The Nature of Nothing | Space Time

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We want to thank The Great Courses Plus for supporting PBS Digital Studios. This episode of Space Time is about nothing because it turns out that nothing is one of the most interesting somethings in all of physics.

How do we study nothing? An empty jar still contains something. Molecules of air and a bath of infrared light from its warm environment. There's also the ambient electromagnetic buzz from the surrounding city and a stream of exotic particles from the surrounding cosmos. But what if we suck out every last molecule of air and chill the jar to absolute zero and shield it from all external radiation? The jar would contain only empty space. But it turns out that empty space is far from nothing. In our last episode we talked about the nature of absolute cold. We saw that it's actually impossible to reduce any substance to absolute zero in temperature. Zero Kelvin means no motion whatsoever in a substance's constituent particles. But that perfect stillness implies that a particle's position and momentum are simultaneously perfectly defined. And this is impossible according to the Heisenberg Uncertainty Principle. Fix a particle's position and its momentum, and so its motion, becomes a quantum blur of many possible momenta. This results in a real minimum average kinetic energy called a zero-point energy. So, the walls of our empty jar will always radiate a faint heat glow.

But hypothetically, what would perfectly empty space look like, far from the nearest particle of matter or radiation? The answer will bring us closer to understanding the nature of space itself.

Our modern understanding of the quantum nature of space is described by quantum field theory. We've talked about QFT a lot recently, but for a refresher, this episode is especially useful. In short, space itself is comprised of fundamental quantum fields, one for each elementary particle. Those fields oscillate, vibrate with different energies, and those oscillations are the electrons, quarks, neutrinos, photons, gluons, etc. that comprise the stuff of our universe. Now, these fields are quantum fields, which means their oscillations can't just have any old energy. They can only be excited in quantized chunks, integer multiples of some baseline energy. In each quantum state, so each combination of particle properties, there's a ladder of energy levels, a bit like electron orbitals in an atom. Each new rung of the ladder represents the existence of one additional particle in that quantum state. In fact, the math of quantum field theory is all about going up and down this particle ladder using so-called creation and annihilation operators. We'll come back to those when we talk about Hawking radiation in the future.

The bottom of this energy ladder corresponds to these quantum oscillators having no energy, which means there are no particles in the given quantum state. We call this the vacuum state of the field. Inside a perfect vacuum, all of the fields at all locations should be in the vacuum state. Exactly zero energy at all times.

But here we run up against that pesky Heisenberg uncertainty principle once again. We saw that it's impossible to simultaneously fix position and momentum. Well, it's also impossible to simultaneously perfectly define time and energy. The more tightly we try to define the time window for the behavior of a quantum oscillator, the less certain we can be of its energy state in that time window.

On extremely short time scales, a quantum field exists as a blur of many energy states. In a vacuum, the most likely state in that blur is the zero energy vacuum state. But sometimes the field finds itself with enough energy to create a particle, seemingly out of nothing.

We call these virtual particles. And they seem to be the machinery under the hood of all particle interactions in the universe, at least as described by quantum field theory. For example, QFT describes the electromagnetic force as the exchange of virtual photons between charged particles. Virtual particles are the links governing all particle interactions in the famous Feynman diagrams. But to properly calculate an interaction of real particles, every imaginable behavior of the connecting virtual particles must be accounted for. This includes seemingly impossible behavior. For example, in QFT, virtual particles can have any mass and any speed, including speeds faster than light, and can even travel backwards in time. We cover that little gem of weirdness in this episode. The ambiguous realness of virtual particles seems to grant them some surreal freedoms. But there are restrictions. For example, quantum conservation laws must be obeyed. So most virtual particles are created in particle-antiparticle pairs. But the ultimate price is that virtual particles can exist only for the instant allowed by the Heisenberg uncertainty principle. And the higher the energy of the particle, the less time it can exist. This restriction defines the range of the fundamental forces. For example, the massless photon can have the tiniest of possible energies. And so virtual photons can exist for any amount of time, long enough to carry the electromagnetic force to any distance. On the other hand, it always takes a baseline chunk of energy to create a gluon, the carrier of the strong nuclear force, because gluons have mass.