Are Virtual Particles a New Layer of Reality? - Script (Patreon)

Let me tell you a story about virtual particles. It may or may not be true. Out there in the emptiest places in the universe, phantom particles appear and vanish again out of nowhere. They borrow the energy for their existence so briefly that they cheat the watchful eye of the universe. Near black holes, virtual matter and anti-matter pairs are separated by the event horizon to create Hawking radiation. And every time two particles interact, an infinite number of virtual particles mediate infinite versions that one interaction. Virtual particles sound pretty cool, I guess. But is this really how they work. Seriously, what ARE virtual particles?

Sometimes our mathematical hacks point to strange new aspects of reality. For example Max Planck used a quantization trick to figure out the spectrum of light emitted by hot objects. The quantization part of his math trick was meant to disappear in the final form of equation, but it remained - it proved fundamental. That math hack turned out to represent the very real quantum nature of the photon. This insight let to the discovery of all quantum physics.  A more recent mathematical hack is the virtual particle. They started out as a trick to make impossible calculations in quantum field theory possible. Possible, at least, for the sort of people who can do quantum field theory. So will virtual particles also prove to represent a new underlying aspect of reality? We’re going to go pretty deep in this one - but it will bring us to a better understanding of the quantum nature of reality, so stick with me.

First, let’s get to the origin of virtual particles. So quantum field theory is the machinery behind the standard model of particle physics. In it, particles are excitations in fundamental fields that exist everywhere in space. In particle interactions, packets of energy are exchanged between these fields. For example, two electrons – excitations in the electron field – will repel each other by exchanging energy through the electromagnetic field. That process is kind of a mess. Each electron jiggles the electromagnetic field, and those jiggles have a back-reaction that jiggles each electron, which in turn affects the way the electrons jiggle the EM field, ad infinitum. It’s a hopelessly tangled feedback cycle of reaction and back-reaction, and it’s impossible to calculate it perfectly. 

But it IS possible to approximate it ... in fact with astonishing accuracy. That’s where perturbation theory comes in. It’s our mathematical hack. The hack is to approximate this single, multilayered mess of an interaction by adding together a set of much simpler, idealized interactions. Those interactions are mediated by virtual particles. In that sense, virtual particles are the building blocks of our approximation of the behavior of quantum fields. 

Let’s do an example. In the case of the interacting electrons you start by saying each electron interacts once with the EM field, transferring between them energy, momentum, and one photon worth of quantum properties in a single packet that we call a virtual photon. Then you add the effects of doing this transfer in two, three, four packets,

as well as every other idealized field interaction you can imagine. 

Every one of these interactions is described with a simple excitation and transfer of particles – virtual particles. The hope is that, by adding together the contributions of enough of these, you can approximate the messy state of the field in the true interaction. 

We call these idealized interactions intermediate states or virtual states of the field, but in reality the field never exists in these states. The virtual particles never exist independently. Instead, virtual photons are the mathematical building blocks we use to approximate the complex states of interacting fields.

Maybe you recognize these things. Feynman diagrams. We’ve definitely talked about them before. Richard Feynman came up with them as a bookkeeping tool to keep track of which intermediate states are important in your calculation of an interaction and which you can ignore. Particles that either enter or leave these diagrams are the real particles, while those that both start and end within the diagram are virtual particles. Feynman diagrams are an absolutely essential tool in most modern quantum field theory calculations, but they also add to the misconception about virtual particles. They sure make it look like virtual particles are doing regular particle stuff, like traveling through space.

But that’s just not the case. Virtual particles share some properties with their real counterparts – in particular, quantum numbers like charge and spin – but they don’t need to obey Einstein’s relationship between energy, mass, and momentum. In fact they ignore a lot of the physics of real particles, they can have any mass, and can even travel faster than light and backwards in time. This isn’t because they’re magic – it’s because they aren’t physical. Virtual particles are our mathematical representation of the quantum mechanical behavior of fields. And that behavior is weird.

Here’s a really good illustration of this weirdness. In our first example we looked at two electrons repelling each other. One electron throws a virtual photon at the other one, causing them to be deflected from each other like a game of quantum dodgeball. But what about attractive forces? What about an electron and a positron? How can throwing photons between particles cause them to be drawn together? Let’s look at the Feynman diagram of a single virtual photon passing from electron to positron. To calculate the effect of this, you add together the possible effect of every possible virtual photon being emitted by the electron and absorbed by the positron. Bizarrely, that includes photons that are pointing in the wrong direction to even make the journey. Their momenta are pointing from positron to electron, rather than from electron to positron. You also count photons emitted by the positron but pointing away from the electron. These are the virtual photons that ultimately provide the attractive force. But how do they make the journey between the particles?

