Once it has fully evaporated, does the swallowed information vanish, or come back? ── ℏ and G collide head-on

The Information Paradox & Quantum Gravity When a black hole evaporates completely, do the 10⁷⁷ bits of information vanish? Quantum mechanics says "they cannot vanish,"
while Hawking's original calculation said "they do." This collision is exactly the diagonal of the cube ── the heart of quantum gravity.

Everything in the series converges here. In Episode 2, the horizon holds \(10^{77}\) bits of information. In Episode 3, a black hole evaporates and, one day, disappears entirely. In Episode 4, information is scrambled on the surface at the fastest possible rate, and "should" trickle back out in the radiation. In Episode 5, the information is written on the surface. So then ── when the black hole has evaporated completely and vanished without a trace, what happens to the information it swallowed? The iron rule of quantum mechanics is that "information is never destroyed (unitarity)." Yet Hawking's 1974 calculation announced that "the radiation is perfectly thermal (random), and the information vanishes." This head-on conflict is the famous black hole information paradox. And it is the final corner of physics' "cube" ── the single point where ℏ (the quantum, unitarity) and G (gravity, Hawking's curved spacetime) collide head-on. It is the heart of quantum gravity.

01Once it has fully evaporated, where does the information go?

Drop a single book into a black hole. The Hawking radiation of Episode 3 is thermal ── random light fixed only by the temperature, which (apparently) carries no trace of whether the book you dropped was a novel or a dictionary. The black hole grows lighter as it radiates, and eventually evaporates completely and disappears. All that remains is featureless thermal radiation. The book's information is nowhere. But in quantum mechanics, every process is in principle reversible, and information changes form but is never destroyed (a pure state stays a pure state). Even a burned book could, in principle, be reconstructed if you measured the smoke and ash perfectly. If black holes alone were the exception and truly destroyed information, the foundation of quantum mechanics would collapse. This is the paradox.

02ℏ and G, in a head-on collision

This contradiction arises because Hawking's calculation was a semiclassical approximation (spacetime is a classical curved background, and only the quantum field on top of it is treated quantum-mechanically). Of \(c\), \(\hbar\), and \(G\), it held spacetime (\(G\)) fixed as classical while adding the quantum (\(\hbar\)) on top ── but the very regime where the fate of the information is at stake is precisely the one in which spacetime itself should also be treated quantum-mechanically. So resolving the paradox demands the diagonal of the cube ── full quantum gravity. Black holes are the "keyhole" through which we glimpse quantum gravity.

03The Page curve ── if information comes back, this is how it should look

Whether "information vanishes or comes back" can be decided by one sharp curve (Page, 1993). Track, over time, the entanglement entropy of the radiation (a measure of how much the emitted radiation is entangled with the black hole).

Which curve it traces ── that is the decisive fork between whether information vanishes or comes back.

04Try it ── the Page curve

The figure below. The horizontal axis is the evaporation progress (0 = freshly formed, 1 = fully evaporated); the vertical axis is the (entanglement) entropy of the radiation. Blue is the black hole's own entropy (area ∝ remaining mass², decreasing). The red dashed line is the radiation entropy of Hawking's calculation (monotonically increasing = information loss). Green is the unitary Page curve (rises, turns around at the Page time, and ends at 0 = information preserved). Move time with the slider and watch the black hole on the right shrink.

Hawking's red keeps increasing to the end, so entropy remains when the hole has fully evaporated = it means the information vanished (and, absurdly, along the way it exceeds the hole's own entropy (blue)). The green Page curve turns around at the Page time and returns to 0 = all the information came back. "Which one is right" was the great problem of a half-century.

05Recent progress, and the diagonal of the cube

In 2019–2020 there was major progress. Calculations that incorporated new contributions to the gravitational path integral ── islands and replica wormholes ── reproduced (in specific models) the radiation entropy actually tracing the Page curve and turning around. This strongly supports "information is preserved (unitary)," pointing toward quantum mechanics and gravity being consistent after all. Hawking himself, in his later years, had come around to thinking that information is not lost.

That said ── this remains the last corner of the cube, unreached by anyone. Even where the Page curve can be reproduced, debate continues over the real-space mechanism of "concretely how the information gets out," and much of it is set in special (low-dimensional, holographic) models. A complete theory of quantum gravity in our expanding universe does not yet exist. String theory and loop quantum gravity keep aiming for this diagonal. Black holes were the one window through which that uncharted corner could be glimpsed, in the dimensionless language of information.