Stephen Hawking and Jacob Bekenstein calculated the entropy of a black hole in the 1970s, but it took physicists until now to figure out the quantum effects that make the formula work.
We finally understand how black holes get their entropy. Physicists have been struggling to figure this out since the early 1970s, when Stephen Hawking and Jacob Bekenstein calculated how much entropy, or disorder, should be present in a black hole. Now, with a little help from quantum mechanics, researchers may have finally solved the problem.
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| An artist’s visualisation of a black hole varuna/Shutterstock |
“For a long time, people have thought that to solve this problem, you have to do all kinds of fancy things in string theory. But what we show is that there exists a set of states for which you don’t have to do that,” says Vijay Balasubramanian at the University of Pennsylvania. “It’s extraordinarily simple, unexpectedly so.”
The entropy in a black hole is related to exactly how many microscopic states fit inside it. Think of one of these cosmic behemoths like a cloud of gas – to calculate the amount of disorder in the gas, we have to know how many atoms or molecules it contains.
Balasubramanian and his colleagues modelled the microstates inside a black hole. Then they found a formula for counting all of these states, allowing them to calculate the black hole’s total entropy. The number of states inside a black hole the mass of the sun, for example, is about 27 followed by 1075 zeroes. For comparison, there are about 1080 atoms in the observable universe.
To visualise how they counted the microscopic states, picture each one as a tennis ball. “If you look inside the black hole, there’s plenty of area there, plenty of volume between the horizon and the singularity, so you can imagine putting a lot of tennis balls there,” says Balasubramanian. “But in fact, you end up putting in way too many tennis balls and overcount the entropy.”
That is because black holes are, at their hearts, quantum objects. For the tennis balls to actually represent the microscopic states within a black hole, they must also be quantum – and quantum states display exotic behaviours that regular ones do not. They create tiny tunnels in space-time and connect to one another via those “quantum wormholes”, which in simpler terms means that they overlap with one another.
Some of the quantum states can therefore be represented as combinations of other states, which makes them unnecessary to describing the entropy of the black hole. When the researchers accounted for these quantum effects, they found a number of states inside the black holes that matched the Bekenstein-Hawking formula.
“While the particular set of microstates described here are a bit artificial… the same basic mechanism should work for arbitrary microstates,” says Don Marolf at the University of California, Santa Barbara. “This is… a solid step in the right direction – an important stone to place on the path.”
Describing the states inside a black hole is important not only for calculating its entropy, but also for trying to solve a cosmic mystery called the black hole information paradox, which posits that, because information cannot be destroyed, a black hole must somehow preserve data about what fell into it.
“This demonstrates the existence of a space of states large enough so that you can preserve the information,” says Balasubramanian. “The question that remains is, how is that information read out when the black hole eventually evaporates?” His question relates to another one of Hawking’s famous equations – but that one remains unanswered for now.
Journal reference:
Physical Review Letters DOI: 10.1103/PhysRevLett.132.141501
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