Entropy evolution of moving mirrors and the information loss problem

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 semiclassical 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 semiclassical 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 semiclassical quantum field theory.

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.