Last June, Boston University professor Gregg Jaeger travelled to Växjö, Sweden for a conference. It was the twentieth time that philosophers had gathered there to discuss questions that strike at the foundations of physics. Jaeger had been invited to give the opening talk, to speak about mysterious and sometimes controversial entities called “virtual particles."

Whereas matter had long since been recognized to be made up of particles, the existence of virtual particles had been debated by philosophers of physics for at least thirty years. Mostly, they leaned towards their dismissal, but Jaeger is a believer.

Like ordinary particles, virtual particles come up incessantly in physicists’ work, in their theories, papers, and talks. But as their name suggests, they are far stranger than ordinary particles, which are already notoriously odd. Particles are the chief representatives of the world of the small, the quantum world. If you scaled everything up so that a particle was the size of a sand grain, you would be as tall as the distance from Earth to the Sun.

Physicists know from experience that particles are undoubtedly there, beyond sight. Virtual particles are much more elusive, to the point that the non-believers say they only exist in abstract math formulas. What does it even mean for “virtual” particles to be real?

## What is a virtual particle?

Jaeger is a physicist-turned-philosopher, who published important quantitative results early in his career before spending the last ten years focused on the philosophy and interpretation of physics. He arrived at virtual particles as only the latest stop in a long journey of making sense of the quantum world.

There are two distinct narratives for virtual particles, and Jaeger subscribes to what philosophers call the realist position. Believers or realists argue that virtual particles are real entities that definitively exist.

In the realist narrative, virtual particles pop up when observable particles get close together. They are emitted from one particle and absorbed by another, but they disappear before they can be measured. They transfer force between ordinary particles, giving them motion and life. For every different type of elementary particle (quark, photon, electron, etc.), there are also virtual quarks, virtual photons, and so on.

A useful analogy to the realist narrative of virtual particles is to imagine going to a big family reunion, full of cousins, parents, grandparents, and others. Each group of relatives represents some different type of particle, so for example, you and your siblings might all represent electrons, and your cousins might all represent photons. At this reunion, everyone happens to be a little stand-offish, mostly tucked away out of sight. When you see your sister, you walk up to shake hands, but when you look at her hand and go to grasp it, you find that your cousin has stuck his hairy hand in. He quickly shakes your hand and then your sister’s. But when you look up, he’s somehow disappeared, and your sister is walking away. Your cousin, the virtual photon, has just mediated the interaction between the two electrons of you and your sister.

Other philosophers have mainly upheld an opposing narrative, where virtual particles are * not* real and show up only in the mathematical theories and equations of quantum physics, which describe the particle world. The equations are correct, the doubters recognize, predicting all sorts of things like the peculiar magnetic properties of electrons and muons, for example.

But the entities called virtual particles are just parts of the math, these experts claim. Virtual particles have never been and cannot be directly observed, by their mathematical definition. They supposedly pop up only during fleeting particle interactions. And if they are real then they would possess seemingly unacceptable properties, like masses with values that can be squared (multiplied by themselves) to give negative numbers. They would be entirely out of the ordinary.

That physicists still claim these things to be real has haunted philosophers. Philosophers of physics, often highly trained physicists themselves, demand a story of reality that makes sense—at least, as much as possible. Can the realist narrative really be true? Do bizarre things called virtual particles pop up and mediate all the interactions between observable particles?

## Virtual particles in physics

As Jaeger explains, there are at least four different overarching mathematical theories of the quantum world. The most basic of these is called quantum mechanics. Virtual particles originate from a more advanced mathematical apparatus known as quantum field theory (QFT). If quantum mechanics is like the children’s book * Clifford the Big Red Dog*, then QFT is the Necronomicon, bound in skin—far more arcane and complex.

Physicists use quantum mechanics to explain the most fundamental quantum phenomena, like the simultaneous wave and particle nature of light. QFT on the other hand is used for predicting the results of extreme experiments at places like the Large Hadron Collider (LHC). QFT does the heavy lifting, in other words.

The LHC is famous for its scattering experiments, where two or more particles are collided together and “scatter” off one another. During the collision, old particles are destroyed and new ones created. Physicists perform collisions over and over again in highly controlled circumstances and try to predict what particles come out and how. Recalling the metaphor of a family reunion, scattering experiments tell the story of how likely it is that your sister walks out from the handshake, and not some other relative—an odd and yet distinct possibility.

