Hawking Radiation

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I get so many headaches every month.

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Matt O'Dowd (1:33)

He was perhaps the greatest genius of our time. Stephen Hawking peered behind the curtain of reality and glimpsed the true workings of the universe. He inspired all of us to pursue our curiosity, no matter the obstacles. However, his true legacy is his work. He made profound contributions across physics, from quantum theory to cosmology. Our tribute is to bring you Stephen Hawking's most famous discovery. I'm Matt O'Dowd. This is Space Time, and it's time for Hawking Radiation.

Soon after Einstein revealed his great general theory of relativity in 1915, physicists realized that it allowed for the possibility of catastrophic gravitational collapse in places of extreme density, like the dead core of a massive star. Space and time could be dragged inwards to create a hole in the universe, a boundary in Space Time called an event horizon, that could be entered but from beyond which nothing could return.

Once formed, there was nothing in theory or imagination that could bring material consumed back to the outside universe. These black holes should exist forever, only growing, never shrinking. Or so we thought until 1974 when a young physicist named Stephen Hawking published a paper in Nature entitled Black Hole Explosions.

In this and in a follow up 1975 paper, he attempted a new union of quantum mechanics and general relativity to show that black holes should not be so black after all. They should leak. They should emit what we now know as Hawking radiation. There's a popular description of how Hawking radiation works. It goes something like this. Empty space seethes with activity as pairs of virtual particles, matter and antimatter, spontaneously appear and then annihilate each other, briefly borrowing energy from the vacuum itself.

But when this happens near a black hole, sometimes one of the pair will be swallowed by the event horizon, leaving the other free to escape and taking its stolen energy with it.

That energy can't come from nothing, and so the black hole itself pays the debt by slowly leaking away its mass. This is a nice picture, but how accurate is it? In fact, if we follow the narrative of Hawking's original calculation, the story sounds rather different. We've come a long way over the past few months, building up the knowledge we'll need to follow that calculation. Rewatching some of those episodes either now or after this video will be helpful.

But if you think you're ready, let's take a deep dive into the quantum field theory of curved spacetime to glimpse the true nature of Hawking radiation. Actually, a quick QFT refresher can't hurt. Space is filled with quantum fields. They can oscillate with different frequencies, much like the many possible vibrational modes on a guitar string. A particle is like a note on the string. And just like a real guitar note, real particles tend to be comprised of many vibrational modes. Those underlying vibrational modes are still present in the absence of real particles, they fluctuate in energy due to quantum uncertainty, and those fluctuations give us what we think of as virtual particles. Now, don't take the existence of virtual particles too seriously. They're really just a tool for calculating the infinite ways in which a fluctuating quantum field can behave. One way that quantum fields are very different to guitar strings is that they can have both positive and negative frequencies. A negative frequency can be thought of as a mode that travels backwards in time, and can be interpreted as corresponding to antimatter. Now, that's a whole level of weird all on its own, and we talk about it here. When a quantum field is in a vacuum state, there's a balance between positive and negative frequency modes, which you can crudely think of as a balance between Chronic migraine is 15 or more headache days a month, each lasting four hours or more.