Conversations About Science with Theoretical Physicist Matt Strassler

Of Particular Significance

Conversations About Science with Theoretical Physicist Matt Strassler

Virtual Particles: What are they?

The term “virtual particle” is an endlessly confusing and confused subject for the layperson, and even for the non-expert scientist. I have read many books for laypeople (yes, I was a layperson once myself, and I remember, at the age of 16, reading about this stuff) and all of them talk about virtual particles and not one of them has ever made any sense to me. So I am going to try a different approach in explaining it to you.

The best way to approach this concept, I believe, is to forget you ever saw the word “particle” in the term. A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle. A particle is a nice, regular ripple in a field, one that can travel smoothly and effortlessly through space, like a clear tone of a bell moving through the air. A “virtual particle”, generally, is a disturbance in a field that will never be found on its own, but instead is something that is caused by the presence of other particles, often of other fields.

Analogy time (and a very close one mathematically); think about a child’s swing. If you give it a shove and let it go, it will swing back and forth with a time period that is always the same, no matter how hard was the initial shove you gave it. This is the natural motion of the swing. Now compare that regular, smooth, constant back-and-forth motion to what would happen if you started giving the swing a shove many times during each of its back and forth swings. Well, the swing would start jiggling around all over the place, in a very unnatural motion, and it would not swing smoothly at all. The poor child on the swing would be furious at you, as you’d be making his or her ride very uncomfortable. This unpleasant jiggling motion — this disturbance of the swing — is different from the swing’s natural and preferred back-and-forth regular motion just as a “virtual particle” disturbance is different from a real particle. If something makes a real particle, that particle can go off on its own across space. If something makes a disturbance, that disturbance will die away, or break apart, once its cause is gone. So it’s not like a particle at all, and I wish we didn’t call it that.

Fig. 1: Two electrons approach each other; they generate a disturbance in the electromagnetic field (the photon field); this disturbance pushes them apart, and their paths are bent outward. One says they "exchange virtual photons", but this is just jargon.

For example, an electron is a real particle, a ripple in the electron field; you can hold one in your hand, so to speak; you can make a beam of them and send them across a room or inside an 20th century television set (a cathode-ray tube). A photon, too, is a real particle of light, a ripple in the electromagnetic field, and you can make a beam of photons (as in a laser.) [Can’t have one in your hand though, since photons (in vacuum) are always moving.]

But if two electrons pass near each other, as in Figure 1, they will, because of their electric charge, disturb the electromagnetic field, sometimes called the photon field because its ripples are photons. That disturbance, sketched whimsically in green in the figure, is not a photon. It isn’t a ripple moving at the speed of light; in general isn’t a ripple at all, and certainly it is under no obligation to move at any one speed. That said, it is not at all mysterious; it is something whose details, if we know the initial motions of the electrons, can be calculated easily. Exactly the same equations that tell us about photons also tell us about how these disturbances work; in fact, the equations of quantum fields guarantee that if nature can have photons, it can have these disturbances too. Perhaps unfortunately, this type of disturbance, whose details can vary widely, was given the name “virtual particle” for historical reasons, which makes it sound both more mysterious, and more particle-like, than is necessary. [Students of math and physics will recognize real photons as solutions of a wave equation, and virtual photons as related to the Green function associated with this equation.]

Fig. 2: As in Figure 1, for a positron (an anti-electron) and an electron; now the slightly different disturbance causes the two particles to attract one another, and their paths are bent inward.

This disturbance is important, because the force that the two electrons exert on each other — the repulsive electric force between the two particles of the same electric charge — is generated by this disturbance. (The same is true if an electron and a positron pass near each other, as in Figure 2; the disturbance in this case is similar in type but different in its details, with the result that the oppositely charged electron and positron are attracted to each other.) Physicists often say, and laypersons’ books repeat, that the two electrons exchange virtual photons. But those are just words, and they lead to many confusions if you start imagining this word “exchange” as meaning that the electrons are tossing photons back and forth as two children might toss a ball. It’s not hard to imagine that throwing balls back and forth might generate a repulsion, but how could it generate an attractive force? The problem here is that the intuition that arises from the word “exchange” simply has too many flaws. To really understand this you need a small amount of math, but zero math is unfortunately not enough. It is better, I think, for the layperson to understand that the electromagnetic field is disturbed in some way, ignore the term “virtual photons” which actually is more confusing than enlightening, and trust that a calculation has to be done to figure out how the disturbance produced by the two electrons leads to their being repelled from one another, while the disturbance between an electron and a positron is different enough to cause attraction.

Fig. 3: An electron may naively be thought of as a ripple of minimum intensity --- the minimal ripple --- in an electron field. But the electron interacts with the photon field (i.e. the electromagnetic field) and can create a disturbance in it; in doing so it too ceases to be a normal particle and becomes a more general disturbance. The combination of the two disturbances (i.e. the two "virtual particles") remains a particle with the energy, momentum and mass of the incoming electron.

