From my last two blog posts on Hawking radiation and the conservation of quantum information, it’s clear that we have a major problem on our hands—the information paradox. We know that black holes decay over unimaginable timescales, seemingly erasing quantum information in the process. But we also know that quantum information has to be conserved. Theoretically, at least, we have to be able to trace particles back through their quantum histories. If black holes were entirely stable, then we could consider this condition met. While the information in a black hole would be inaccessible, it wouldn’t be destroyed. But if black holes do decay into random radiation, then what does that mean for our conservation of information? Is there a way to solve this information paradox, or must we assume that, eventually, black holes will erase the universe completely?
In the 1970s, Stephen Hawking discovered that black holes, entities of infinite density that exert gravitational pulls so strong that not even light can escape, actually leak out radiation. This radiation, called Hawking radiation, arises from a strange marriage of quantum field theory and general relativity. Historically, it has been impossible to reconcile quantum field theory with general relativity—they each seem to govern the universe from their own narrow perspectives. Quantum field theory describes the universe at the smallest of scales, predicting how atomic structure forms and changes. General relativity describes the universe on cosmic scales, predicting how gravitational forces bend the fabric of spacetime. Both of these theories are extremely accurate within their individual scales, but they don’t play well together.
Because no unified “theory of everything” exists, Stephen Hawking had to hack quantum field theory and general relativity to make the calculations that proved Hawking radiation. He did this by calculating what would happen to quantum fields at the instant a black hole formed—essentially a boundary where the perspectives of quantum field theory and general relativity overlap. His calculations demonstrated that black holes radiate “virtual particles” derived from random quantum fluctuations around the event horizon. These random fluctuations take the form of thermal radiation, meaning that black holes have a temperature that is proportional to their mass, or the surface area of their event horizons. But black holes radiate away their masses very slowly, so their temperatures at any given moment are just barely above absolute zero. For example, the black hole at the center of the Milky Way galaxy, Sagittarius A*, has a mass equivalent to about 4 million solar masses which gives it a Hawking temperature of 0.000000000000015 Kelvin (1.5 x 10-14 K).
Hawking’s calculations demonstrate that black holes radiate away their mass extremely slowly, over inconceivable scales of time. As this happens, the event horizon shrinks imperceptibly until the black hole completely evaporates. This may easier to visualize than you think. Imagine a normal party balloon filled with air and tied off at the stem. As long as there is no puncture in the balloon’s surface, the balloon should not visibly deflate. But over days and weeks, the balloon does deflate. Particles of air slowly escape through the balloon’s molecularly porous surface. This happens too slowly for you to perceive any noticeable leak. Instead, you probably notice that the balloon appears smaller each day. The previously stretched surface of the balloon slackens and gradually contracts. The overall surface area of the balloon decreases until it is completely deflated.
Similarly, over a much longer time span, black holes leak imperceptible amounts of their masses through Hawking radiation, causing their surface areas to contract (the surface area of a black hole’s event horizon is directly tied to its mass just like a balloon’s surface area is tied to the mass of air it contains). A black hole can also gain mass, and surface area, by swallowing the mass of other objects that cross its event horizon. Based on the Schwarzschild radius formula, an object the mass of the earth (roughly 6 x 1024 kg) would add 8.9 mm to the radius of a black hole (ignoring that some of this mass gets converted to energy in the extremely hot accretion disk). This would translate to a 995 square-mm increase in surface area. For comparison, the surface area of a standard ping pong ball (radius=18.8 mm) is 4,440 square-mm.
Black holes that wander into dense regions of space, may find lots of stars, gas, and planets to snack on (if these objects happen to wander too close or if they lose the speed needed for a stable orbit of the black hole). These objects that travel beyond the event horizon contribute their masses and a small amount of surface area. In turn, the surface area, and corresponding mass, of the black hole are eventually lost through Hawking radiation. Information goes into the black hole, gets fairly extensively compressed, and then is radiated away as seemingly senseless thermal radiation. Solving the information paradox requires that the information persists in some way. As it turns out, the solution may have something to do with the black hole’s surface area.
As we saw above, an object that falls into a black hole adds a small amount of surface area to the black hole’s event horizon. And, as we saw during our journey into a black hole, objects that fall into a black hole don’t actually appear to fall in, from an outsider perspective. Instead, an object falling towards the black hole freezes at the event horizon, perfectly smeared on its surface, and then becomes dimmer and dimmer until it is no longer visible. These two properties of objects falling into black holes led physicists to speculate that the quantum information from these objects might actually be printed on the event horizon where it could be released back into the universe with the Hawking radiation. This is a complicated set of theories that I will more thoroughly explain in next week’s blog. But if these theories do hold up and they resolve the information paradox, then they could also indicate that the entire universe is actually. . . a hologram.
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