In QFT, the probability of what particle comes out is decided by a complicated equation. Physicists solve it with a clever trick. They write out the solution as a sum of much simpler terms (summands), which is then squared. Technically, the sum contains infinitely many terms, but for many scenarios only the first few terms matter. Each of the terms in the sum contains physical quantities related to the incoming and outgoing particles, like their momentum, mass, and charge, all of which can be directly observed. However, each term can also contain physical quantities (like mass or charge) that correspond to entirely different particles, which are never observed. These are what are known as the virtual particles.

Before the LHC existed, in the 1940s, the renowned physicist Richard Feynman introduced a diagrammatic technique that made the role of the virtual particles clear. For each term in the sum for the QFT calculation, a so-called Feynman diagram can be drawn that depicts the incoming and outgoing particles. Virtual particles are drawn popping up in the center. These diagrams greatly aid in doing the complicated calculations. For every line in a diagram, for example, a physicist simply sticks another variable in their solution.

Feynman diagrams can seem to provide a temptingly accurate picture of what goes on in an experiment. However, for any experiment, there are actually infinitely many different Feynman diagrams, one for each term in the sum. This poses an interpretive problem because it seems incoherent. The theory suggests that anytime particle relatives shake hands at the family reunion, every other relative (an infinite number of them!) also stick theirs hands in.

One of Feynman’s well-known contemporaries, Freeman Dyson, addressed this problem by making it clear that Feynman diagrams did not show a literal picture of reality. They were only supposed to be used as an aid to doing the math. On the other hand, Feynman sometimes suggested that the pictures actually * were* representative of reality.

But regardless of their interpretation, the diagrammatic technique caught on. And the virtual particles in the diagrams and the mathematics became objects of constant reference for physicists—even though the math was only meant to predict the outcomes of scattering experiments. The process of particles colliding into each other, which one would naively expect to be about forces and energy, turned out to be about virtual particles.

“The fundamental thing that makes you know that the physical world is there is forces. Like you bang into things, right?” Jaeger said, hitting his hand on the desk in his office. “Ow! So that’s something there. There's a world out there that's transmitted by a force. But when you try to [mathematically] understand this process of transmission, from the point of view of what’s out there, and what’s its structure, you end up with these virtual particles.”

Many physicists who focus on quantitative results believe in a reality * filled* with virtual particles because QFT performs astoundingly well, predicting the outcomes of countless experiments. And QFT is rampant with virtual particles.

“I have no problem at all with the fact that these virtual particles are real things that determine the forces in nature (except for gravity),” said Lee Roberts, an experimental physicist and professor at Boston University, located only two blocks down from Gregg Jaeger’s office.

Roberts helps lead current efforts to measure the magnetic properties of muon particles with greater precision than ever before at Fermilab’s Muon g-2 experiment. And whatever the questions may be around the existence of virtual particles, physicists like Roberts can hardly interpret the properties of muons without them.

Muons are like heavy electrons, carrying negative electric charge and a quantum property called spin. Roughly speaking, the muon’s spin can be thought of like the actual spin of a tiny rotating top. The rotation of the muon’s intrinsic charge produces a small magnetic field, called its magnetic moment.

Because it acts like a tiny magnet, the muon interacts with other electromagnetic fields, which are represented in the particle world by photons. To calculate the interaction, physicists use a similar process as for scattering experiments, writing the solution as an infinite sum. The terms in the sum are represented by nothing other than Feynman diagrams, where one muon particle and one photon flies in, and one single muon flies out. Virtual particles are drawn in the center —hairy relatives, sticking their hands in.

All these interactions sum up to give the muon an “anomalous” magnetic moment, anomalous compared to the results of theories that came before QFT. But * with* QFT, physicists have predicted the magnetic moment almost exactly, like marking off the lines on a football pitch blindfolded and getting them accurate to the width of a hair. The accuracy of these calculations relies indispensably on the virtual particles.

With QFT being so accurate, it is clear that there * must *be some kind of reality to it. Perhaps the question then is not so much whether virtual particles are real, but what exactly the general picture of reality is, according to QFT.

## Virtual particles and the nature of reality

Oliver Passon is one of the physicist-philosophers who object to the notion that virtual particles are real. He earned his Ph.D. in particle physics and is a highly experienced physicist, but now focuses on education research at the University of Wuppertal in North Rhine-Westphalia, Germany. He studies how particle physics should be taught to high-school students, for whom it has become part of the standard curriculum.

