Do black holes emit information?

For decades, physicists have theorized on this high-stakes question. At the heart of the so-called “black hole information paradox” is a fundamental incompatibility between the two pillar theories of theoretical physics: general relativity and quantum mechanics.

But in the past two years, a series of breakthrough calculations by researchers – including Tom Hartman, associate professor of physics in the College of Arts and Sciences – have led to proclamations in the field of theoretical physics that “the most famous paradox in physics,” according to Quanta Magazine, is nearing its end.

“It’s fair to say that these calculations have given us a new way to think about black hole information and given us hints about how to make sense of quantum gravity,” Hartman said, confirming the progress and his significant contribution. “It solves some corner of the paradox.”

Hartman researches quantum gravity, a theory to reconcile quantum mechanics and general relativity. His paper, “Replica Wormholes and the Entropy of Hawking Radiation,” published in May in the Journal of High Energy Physics, reports a mathematical technique for calculating the physics of a black hole. Collaborators on the paper included former Cornell postdoctoral researcher Edgar Shaghoulian, now a postdoc at the University of Pennsylvania; and Amir Tajdini, Ph.D. ’20, now a postdoc at the University of California, Santa Barbara.

“Black holes are a place where both quantum mechanics and gravity can be important at the same time,” Hartman said. “If you’re thinking about quantum gravity and how to put the two theories together, black holes are a great way to study that problem.”

Although we think of black holes as having nothing coming out from them, Hartman said, late physicist Stephen Hawking showed that when quantum effects are included, black holes do have a temperature.

This leads to the paradox: The fact that black holes have a temperature, Hartman said, means that particles are escaping the black hole. Hawking found that these particles are “pure thermal radiation,” or radiation that is completely random and does not carry any information, Hartman said. If this is true, then when a black hole evaporates away and disappears, the information that was originally contained in the black hole has been destroyed, he said.

“It is a fundamental principle of quantum mechanics that information cannot be destroyed,” Hartman said. “So the paradox is a contradiction between quantum mechanics and Hawking’s calculation showing that black holes radiate randomly.”

In the paper, Hartman and collaborators used a mathematical trick involving extra copies of the black hole called “replicas” to calculate the physics of a single black hole.

“It turns out that a powerful way to learn about one black hole is to study two black holes,” he said. “The reason is that there are statistical properties of radiation that are hard to understand if you look at one black hole but easier to understand if you look at two at once.”

Using this technique, they found evidence that the particles emitted in Hawking radiation are not random, after all.

In November, Hartman published further research in the Journal of High Energy Physics. In the paper, “Islands in Cosmology,” he and Shaghoulian, along with Yikun Jiang, a Ph.D. student in the field of physics, explore the possibility that the new theory of Hawking radiation could also apply to the early universe.

Hartman co-organized a virtual workshop on this and related topics in November with researchers from Stanford and the University of California, San Diego, joined by 40 participants from around the world.

Far from being near an end, the information paradox is a problem that multiplies as physicists look into it, Hartman said. What started as one paradox has grown into a whole field of study.

“There are many aspects of it,” he said. “It’s something thousands of people will work on for decades.”