Nature of Nothing (Script) (Patreon)

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 of the surrounding city and a stream of exotic particles from the surrounding cosmos. But what if we suck out every last molecule of air, 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. This is impossible according to the Heisenberg uncertainty principle. Fix a particle’s position and its momentum – 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 set 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 the pesky Heisenberg uncertainty principle once again. We saw that it’s impossible to simultaneously fix position and momentum. 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 timescales, 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 covered 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 need to 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 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 the gluon - the carrier of the strong nuclear force - because gluons have mass. That means there’s a limit to how long virtual gluons can exist and travel, which in turn makes the strong nuclear force a very short-range force.

It can be argued that virtual particles are just a mathematical tool to describe the behavior of a dynamic vacuum; and that no such particles actually exist. Or that they are only the “quantum possibilities of particles”, which somehow govern the interactions of real particles without themselves being burdened with reality. Real or not, the calculations of QFT, which hinge entirely on these particles, are stunningly accurate. But how do we verify the existence of these elusive critters? They live in the interval between measurements of real particles; by definition they can only exist when we aren’t watching. But they nonetheless leave their ghostly mark on the universe.

The first hint of the existence of virtual particles came in 1947, when Willis Lamb and Robert Retherford noticed a tiny energy difference in the the two electron orbitals that comprise the second energy level of the hydrogen atom. According to the best existing theory of the time, those orbitals should have had exactly the same energy. The slight difference - now called the Lamb shift - inspired theorists to dig deeper. They didn’t take long; in the same year that the Lamb shift was first observed, German physicist Hans Bethe successfully explained it in terms of a fluctuating vacuum energy. Virtual particle-antiparticle pairs in the space between these orbitals and the nucleus align themselves with the electric field. This partially shields the orbiting electrons from the positive charge in the nucleus, with the amount of shielding being slightly different between these orbits. The calculation of the size of the Lamb shift is now one of the most accurate predictions in all of physics.

Another way to hunt for virtual particles is through their bulk effect on the vacuum. See, if quantum fields are abuzz with particles popping into and out of existence, then the so-called zero-point energy of those fields should not be zero. Completely empty space should contain some real energy – it should have vacuum energy. In 1948 the Dutch physicist Hendrick Casimir came up with a brilliant scheme to detect this. He imagined two conducting plates brought so close together that only certain virtual photons can exist between the plates; in the same way that an organ pipe or guitar string of a particular length only resonates with waves of certain frequencies. Any non-resonant virtual photon would be excluded, reducing the vacuum energy in that region. However, on the outer surface of the plates all frequencies of virtual photon are allowed. The higher vacuum energy outside compared to inside the plates should result in a pressure differential that pushes the plates together.

The Casimir effect was only successfully measured in 1996 by Steven Lamoreaux at the University of Washington, based on the initial ideas of his student Dev Sen. When separated by less than a micrometer, conducting surfaces were drawn together by a force that matched the predictions of quantum field theory. While there are potentially other explanations for the observed force, this is taken as strong evidence that vacuum energy is real. 

Neither the Casimir effect nor the Lamb shift allow measurement of the absolute strength of vacuum energy; they just measure its relative effect inside versus outside Casimir plates, or between electrons in neighboring orbits. So how much vacuum energy is there? There are two main ways to estimate this: one is through an observation, and the other is theoretical. The observation is the accelerating expansion of the universe. Dark energy itself may be vacuum energy. If so, then the amount of vacuum energy needed to produce the observed acceleration is tiny - around one-hundred-millionth of an erg per cubic centimeter. The theoretical calculation of the strength of the vacuum energy is a little higher than that. In fact it’s 120 orders of magnitude higher. This wild discrepancy between theory and observation is considered by some to be one of the greatest unsolved mysteries in physics. 

Quantum field theory, with its dependence on virtual particles and vacuum fluctuations is one of the most successful theories in all of science. And yet its prediction of the strength of vacuum energy seems to be wildly off. This is actually very exciting; it tells us that we don’t yet have the whole picture, and may provide a clue as to the next step we need to take. In an upcoming episode we’ll look deeper at this perplexingly mismatch between our theory and observation of the behavior of nothing, and what it might tell us about the underlying workings of space time.