What Is the Black Hole Information Paradox? Where It Stands Now

Throw a book into a fire and, in principle, the information in it survives: scrambled into smoke, ash and light, but recoverable if you could track every particle. Quantum mechanics insists on that kind of bookkeeping. Throw the same book into a black hole and, according to Stephen Hawking’s calculation, the hole eventually radiates away as featureless heat that seems to remember nothing. That clash is the black hole information paradox. Our Stephen Hawking sticker is here because his calculation started it.

Why should information be conserved at all?

In quantum mechanics, an isolated system evolves so that its future state determines its past state uniquely, a property called unitarity. Different starting states never end up as the identical final state. Practically, this means information can be scrambled beyond any hope of reading it, but never truly erased from the universe’s ledger. Most particle physicists treat this as a principle not to be given up lightly.

How did Hawking create the paradox?

Two results set it up. In 1973 Jacob Bekenstein argued that a black hole has an entropy proportional to the area of its event horizon (Bekenstein 1973^[1]). In 1974 Hawking showed that, once quantum effects near the horizon are included, a black hole should emit thermal radiation and slowly lose mass (Hawking 1974^[2]; Britannica^[3]). The temperature is T = ħc³ / (8πGMk_B), inversely proportional to the mass M; for a black hole of one solar mass that is only about 6 × 10⁻⁸ K, far colder than the cosmic microwave background.

Then the problem. Thermal radiation, in Hawking’s calculation, depends only on the hole’s mass, charge and spin, not on what fell in. Quanta Magazine’s George Musser gives the image: if a 100-kilogram astronaut falls in, the hole gains 100 kilograms; when it later emits the equivalent of 100 kilograms of radiation, nothing in that radiation reveals whether it came from an astronaut or a lump of lead (Quanta Magazine^[4]). In 1976 Hawking argued that gravitational collapse therefore produces a genuine “breakdown of predictability” (Hawking 1976^[5]): information is destroyed, and quantum mechanics must be modified.

An important caveat our house rules require: Hawking radiation has never been observed from a real astrophysical black hole. The predicted temperatures are far too low. Laboratory analogues, such as sound waves in a Bose–Einstein condensate, have produced signals with the predicted character (Steinhauer 2016^[6]), but analogues test the mathematics, not black holes themselves. Our explainer Do Black Holes Evaporate? covers that evidence in detail.

What is the Page curve?

In 1993 Don Page turned the argument into something calculable (Page 1993^[7]). Track the entanglement entropy of the radiation as the black hole evaporates. If information is lost, that entropy just keeps rising until the hole is gone. If information escapes, the entropy must rise at first, then turn over roughly halfway through the evaporation and fall back to zero, an inverted V now called the Page curve. As Quanta puts it, Page “transformed a debate into a calculation” and made the test explicit: follow the inverted V and information is preserved; fail to and it is destroyed or bottled up (Quanta^[4]).

What are firewalls?

In 2012 Ahmed Almheiri, Donald Marolf, Joseph Polchinski and James Sully sharpened the paradox. They argued that three reasonable statements cannot all be true: that Hawking radiation is in a pure quantum state (information preserved), that ordinary physics holds near the horizon, and that someone falling in notices nothing unusual at the horizon. Their “most conservative resolution” was that the infalling observer burns up at the horizon, a firewall (AMPS 2012^[8]). Few physicists liked the conclusion, which is exactly why the paper mattered.

Has the information paradox been solved?

Partly, and the honest status is open. In 2019, two groups of theorists showed that a semiclassical calculation of the radiation’s entropy, done with a newer rule that includes so-called islands, reproduces the Page curve. Geoff Penington’s paper derived the Page curve using entanglement-wedge reconstruction (Penington 2019^[9]), and follow-up work traced the result to “replica wormholes” in the gravitational path integral (Penington et al. 2019^[10]). Quanta reports that these calculations confirm the information gets out, but that the calculation “does not say how it is transferred, only that it is” (Quanta^[4]).