They don’t. There is no “journey” per se. These virtual particles sort of exist everywhere at once. Uh, what? Each one of these infinite possible virtual particles represents a quantum of energy in a single possible vibrational mode of the underlying quantum field. In a way, a virtual particle represents a pure excitation of the field – an idealized case of perfectly defined momentum.  Heisenberg uncertainty principle tells us that the perfectly defined momenta of virtual particles means completely undefined position. In contrast, real particles are mixed up combinations of many excitations – many different momentum modes, and that uncertain momentum gives them real locations, real trajectories through space.

Our virtual photon doesn’t have a location so it doesn’t travel a real path. It can move between our electron and positron even if its momentum is pointing in the wrong direction. It’s a bit like the photon starts out moving in the wrong direction and then quantum-tunnels between the particles, kicking them towards each other, like a teleporting boomerang. But even that description is way too physical. No individual virtual photon can be credited with producing the attractive force. In fact you only see that force in the sum of all possible virtual photons over all possible Feynman diagrams. Bizarrely, you also have to include the case where the electron and positron totally ignore each other to even see an attractive force. Did I mention quantum mechanics is weird?

So that’s the deal with the virtual particles in particle interactions. But we also hear about the role of virtual particles in a complete vacuum. You might have heard the quantum vacuum described as this roiling ocean of virtual particle-antiparticle pairs popping into and out of existence. So-called vacuum fluctuations or zero-point fluctuations. What’s the deal with that?

So the quantum fields are composed of these vibrational modes of all different frequencies-slash-momenta that can be excited to become particles. These modes also exist in a vacuum, just without the excitations. Each mode should have zero energy in a vacuum, but in quantum mechanics nothing can be so exact, thanks again to the Heisenberg uncertainty principle. In order to remain “uncertain”, there has to be a slight chance that, when you look at the vacuum, any given mode will have non-zero energy. This leads to a non-zero average energy called, confusingly, the zero-point energy. So there’s a chance that, when measured, the vacuum will appear to have energy, and so have particles. But the key word here is “measured”. Do those particles exist if you’re not looking? Or, more to the point, do vacuum fluctuations produce actual particles when there’s nothing else around?

The answer seems to be … no. At least, as far as you can answer such a question. In the math of QFT the perfect vacuum is a steady state. It doesn’t change over time – it has a constant zero-point energy. Regarding its particle content it remains in a steady state of uncertainty. Its quantum state is a superposition of “yep, particles” and “nope, no particles”. That quantum state is not fluctuating on its own, but it will randomly collapse into one of these possibilities when something interacts with the vacuum. This is a pretty subtle point, but it makes a huge difference in how we think about the vacuum. Virtual particles are NOT popping into and out of existence in the absence of anything else. Instead, they’re a fanciful way of talking about what might happen if something interacts with the vacuum.

The classic example of this is Hawking radiation. Stephen Hawking himself was the first to use virtual particles as an intuitive way to describe his radiation. He painted a picture of virtual matter-antimatter pairs being separated by the black hole event horizon, allowing one of the pair to escape to beautiful freedom and reality. But Hawking himself also cautioned against taking this picture too seriously. In his actual mathematical derivation he instead talks about vibrational modes of the quantum vacuum being cut off by the event horizon. This disturbance of the vacuum generates particles, but without the black hole the vacuum stays a vacuum. A similar perturbation of the quantum vacuum is also seen in the Casimir and Unruh effects. We also did episodes on these. And just like with Hawking radiation, you don’t need for virtual particles to have an independent existence to explain these effects.

So to recap: Virtual particles best thought of as are a mathematical device to used represent the behavior of quantum fields. The original idea of virtual particles came about as a calculation tool in perturbation theory as we tried to approximate the behavior of quantum fields. Now, in the case of Max Planck’s discovery of the quantum nature of photons, it turned out that a mathematical artifact represented new, real physics - the quantum nature of the photon in that case. Planck knew he was onto something because there was no way to express his Planck law without an artifact of that quantum nature - namely, the Planck constant. So, what about virtual particles. If they represent a physical reality, then there should be no way to do QFT calculations without them. 

It turns out there IS a version of quantum field theory that doesn’t use virtual particles at all. That would be the family of lattice field theories, in which spacetime itself is defined on a discrete grid. It doesn’t rely on perturbation theory and so it doesn’t use virtual particles at all, while ultimately giving the same results. Ergo, virtual particles are probably just a mathematical artifact. 

There’s no good reason to believe virtual particles exist outside the math we use to approximation the behavior of quantum fields. At best they can be interpreted as a small component of possibility space for a quantum field doing something real. That said, for something that doesn’t exist, they’re surprisingly useful for describing the weird underlying machinery of our quantum space time.