November 30, 2023
The origins of the black hole information paradox

The origins of the black hole information paradox

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Artist’s impression of an ultramassive black hole (UBH). Credit: ESA/Hubble/DSS/Nick Risinger/N. Bartmann

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Artist’s impression of an ultramassive black hole (UBH). Credit: ESA/Hubble/DSS/Nick Risinger/N. Bartmann

Although physics tells us that information can neither be created nor destroyed (if information could be created or destroyed, then the entire raison d’être of physics, which is to predict future events or identify the causes of existing situations, would be impossible), does not require information to be accessible. For decades, physicists have assumed that information that falls into a black hole is still there, still existing, just hidden from view.

That’s fine, until the 1970s, when Stephen Hawking discovered the secret intricacies of the event horizon. It turns out that these shadowy beasts were not as simple as we were led to believe, and that the event horizons of black holes are one of the few places in the entire cosmos where gravity meets quantum mechanics in a manifest form.

The search for the unification of quantum mechanics and gravity dates back more than a century, shortly after the development of these two great domains of physics. What prevented their unification was a proliferation of infinities in mathematics. Whenever gravity became strong on small scales, our equations diverged to infinity and gave useless results. But here we are on the edge of black holes, which by definition are places of strong gravity. And since event horizons are mathematical constructs, not real surfaces of finite extent, to truly understand them we must examine them microscopically, which places them firmly in the quantum realm.

Strong gravity on small scales. While our math blows up, black holes certainly don’t. Something must marry gravity with quantum mechanics, some trick of mathematics or a feat of physical perception, and whatever accomplishes the task does so here, at the event horizon of every black hole in the universe.

Hawking, among others, embarked on a program in the 1970s to use black hole event horizons to poke and probe the combined nature of gravity and quantum mechanics under extreme conditions, hoping to discover some clue to their union. And although this program has not yet reached its full potential, Hawking discovered something absolutely extraordinary about black holes, as if they weren’t already extraordinary enough.

Credit: Universe Today

He discovered that black holes are not, strictly speaking, completely black. Through a bizarre interplay between the quantum nature of reality and the formation of event horizons when black holes are born, they are able to emit a small amount of radiation. To be perfectly clear, the amount of radiation coming from black holes is almost zero. A typical black hole with a mass a few times that of the Sun, for example, will emit around a single photon per year. So you’re unlikely to find a glowing black hole with your backyard telescope (and since the universe is literally on fire with radiation, black holes are, for now, consuming far more than they emit).

See how this radiation, now known as Hawking radiation after Stephen, affects the pristine picture of black holes painted by general relativity and the hairless theorem. Let’s pretend you build a black hole by compressing enough matter into a small enough volume for one to appear before you. The construction of this black hole consumed an enormous amount of information about all the particles that once enjoyed freedom, and all of that information is now stored safely behind the event horizon.

You then isolate a black hole from any source of growth: no matter, no radiation, no energy for it to feed on. The black hole emits Hawking radiation, spitting out one photon at a time. With each emission, the black hole loses a little mass (after all, there is no free lunch and someone has to pay the energy bill for this newly discovered radiation in the cosmos). Eventually, if you wait long enough, the black hole will evaporate completely, disappearing into a cloud of energetic emission.

A problem. This Hawking radiation is…unimpressive. In physics jargon we say that the emission is thermal, which is another way of saying that it does not contain unique information. You can sit in front of your homemade black hole and record the energies and momentum of each emitted particle of Hawking radiation until it collapses in on itself in 10100 years and you will learn absolutely nothing other than the stupid fact that the black hole is, in fact, evaporating at a certain temperature.

Here is the black hole information paradox, a paradox that has plagued theoretical physics for more than half a century, a paradox whose resolution lies in the uncharted lands of quantum gravity, a resolution that promises to give rise to a new understanding of physics: the information goes into a black hole. No information comes out. Hawking radiation evaporates the black hole. The black hole disappears. Information cannot be destroyed… so where did all the information go?

There must be a flaw in Hawking’s reasoning, because the universe does not support paradoxes. Political revolutions arise when two opposing groups are unable to reach a compromise: a paradox of interests and objectives. Scientific revolutions arise when two opposing facts cannot find a common thread: a paradox of reasoning and deduction.

I will be straight with you. As of this writing, we have no confirmed, agreed upon, tested, and reliable solution to the black hole information paradox. But we have a series of intriguing clues, mathematical crumbs that seem to be leading us somewhere, and the suggestive glint of something else on the horizon.

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