“Virtual particles are a mess,” Passon summarized for Motherboard.

For Passon, the realist view arises from a sloppy interpretation of the math, and it has led physicists to make other interpretive mistakes, for example, in explaining the discovery of the Higgs boson at the LHC. He wrote about his views in a paper last year.

Passon’s objections can be explained in the context of the famous quantum mechanics test-case known as the double-slit or two-slit experiment. In a two-slit experiment, physicists fire particles such as photons one at a time at a wall with two tiny slits. The probability of where exactly a particle lands on the other side of the wall is related to the square of a sum, similarly as in a scattering calculation from QFT. But in this case there are only two terms in the sum, each reflecting the narrative of the particle passing through only one of the slits. Which slit does the particle pass through? Quantum mechanics cannot say, because the mathematics requires the term that represents each possibility to be summed with the other and squared.

“The question whether one or the other thing happens makes no sense. It’s not a tough question—it’s not even reasonable to ask,” Passon said. “This is what I take to be the key message of all of quantum mechanics.”

The two-slit experiment seems to show that individual mathematical terms by themselves have no realism, and only their superposition (summation and squaring) have meaning. Thus, in Passon’s view, virtual particles that show up in individual QFT terms should not be considered real. This argument against virtual particles is known to philosophers as the superposition argument, and it can seem like a strong one.

But Jaeger thinks the argument is besides the point. Ironically, he sees this critique as being stuck in mathematical abstractions itself. He agrees that the individual terms cannot tell the whole story, "but it doesn’t mean the particle didn’t go through space,” he said.

The mathematics may not tell which slit the particle passes through, but it doesn’t mean that the mathematics is wrong. The mathematics still correctly predicts the passage of a particle through intervening space, and the probability of where it eventually lands. And in QFT, the mathematics indisputably relies on the presence of virtual particles.

Interestingly, quantum field theory actually says matter is fundamentally made up of fields rather than particles, let alone virtual particles. For every elementary particle, such as a photon, QFT says there is a fundamental field (such as a photon field) existing in space, overlapping with all of the other particle fields. Most of these fields are invisible to our eyes, with notable exceptions like the photon field.

“Ask any physicist on the planet, what’s our current best theory of physics, and they’re going to give you a theory of fields,” said David Tong, a theoretical physicist and professor at the University of Cambridge. “It doesn’t include one particle in those equations [for fields].” Still, physicists more commonly refer to particles than their underlying fields, as particles can provide a more convenient and intuitive concept.

To question the existence of ordinary (non-virtual) particles would be counterproductive, according to Brigitte Falkenburg, a professor at the Technical University of Munich who wrote a comprehensive book on the subject, * Particle Metaphysics*.

“The evidence against their existence is that they cannot be directly observed, but then, this was the argument of Galileo’s enemies, who refused to look through the telescope to observe Jupiter’s moons,” Falkenburg said.

Particles and fields might instead be looked at as two different interpretations of the same thing. The physicist Matt Strassler has blogged extensively to try and clarify the interpretation of virtual particles based on an understanding of fields.

As he writes on his blog, particles can be thought of like permanent ripples in the underlying particle fields, like ripples fixed on the surface of water. Virtual particles on the other hand are more like fleeting waves.

As Jaeger points out, under this interpretation, the narrative of infinitely many virtual particles popping up makes more sense. There are only a finite number of particle fields, since only a finite number of elementary particles have been discovered. An infinitude of virtual particles popping up would be just like the infinitude of small changes that we can feel in a single gusting wind.

Jaeger is currently refining his own picture of virtual particles as fluctuations in the underlying quantum fields. The key part about these fluctuations for Jaeger is that they must conserve overall quantities like energy, charge and momentum, the key principles of modern physics.

In the end, there seems to be good reason not to think of virtual particles as ordinary, observable particles, but that whatever they are, they are real. The difficulty of interpreting their existence points at the complexity of the quantum field theory from which they originate.

As of now, no one knows how to replace QFT with a theory that is more straightforward to explain and interpret. But if they did, then they would have to settle the question of the true nature of the virtual particle, perhaps the most enigmatic inhabitant of the smallest of scales.

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