An Introduction To The Famous Black Hole Information Paradox.

This article on the black hole information paradox is a guest article by Anja Sjöström, an IB diploma student from Switzerland.

The Information Paradox

Amongst the conundrums which arise when quantum mechanics and general relativity come to combine in an area where spacetime slowly comes to break down is a problem known as the black hole information paradox. Black holes are defined by a set boundary, the event horizon, beyond which the gravitational pull is so strong, nothing, not even light, is able to escape. However, even though any type of information which falls into a black hole is essentially irrecuperable, it is not destroyed nor erased. The said paradox, however, which arose as physicist Stephen Hawking proposed a theory stating black holes were able to emit radiation, came to assert that this radiation would be able to erase quantum information.

Black hole information paradox

Quantum information is what describes the state of matter in the universe, the position, velocity, and spin of atoms. It is what theoretically would accurately allow us to have knowledge of the past, present, and future state of the universe, and resolves the uncertainty in a said physical system. And the information paradox, which arose as physicist Stephen Hawking proposed a theory stating black holes were able to emit radiation, came to assert that this radiation would be able to erase quantum information, as the black hole containing it would essentially completely evaporate.

Such paradoxes often come to reshape our understanding of the universe, challenging our current models and opening doors towards discoveries. As such, scientists are hoping that an answer to the information paradox will come from a resolved unification in the theories which make up our understanding of everything. In short, the destruction of quantum information, in direct contradiction with important properties which act as foundation for most of modern science, would force us to rewrite some of the structure underpinning our perception and way of explaining the universe and its phenomena.

Conservation of Quantum Information

In the quantum world, information can neither be created nor can it be destroyed. The law known as the conservation of quantum information states that this information must be preserved forever in order to be able to flawlessly trace the universe backward and forward in time: causal determinism, the predictable unfolding of the universe, must be possible.


And although the information about an object fallen into a black hole is seemingly lost, the information still exists within the black hole but is simply not accessible anymore. Scientists either seem to argue that indeed information does fall into black holes while others claim it never passes the barrier of the event horizon and is encoded on its surfaces.

However, in both scenarios, the information is somehow reflected in the properties of the black hole, as every time a black hole ‘swallows’ an object, it grows large enough to conserve this information, to reflect it in its properties, should it be mass, spin, or electric charge. Thus, the laws of physics, and more specifically the law of conservation of quantum information, remain intact.

Hawking Radiation

The complication arose in 1974 when Stephen Hawking came up with his postulation of black hole radiation. According to his calculations and his thought experiments, Hawking claimed that black holes are slowly evaporating out of existence, a process which would irreversibly destroy the information contained within it, an assertion that deeply contradicts the previously mentioned law of conservation of quantum information.

In addition, a principle known as the no-hair theorem, a consequence of general relativity, states that two black holes with the same values in each of the three fundamental properties, spin, mass, and charge, are essentially the same black hole. These two black holes have ‘no-hair’: are indistinguishable from one another.

As such, for Hawking radiation to remain in line with this principle, the particles emitted from the black hole cannot contain any information from within the black hole, as each black hole does not have the same constituents. If this were the case, the radiation would be revealing the information which created the black hole, its ‘configuration’, essentially showing the black hole’s hair, a contradiction of the no-hair theorem. The seeming incompatibility between general relativity and quantum mechanics.

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As such, if these two theories are combined, that Hawking radiation exists but does not encode the information that is contained within black holes, when the black hole will have evaporated itself out of existence, information about it will have been erased, irreversibly lost, leaving no clue about what was in the black hole in the first place.

In addition, the temperature of Hawking radiation, what determines its properties, is said to be inversely proportional to the mass of the black hole, the mass being the only factor determining the nature of the radiation, once again supporting the paradox in which no information about the black hole’s ‘hair’ is encoded in its radiation. But a paradox can never stand on its own and as far as scientists’ capacities go, they are today working towards altering the observer’s perception of a black hole and the event horizon.

Read all the articles of the Basics of Astrophysics series here

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