The Hidden Reality_ Parallel Universes and the Deep Laws of the Cosmos - Brian Greene [139]
Hawking Radiation
Because quantum mechanics plays no role in Einstein’s general relativity, Schwarzschild’s black hole solution is based purely in classical physics. But proper treatment of matter and radiation—of particles like photons, neutrinos, and electrons that can carry mass, energy, and entropy from one location to another—requires quantum physics. To fully assess the nature of black holes and understand how they interact with matter and radiation, we must update Schwarzschild’s work to include quantum considerations. This isn’t easy. Notwithstanding advances in string theory (as well as in other approaches we haven’t discussed, such as loop quantum gravity, twistors, and topos theory), we are still at an early stage in our attempt to meld quantum physics and general relativity. Back in the 1970s, there was still less theoretical basis for understanding how quantum mechanics would affect gravity.
Even so, a number of early researchers developed a partial union of quantum mechanics and general relativity by considering quantum fields (the quantum part) evolving in a fixed but curved spacetime environment (the general relativity part). As I pointed out in Chapter 4, a full union would, at the very least, consider not only the quantum jitters of fields within spacetime but the jitters of spacetime itself. To facilitate progress, the early work steadfastly avoided this complication. Hawking embraced the partial union and studied how quantum fields would behave in a very particular spacetime arena: that created by the presence of a black hole. What he found knocked physicists clear off their seats.
A well-known feature of quantum fields in ordinary, empty, uncurved spacetime is that their jitters allow pairs of particles, for instance an electron and its antiparticle the positron, to momentarily erupt out of the nothingness, live briefly, and then smash into each other, with mutual annihilation the result. This process, quantum pair production, has been intensively studied both theoretically and experimentally, and is thoroughly understood.
A novel characteristic of quantum pair production is that while one member of the pair has positive energy, the law of energy conservation dictates that the other must have an equal amount of negative energy—a concept that would be meaningless in a classical universe.* But the uncertainty principle provides a window of weirdness whereby negative-energy particles are allowed as long as they don’t overstay their welcome. If a particle exists only fleetingly, quantum uncertainty establishes that no experiment will have adequate time, even in principle, to determine the sign of its energy. This is the very reason why the particle pair is condemned by quantum laws to swift annihilation. So, over and over again, quantum jitters result in particle pairs being created and annihilated, created and annihilated, as the unavoidable rumbling of quantum uncertainty plays itself out in otherwise empty space.
Hawking reconsidered such ubiquitous quantum jitters not in the setting of empty space but near the event horizon of a black hole. He found that sometimes events look much as they ordinarily do. Pairs of particles are randomly created; they quickly find each other; they are destroyed. But every so often something new happens. If the particles are formed sufficiently close to the black hole’s edge, one can get sucked in while the other careens into space. In the absence of a black hole this never happens, because if the particles failed to annihilate each other then the one with negative energy would outlive the protective haze of quantum uncertainty. Hawking realized that the black hole’s radical twisting of space and time can cause particles that have negative energy, as determined by anyone outside the hole, to appear to have positive energy to any unfortunate observer inside the hole. In this way, a black hole provides the negative energy particles a safe haven, and so eliminates the need for a quantum cloak. The erupting particles can forgo mutual annihilation