Hawking's Information Loss

1976Stephen HawkingFrontier7 primary sources, 6 established Reviewed October 17, 2026

Hawking's 1976 claim that black hole evaporation destroys information and limits what physics can predict.

Historical

Visualisation · Black Hole Information Paradox

Hawking radiation: A faint thermal glow predicted to leak from black holes, slowly draining their mass over time.
general relativity: Einstein's theory of gravity, in which mass and energy curve spacetime, and we experience that curvature as gravitational pull.
unitarity: The principle that total probability of all possible outcomes of a quantum measurement equals one. Quantum gravity proposals must preserve unitarity to remain consistent with quantum mechanics.
Page curve: The specific shape the entropy of Hawking radiation must trace over time if quantum mechanics is preserved during black hole evaporation. Don Page derived it in 1993; the 2019 replica wormhole calculations finally reproduced it from gravity.
anti-de Sitter space: A spacetime of constant negative curvature, the natural setting for the AdS/CFT correspondence. Distinct from our universe, which has positive cosmological constant (de Sitter), but the framework provides the cleanest testing ground for holographic ideas.

§1 · The claim, in one sentence

Hawking argued in 1976 that an evaporating black hole destroys the information about what fell in, which limits prediction beyond ordinary quantum uncertainty.

§2 · Why it might be true

In 1976 Hawking followed his own radiation result to its end. A black hole creates particles in pairs. One particle always falls in, and the other may escape to infinity as Hawking radiation. Part of the information about the original state goes down the hole with the infalling partners. Hawking concluded that the final state is a statistical mixture, a density matrix, and no longer a pure quantum state.

Burning a book turns its pages into smoke and heat, yet in principle the words could be read back from them. Hawking claimed a black hole keeps no such record. To an outside observer it is known only by its mass, angular momentum and charge. It emits every outcome compatible with those three numbers with equal probability, which he called a principle of ignorance.

If he was right, black hole formation and evaporation would have no S-matrix, the standard map from incoming to outgoing quantum states. Physics would then face a limit on prediction on top of ordinary quantum uncertainty. Hawking held this position for almost three decades, then argued in 2005 that information survives. Every other variant in this family proposes a way for it to survive.

The family stance

Most physicists now accept that information is preserved when matter falls into a black hole. Hawking conceded this point publicly in 2004, paying off a 1997 bet with John Preskill. The contested question is the mechanism. Black hole complementarity, ER=EPR, soft hair, and fuzzballs each propose different machinery for how information escapes; the firewall paradox is the argument that exposed why a naive resolution cannot work. The 2019 Page curve calculations using replica wormholes have shown that unitarity can be recovered within semiclassical gravity, but the question of what an infalling observer experiences at the horizon locally remains open.

§2.5 · Evidence

The argument uses only general relativity and quantum theory on a curved background, with no speculative new physics added
Unruh and Wald argued in 2017 that semiclassical reasoning still strongly suggests a pure state evolves into a mixed one during evaporation
Preskill's 1992 review found that every proposed way of getting the information back out had serious drawbacks at the time

§3 · What you'd need to test it

A black hole that forms and then evaporates completely turns a pure quantum state into a mixed one, so unitarity fails for the process as a whole
The outgoing radiation carries no record of what fell in beyond the black hole's mass, angular momentum and charge
No S-matrix exists for black hole formation and evaporation. A superscattering operator, which maps density matrices to density matrices, takes its place
The entropy of the radiation never turns back down as the black hole shrinks, so the radiation does not follow the Page curve
Gravitational collapse sets a limit on prediction that is fundamental and comes on top of quantum uncertainty

§4 · Where it breaks

Banks, Susskind and Peskin argued in 1984 that any evolution law of this kind violates either locality or energy-momentum conservation
Page estimated in 1993 that information may leak out so slowly at first that a calculation expanded in the ratio of Planck mass to black hole mass would miss it
Hawking argued in 2005 that information is preserved, using a Euclidean path-integral argument restricted to asymptotically anti-de Sitter spacetimes. It was not a microscopic account of how the information gets out
Penington derived the Page curve in 2019 within a semiclassical gravity calculation for an evaporating black hole in anti-de Sitter space. It shows how information can escape in that framework; it is a calculation, not an observation

Go deeper

Hawking framed the argument through the causal structure of general relativity. An interaction region can be bounded by an initial surface, a final surface, and a hidden surface about which the observer knows only mass, angular momentum and charge. His principle of ignorance says the hidden surface emits all compatible particle configurations with equal probability. He presented the resulting loss of predictability as analogous to the uncertainty principle, but additional to it.

In ordinary quantum mechanics an S-matrix maps pure initial states to pure final states. Hawking's superscattering operator acts on density matrices instead, so a pure initial state can end as a mixed final state. Banks, Susskind and Peskin studied general evolution equations for the density matrix of this kind. They argued that any such generalisation of the Schrödinger equation violates locality or energy-momentum conservation. Unruh and Wald's 2017 review sets out the case for information loss and analyses the counter-arguments.

Hawking's 2005 paper treats black hole formation and evaporation as a scattering problem with all measurements made at infinity. He argued this is well formulated only in asymptotically anti-de Sitter spacetimes. The Euclidean path integral over metrics with trivial topology is unitary and preserves information. Metrics with non-trivial topology give correlation functions that decay to zero, so only the unitary contribution survives at late times.

▸§5 · Who built it, and when(7 sources, 6 established, 1 needs verification)

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