Towards experimentally testing the paradox of black hole information loss

Information about the collapsed matter in a black hole will be lost if Hawking radiations are truly thermal. Recent studies discover that information can be transmitted from a black hole by Hawking radiations, due to their spectrum deviating from exact thermality when backreaction is considered. In this paper, we focus on the spectroscopic features of Hawking radiation from a Schwarzschild black hole, contrasting the differences between the nonthermal and thermal spectra. Of great interest, we find that the energy covariances of Hawking radiations for the thermal spectrum are exactly zero, while the energy covariances are nontrivial for the nonthermal spectrum. Consequently, the nonthermal spectrum can be distinguished from the thermal one by counting the energy covariances of successive emissions, which provides an avenue towards experimentally testing the long-standing “information loss paradox.”

Figure 1

The two spectra compared for a black hole at the Planck mass scale. The red solid (blue dashed) line refers to the nonthermal (thermal) spectrum.

Figure 2

The average emission energies compared, as in Fig. 1.

Figure 3

The average number of emissions compared for the two spectra as in Fig. 1.

Figure 4

The radiation energy variances compared for the two spectra as in Fig. 1.

Figure 5

The covariances of successive emissions are zero for the thermal spectrum; i.e., there is no correlation among Hawking radiations for the thermal spectrum. The “zero” noise feature is a result of numerical round-off error.

Figure 6

The covariances of successive emissions is nontrivial for the nonthermal spectrum. One can distinguish the nonthermal spectrum from the thermal one by counting the covariances. This provides an avenue towards experimentally testing the paradox.