Entropy evolution of moving mirrors and the information loss problem

TL;DR

The black hole information loss problem is examined through a two-dimensional moving-mirror toy model in a conformal field theory, using entanglement entropy as a diagnostic of unitarity. By computing the renormalized entanglement entropy $S(A|B)$ from mirror trajectories and linking it to the energy flux $F(t)$, the authors map three representative mirror histories to candidate resolutions: a final information burst, information carried by thermal Hawking radiation, and a long-lived remnant. They find that a sudden final burst cannot plausibly carry all information due to energy constraints, while a slowly stopping or a long propagating mirror can preserve unitarity either via radiation or via a remnant, respectively; however, they uncover an apparent tension between the entanglement-based picture and semiclassical radiation, hinting at firewall-like effects during deceleration. The work suggests potential tabletop plasma-mirror experiments to probe these ideas and highlights the need to measure or constrain entanglement-entropy dynamics in quantum field theories as a test of information-loss resolutions.

Abstract

We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semi-classical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semi-classical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semi-classical quantum field theory.

Figures (5)

• Figure 1: Left: the causal structure of a moving mirror. Right: if the mirror is partially reflective, then some information can be transmitted to the left boundary.
• Figure 2: Entropy-information flow for a mirror.
• Figure 3: $S(t)$ and $F(t)$ for three cases (black: $t_{\mathrm{f}}=15$, red dotted: $t_{\mathrm{f}}=20$, blue dashed: $t_{\mathrm{f}}=50$).
• Figure 4: Total amount of out-going energy after the Page time: $E = \int_{t_{\mathrm{P}}}^{t_{\mathrm{f}}} F(t) (1-\dot{x}) dt$ as a function of $t_{\mathrm{f}} - t_{\mathrm{P}}$ (fixing $t_{\mathrm{P}} = 10$).
• Figure 5: Left: the AMPS thought experiment for the original black hole version. Right: the AMPS thought experiment for the moving mirror.