Why The Black Hole Information Paradox Is Such A Problem
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You might think it takes a lot of energy to escape Earth’s gravity, but our planet’s pull is tiny compared to many other things in the Universe. Same for our Sun, the galaxy, or even an extreme object like a neutron star. Instead, imagine a small, compact region of space that’s filled with so much matter and energy that you’d have to move faster than the speed of light to escape its gravitational pull. That’s exactly what a black hole is: a region where gravity is so intense that nothing — not even light — can escape from it.
Image credit: NASA / JPL-Caltech.
Normally formed from the collapse of an ultra-massive star’s core, a black hole has such extreme properties that it inevitably collapses down to a singularity, where no known form of matter — even the fundamental particles — can stand up against it. Instead, the number of spatial dimensions is reduced to either a point a ring, and the known laws of physics break down.
The problem with black holes is with the information that goes into them. In the Universe as we understand it, there are certain properties of matter and energy that contain information. A particle like a proton or an electron contains not only a mass, an electric charge and a spin, but also other quantum properties like baryon number, lepton number, weak hypercharge, color charge, and quantum entanglements connecting one particle to another. If you form a black hole out of a whole host of particles (it normally takes some 10^58 of them), each with their own unique properties, including not just protons and electrons but also neutrons, photons, neutrinos, antineutrinos, positrons and more, you expect that information to meaningfully make its way into the black hole.
Credit: Illustration: NASA/CXC/M.Weiss; X-ray (top): NASA/CXC/MPE/S.Komossa et al. (L); Optical: ESO/MPE/S.Komossa (R).
But black holes have no memory of that. In fact, as far as we can tell, black holes are completelydescribed by only three properties: their mass (governed by the total amount of matter and energy that went into them), their electric charge, and their angular momentum (which describes their spin).
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So where did all that information go? A black hole made from the collapse of a normal star should, in theory, have wildly different information encoded in it than a black hole made from the collapse of (theoretically) an antimatter star, and yet that information is not encoded in a black hole! If I had two identical black holes, and added a bunch of neutrons to one while adding an equal mix of protons and electrons to the other until their masses were the same again, they should have different properties, as they should have different baryon (and lepton) numbers inside. Yet it’s known that no such difference exists. There’s no way to tell them apart.
Image credit: Dana Berry/NASA.
You might think the event horizon of the black hole will save you, since that special location — the border between where light can and cannot escape — appears “frozen” in the sense that anything falling into it will always remain as encoded information on the surface, a property discovered back in 1939. But in 1974, Stephen Hawking showed that was inadequate. On long enough timescales, the quantum nature of the Universe, and the fact that there are particle-antiparticle fluctuations occurring in the curved space at the event horizon, means that black holes will emit a thermal, blackbody radiation that eventually leads to their decay.
Image credit: E. Siegel, on the quantum origin of Hawking Radiation.
This is a huge problem for physics, because that type of quantum information that went into the black hole is supposed to be one of those quantities that’s fundamentally conserved. But what comes out of that black hole — that thermal, blackbody radiation — contains none of that extra information!
So that’s what the paradox is. How do we resolve it? The general consensus among physicists is that there must be some way that we don’t yet understand (perhaps requiring a quantum theory of gravity) that actually does encode the information “frozen” on the event horizon into the outgoing radiation. But does that happen? And if so, how does that happen? The answer is this: nobody knows. Stephen Hawking’s big announcement last week was at best a small step only towards that answer, and most likely is a dead-end of an idea, like most hypothetical ideas on this front.
Image credit: ESO/L. Calçada.
Whenever there’s a conflict between what our best theories predict:
- that there are certain quantities that must be conserved,
- and that the final state of a system contains different amounts of those conserved quantities than the initial state,
that’s an omen of scientific advance. That paradox is such a problem because it tells us that something about our present understanding is, in some way, incomplete. Is there a new law of physics? Is there a new application of the currently existing laws that we’ve missed? Are these quantities not fundamentally conserved after all? Is the information really encoded in the final state somehow? Will quantum gravity eventually make this all clear?
We hope to have the answer to this. But in the meantime, this paradox means we have a problem, and hence that we have more to learn. And for anyone curious about the scientific truths of the Universe, that’s an incredible thing: evidence that there’s still a whole lot more to be figured out.
Ethan Siegel is the writer and founder of Starts With A Bang, a NASA columnist and professor at Lewis & Clark College. Follow him on Twitter, Facebook, Google+, and support his Patreon.
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