So the debate has shifted. Many theorists now think information is preserved. What is not settled:

• Mechanism. How, physically, the information is encoded in the radiation is not known. Penington himself is quoted saying that seeing the information come out would require learning about the microscopic theory of quantum gravity (Quanta^[4]).
• Scope. Much of the cleanest work uses simplified models and theoretical tools whose application to real, astrophysical black holes is still argued over.
• The interior. Whether an infalling observer meets smooth space or something drastic at the horizon remains contested in the wake of the firewall argument.

What black holes do show us, observationally

Real black holes are no longer hypothetical. The Event Horizon Telescope released the first image of a black hole, in the galaxy M87, in April 2019 (Event Horizon Telescope^[11]), and gravitational-wave detectors have heard black holes merge; NASA’s overview summarises what is known (NASA Science^[12]). None of these observations probes the information question directly. That remains a problem in theory, which is part of why it is so stubborn.

Wear the paradox

Our Photon Sphere hoodie draws the ring where light can orbit a black hole, and the Hawking sticker is the man who asked the question. More of the dark side lives in relativity and cosmos tees. For the myths that cluster around black holes, see Physics Myths Busted.

FAQ

What is the black hole information paradox, simply?

Quantum mechanics says information is never destroyed; Hawking’s calculation suggested an evaporating black hole leaves only featureless heat. Both cannot be fully right.

Has it been solved?

Not completely. 2019 calculations reproduced the Page curve, suggesting information escapes, but the mechanism and full scope are still open.

Has Hawking radiation been detected?

Not from any real black hole. Only laboratory analogues have shown related effects.

What is a firewall?

A proposed high-energy barrier at the horizon, put forward in 2012 as the most conservative way out of a sharpened version of the paradox. It remains controversial.

References

1. J. D. Bekenstein (1973), “Black Holes and Entropy,” Phys. Rev. D 7, 2333. https://doi.org/10.1103/PhysRevD.7.2333
2. S. W. Hawking (1974), “Black hole explosions?” Nature 248, 30. https://www.nature.com/articles/248030a0
3. Encyclopaedia Britannica, “Hawking radiation”. https://www.britannica.com/science/Hawking-radiation
4. George Musser, “The Most Famous Paradox in Physics Nears Its End,” Quanta Magazine (2020). https://www.quantamagazine.org/the-most-famous-paradox-in-physics-nears-its-end-20201029/
5. S. W. Hawking (1976), “Breakdown of predictability in gravitational collapse,” Phys. Rev. D 14, 2460. https://doi.org/10.1103/PhysRevD.14.2460
6. J. Steinhauer (2016), “Observation of quantum Hawking radiation and its entanglement in an analogue black hole,” Nat. Phys. 12, 959. https://www.nature.com/articles/nphys3863
7. D. N. Page (1993), “Information in black hole radiation,” Phys. Rev. Lett. 71, 3743. https://doi.org/10.1103/PhysRevLett.71.3743
8. Almheiri, Marolf, Polchinski & Sully (2012), “Black Holes: Complementarity or Firewalls?” arXiv:1207.3123. https://arxiv.org/abs/1207.3123
9. G. Penington (2019), “Entanglement Wedge Reconstruction and the Information Paradox,” arXiv:1905.08255. https://arxiv.org/abs/1905.08255
10. Penington, Shenker, Stanford & Yang (2019), “Replica wormholes and the black hole interior,” arXiv:1911.11977. https://arxiv.org/abs/1911.11977
11. Event Horizon Telescope, press release, 10 April 2019. https://eventhorizontelescope.org/press-release-april-10-2019-astronomers-capture-first-image-black-hole
12. NASA Science, “Black Holes”. https://science.nasa.gov/universe/black-holes/

Written by Pixelated Physics. Every factual claim is linked to the source we checked; points that are still debated are labelled open.