Now there are many other types of disturbances that fields can exhibit that are not particles. Another example, and scientifically one of the most important, shows up in the very nature of particles themselves. A particle is not as simple as I have naively described. Even to say a particle like an electron is a ripple purely in the electron field is an approximate statement, and sometimes the fact that it is not exactly true matters.

It turns out that since electrons carry electric charge, their very presence disturbs the electromagnetic field around them, and so electrons spend some of their time as a combination of two disturbances, one in in the electron field and one in the electromagnetic field. The disturbance in the electron field is not an electron particle, and the disturbance in the photon field is not a photon particle. However, the combination of the two is just such as to be a nice ripple, with a well-defined energy and momentum, and with an electron’s mass. This is sketchily illustrated in Figure 3.

Fig. 4: The Feynman diagram needed to calculate the process in Fig. 3. One says "the electron emits and reabsorbs a virtual photon", but this is just shorthand for the physics shown in Fig. 3.

The language physicists use in describing this is the following: “The electron can turn into a virtual photon and a virtual electron, which then turn back into a real electron.” And they draw a Feynman diagram that looks like Figure 4. But what they really mean is what I have just described in the previous paragraph. The Feynman diagram is actually a calculational tool, not a picture of the physical phenomenon; if you want to calculate how big this effect is, you take that diagram , translate it into a mathematical expression according to Feynman’s rules, set to work for a little while with some paper and pen, and soon obtain the answer.

Fig. 5: As in Figure 3, for a photon. The photon can become a disturbance in the electron field. This disturbance has some regions with negative electric charge and some with positive electric charge, but with total charge zero, like the incoming photon itself. The photon can do the same with other charged fields, such as the muon field.

Another example involves the photon itself. It is not merely a ripple in the electromagnetic field, but spends some of its time as an electron field disturbance, such that the combination remains a massless particle. The language here is to say that a photon can turn into a virtual electron and a virtual positron, and back again; but again, what this really means is that the electron field is disturbed by the photon. But why are we seeing a positron — an anti-electron — and yet I am only referring to the electron field? The reason ties back to the very reason that there are anti-particles in the first place: every field, by its very nature, has particle ripples and anti-particle ripples. For some fields (such as the photon field and Z field) these particle and anti-particle ripples are actually the same thing; but for fields like electrons and quarks, the particles and anti-particles are quite different. So what happens when the electron field is disturbed by a passing photon is that a disturbance is set up that has some electron-like disturbance with net negative electric charge, and some positron-like disturbance with net positive charge, but the disturbance as a whole, like the photon itself, carries no net charge at all.

For those who learned (and recall a bit of) freshman physics, what is happening is that the oscillating electric field that makes up the photon is polarizing the electron field — inducing a dipole moment. Remember dielectrics and how electric fields can polarize them? Well, the vacuum of empty space itself, because it has an electron field in it, is a polarizable medium — a dielectric of sorts.

Fig. 6: The Feynman diagram needed to calculate the process in Fig. 5. One says "photon becomes a virtual electron-positron pair", but this is just shorthand for the physics shown in Fig. 5.

The same is true, by the way, for all the other electrically charged fields, including those of the muon, the up quark, and so forth.

[Here, by the way, we come across another reason why “virtual particle” is a problematic term. I have had several people ask me something like this: “ Since the diagram in Figure 6 seems to show that the photon spends some of its time as made from two massive particles [recall the electron and the positron both have the same mass, corresponding to a mass-energy (E = m c-squared) of 0.000511 GeV], why doesn’t that give the photon a mass?” Part of the answer is that the diagram does not show that the photon spends part of its time as made from two massive particles. Virtual particles, which are what appear in the loop in that diagram, are not particles. They are not nice ripples, but more general disturbances. And only particles have the expected relation between their energy, momentum and mass; the more general disturbances do not satisfy these relations. So your intuition is simply misled by misreading the diagram. Instead, one has to do a real computation of the effect of these disturbances. In the case of the photon, it turns out the effect of this process on the photon mass is exactly zero.]

Fig. 7: The electron can generate disturbances in the photon field; the resulting photon disturbance can in turn create disturbances in other electrically charged fields, such as the muon field.

And it goes on from there. Our picture of an electron in Figure 3 was itself still too naive, because the photon disturbance around the electron itself disturbs the muon field, polarizing it in its turn. This is shown in Figure 7, and the corresponding Feynman diagram is shown in Figure 8. This goes on and on, with a ripple in any field disturbing, to a greater or lesser degree, all of the fields with which it directly or even indirectly has an interaction.

Fig. 8: The Feynman diagram needed to calculate the process shown in Figure 7.

So we learn that particles are just not simple objects, and although I often naively describe them as simple ripples in a single field, that’s not exactly true. Only in a world with no forces — with no interactions among particles at all — are particles merely ripples in a single field! Sometimes these complications don’t matter, and we can ignore them. But sometimes these complications are central, so we always have to remember they are there.