Where Physics Cannot Follow: Stephen Hawking’s Black Hole Paradox

A black hole, as many astronomy fans know, is a region of space so dense and heavy that not even light can escape. Typically created by collapsing stars, they operate as a sort of cosmic vacuum cleaner. Matter and energy are sucked up and lost forever behind the event horizon—the point at which escape is no longer possible—and join the infinitely-dense ball of matter at the black hole’s core. At that point, known to scientists as a “singularity,” the black hole gets a little bigger, its influence expands a little farther, and the universe continues on its merry way. No mystery involved. Anything that falls into a black hole is gone forever.

Sure, it might technically still exist—matter and energy, after all, cannot be created or destroyed—but only as one more digit of the black hole’s mass. A fifty-ton asteroid gets sucked up, the black hole gets fifty tons heavier, its gravity gets a tiny bit stronger, and its event horizon a little bit bigger. Details like “what was the asteroid made of?” or “where did it come from?” cease to matter. Since nothing can escape a black hole, it can no longer have any impact on the rest of the universe, and everything about the original mass can be forgotten.

But there’s an important caveat to that statement—“forgotten” isn’t the same thing as “gone.” The matter and energy that made up the asteroid might be part of the black hole now, but it still follows the same laws of physics as everything else in the universe. Astronomers might not be able to follow the chain of events any further—the equations of general relativity break down when used to probe what’s happening inside the event horizon—but that just means there’s a problem with those equations. The universe is fine.

For comparison purposes, imagine throwing a book into a fire. In a matter of moments, the combustion reaction will turn the pages into dust and ash; let it burn long enough and hot enough, and eventually nothing will be left but carbon dioxide and water vapor. Whatever was once written in the book is gone.

But imagine a super-powerful microscope, so strong it can track individual atoms as they dance their way through chemical reactions, and a platoon of nanobots capable of moving those same atoms around however you want. If your record of events are good enough, and your tools fine enough, there’s nothing to stop you from reversing each step of the combustion process and returning each particle to the place it started—recreating the book in the process.

This idea—that any physical process can be followed and reversed—is crucial to any attempt to understand the universe. The fact that every effect has a cause, that “every state has one arrow in and one arrow out,” says physicist Leonard Susskind, is “the most fundamental of all physical laws—the conservation of information.” 

The stuff inside a black hole isn’t exempt just because it’s hidden behind an event horizon. Einstein’s theory of relativity can no longer make sense of the conditions, but some laws of physics must still apply, and with a more holistic understanding of gravity it would still be possible to continue to track every particle and determine exactly where each winds up. Somewhere, somehow, the great pattern of cause and effect remains unbroken.

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So far, so good. Whatever falls into a black hole still exists in some sort of predictable state, even if current theory can’t describe it. Its mass isn’t destroyed, and neither is its information. For that to happen, the black hole itself would have to be utterly destroyed—not just broken up, but erased so thoroughly that nothing is left but noise, a signal so fundamentally random that not even an omniscient being could put the pieces back together again.

Enter Stephen Hawking.

In the 1970s, Stephen Hawking realized that black holes aren’t actually black. Instead, they emit a sullen glow of energy, the result of innumerable matter-antimatter interactions at its border. The very idea sounds paradoxical, but according to Hawking, that energy is actually a direct consequence of the black hole’s inescapability.

Space, he reasoned, is never truly empty. Energy of all sorts is constantly streaming through the universe, the most familiar being light and magnetism. This is true of the space around black holes, too, even inside their event horizon—the radius where their gravity becomes strong enough that not even light can escape. And where there’s energy, there’s action. According to Hawking, if you zoom in far enough, until concepts like “location” start to break down, you’ll see a constant froth of activity. At the quantum level, everything that can happen does happen, to some probabilistic extent.

One such possibility is the appearance of “virtual particles.” Every so often, a particle and its antimatter counterpart will appear seemingly out of nowhere. Energy converts to mass, enjoying an impossibly brief moment of existence before particle and antiparticle collide and annihilate one another, returning to their former existence as pure energy.

But, noted Hawking, imagine a pair of virtual particles appearing right at the edge of a black hole’s event horizon. It’s possible that one pops up just outside the horizon, and the other JUST inside. And it’s possible that the outside particle follows a path that takes it away from the black hole and its virtual counterpart, while the other remains trapped behind the event horizon. One lucky particle escapes into the universe at large; the other vanishes into the singularity, never to be seen again.

In other words, a particle appears out of nowhere, right at the edge of the event horizon, and flies off in a different direction. In honor of the man who first predicted their existence, these emissions are known as Hawking radiation.

The process is random as all get-out. The appearance of virtual particles isn’t governed by any property of the black hole—it’s just something that happens whenever energy exists. Which particle is captured and which goes free is pure, wild chance—matter and antimatter are affected by gravity in the same way. The exact makeup of the black hole doesn’t matter; Hawking radiation is about as random a process as it’s possible to imagine.

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There’s just one problem—mass and energy can’t be created or destroyed. So if black holes are giving off radiation—that is, energy—it has to come from somewhere. Just because the word “quantum” crops up a lot in the explanation doesn’t mean we get to ignore the conservation of energy. If that particle of Hawking radiation is going to enter the universe, the black hole is going to have to pay for it, and it has only one currency to offer—mass. Every time a virtual particle flies free, the black hole loses an equal amount of mass. But while black holes have infinite density, the same can’t be said for their mass. If it doesn’t keep absorbing new matter, it’ll eventually wither away to nothing, like an ice cube melting in the sun.

And as for the stuff inside—

Well, that’s the point where science draws a blank. Without a better understanding of gravity, we might never be able find an answer. Two fundamental laws of nature are at an impasse. If the stuff inside a black hole truly is gone without a trace, if there’s no record whatsoever about what happened to it, then it’s not just quantum physics that are wrong—something deeply strange is going on with time itself, and the laws of cause and effect can no longer be taken for granted. On the other hand, if information does escape a black hole, if there is some way to tell what’s been happening behind the event horizon, than general relativity—our understanding of the fundamental nature of space-time itself—has holes in it big enough to drive a truck through.

It’s been fifty years since Hawking discovered the issue, and physicists are still no closer to an answer. The black hole paradox, it seems, is just as hard to escape as a literal black hole.

References

Ouellette, Jennifer. “Why Stephen Hawking’s Black Hole Puzzle Keeps Puzzling.”  Quanta Magazine, March 14, 2018. ttps://www.quantamagazine.org/stephen-hawkings-black-hole-paradox-keeps-physicists-puzzled-20180314/

Ouellette, Jennifer. “Alice and Bob Meet the Wall of Fire.”  Quanta Magazine, December 21, 2012. https://www.quantamagazine.org/black-hole-firewalls-confound-theoretical-physicists-20121221/

Bawden, David. “Can Information be Conserved, and Why Would It Matter?”  The Occasional Informationist, June 1, 2018. ttps://theoccasionalinformationist.com/2018/06/01/can-information-be-conserved-and-why-would-it-matter/#:~:text=The%20conservation%20of%20information%20is,track%20of%20where%20you%20started.

Horgan, John. “Conservation of Ignorance: A New Law of Nature.” https://johnhorgan.org/cross-check/conservation-of-ignorance-a-new-law-of-nature