability rates $R_{A}(\omega)$ are plotted as functions of the detection time $\tau$. On the left, we have considered fixed $T_\star=16$, and on right we have considered $T_\star=20$. In both cases we have fixed $g=2$. From these plots one can observe that there are certain peaks and dips whenever the probe $A$ with non-uniform acceleration changes the direction of its acceleration.
• Figure 4: Negativity $\mathcal{N}$ at different times of simultaneity. The dashed curve indicate the geodesic interval along the lines of simultaneity - i.e it refers to the separation measured using geodesics connecting same values of proper time. The scaled energy gap, $\omega/\widetilde{T}$ is chosen as unity for all the plots.
• Figure 5: The non-local part of Negativity $\mathcal{N}^{+}$ that quantify the genuine entanglement at different times of simultaneity. The dashed curve indicate the geodesic interval along the times of simultaneity. The genuine entanglement retrieved is saturates before reaching the initial value of negativity. The solid horizontal line indicate the zero of the negativity. Counting from clockwise, all three except the second scenario, the geodesics interval changes from spacelike to timelike. The scaled energy gap, $\omega/\widetilde{T}$ is chosen as unity for all the plots.