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.

496 thoughts on “Virtual Particles: What are they?”

  1. Thanks for a great and understandable explanation.

    Is it correct to say that these quantum fields pervade spacetime – or is it better to say the set of fields actually composes (creates?) spacetime? Also, what is the complete list of fields currently known?

    • Most fields are best thought of as pervading three-dimensional-space and time, except for the graviton field, also known as the “metric” of space-time (the object that is needed to decide how far part two points are) which is really intrinsic to space-time.

      In most theories with extra dimensions, some of the fields that we observe would actually form a part of the metric of the higher-dimensional spacetime. In other words, one explanation as to why there are so many fields in nature might be that we live in a world that has some of its dimensions wrapped up (think of how a hose has a large dimension along the hose and small dimension around the hose) and that the metric of the full space-time looks to us, in three-dimensional space, like a metric for three-dimensional space and time along with many other fields whose explanation seems non-obvious.

      A complete list of fields is ill-defined, but I can give you the list of apparently-elementary fields. [There are many non-elementary fields too, including the proton field; just as a proton is composite made from quarks, antiquarks and gluons, so is its field made from other fields. And the wind field and temperature fields in air, or a density field in a metal, are composite too.] The list of known apparently-elementary fields is essentially just the list of known particles,, or even more completely, the list of particles before the Higgs gets a non-zero value, (plus the graviton field, which I didn’t put on the slides.)

  2. Hi,

    I have some questions about the meaning(s) of the word “particle” in the field of high energy physics:

    1-What is the safest way to call a quantum object: an elementary particle? or a quantum particle? or a quantum wave? or we just call them by their names like electrons or neutrinos..etc? or the question is just meaningless?

    2-What is the meaning of the word particle in “the branch of particle physics”?

    3-Which is more fundamental, the quantum particle, or the quantum field? (I did not find consensus in this one)

    4-And finally, what confuses me most, why “elementary particles” are irreducible representations of the Poincare group? and what is the meaning of the word particle in this context?


    • 1) A name’s a name (see Shakespeare) — what matters is not what you call it but whether you understand it… fair? As long as you understand the object does not correspond to any concept in English or in daily life, and that it has some properties that you just have to learn about, you can call an electron an elementary particle, a quantum of the electron field, or a quantized wave in the electron field. Elementary particle is rather short and the least mysterious sounding. “Quantum” is shortest and most accurate, but sounds very mysterious.

      2) You mean, what does “particle physics” mean when referring to it as a subject of study? Just that many experiments on the basic properties of nature require studying its particles, and if you do those experiments, propose them, study them, interpret them, etc., you’re doing “particle physics.”

      3) Field is more fundamental. Not all fields have particles, while all particles are quanta of fields. That’s why the equations used to describe the physics of the standard model are called quantum field theory, not quantum particle theory. [An example of a quantum field theory that has no particles is a “conformal field theory”, very important in studying matter at a phase transition, such as a magnet at the critical temperature where it loses its magnetization.]

      4) Start with classical physics (no uncertain principle) to keep things simple. Then a massive particle is a localized object with a definite mass, energy, momentum and position, and orientation. Let’s put one in front of you, at rest. I can now generate a representation of the Poincare group — the group of all translations, rotations, and changes of reference frame (boosts with a constant velocity) — by simply moving the particle to a new position, rotating the particle, or looking at the particle from a different frame. That set of particle states (with all those different positions, orientations, and velocities) form a complete representation of the Poincare group.

      The only thing different in quantum mechanics is that I can’t precisely localize the particle at the same time I precisely determine the momentum and energy. But I can do a pretty good job on both, or a perfect job on either one. This complication doesn’t change the argument that the full set of things that a particle can do form a representation of the Poincare group.

      For a massless particle I can’t start with a particle at rest, but the basic strategy for finding the full representation is the same.

  3. In dense aether theory the water surface can serve as a low dimensional analogy of 4D space-time and the density fluctuations of the underwater are the analogy of virtual particles, after then.

  4. So what you are saying essentially is that transient ripples, which are not stable or sustainable, are caused by every particle in every other field with which they can interact. If another particle is present, their ripples combine and the particles DO interact. These ripples look in *some* ways like the ghost of a particle in that field, enough that we can use the equations of particles to calculate effects. But in other ways, including their stability, they’re not really like particles at all.

    Okay. I got everything except how “virtual particles” are involved in particle CREATION. At some point, wouldn’t the transient ripples have to coalesce into wave(s) that ARE stable?

    • That’s basically right. I wouldn’t use the term “ghost” (for two reasons, one being that ghost is used as a technical term elsewhere, but more importantly that the relation is really that disturbances are the more general case, while a particle is an extremely special form of disturbance.)

      How “virtual particles” can create something: the transient ripples themselves are still not stable in this case. They fall apart, into true particles.

      For example, if the two electrons in my picture came together with enough energy, the transient ripple shown in the figure could have enough energy to produce an electron-positron pair (so that there would be four particles in the final part of the picture, three electrons and a positron.) The disturbance in the field can carry lots of energy, and that energy can be turned into particles. But the disturbance itself is still transient. Does that answer the question?

      • Hold on, I thought transient ripples weren’t necessarily a result of other disturbances, and can arise just due to the uncertainty principle. Is this true? The original asker seemed to purport this

  5. One of the things that tripped me up as a student, was also just how arbitrarily small you could make the difference between real and virtual.
    Usually the definition of a virtual particle is a ‘thing’ that does not satisfy the usual energy-momentum rules, or the ‘thing’ which is an internal leg in a Feynman diagram.

    But then every particle we have ever observed is an internal leg of a bigger Feynman diagram. For instance, the electron we measured from a particle accelerator eventually is absorbed by an atom somewhere, and hence becomes an internal leg in that diagram. So then most people say, well its just a question of lifetime. Long lived particles are called real, short lived particles are virtual.

    But then suppose you have a photon that was emitted from the Pleiades, and it presumably is real (or almost real) all the way until it is absorbed in your retina. So have you just measured a real or virtual photon? It sorta depends on how you draw the diagram!

    • You are absolutely correct to point out this subtlety! It is, in the end, a matter of degree.

      In general, what we have in quantum fields are disturbances of many types. There is a very special disturbance we may call a particle, which is a ripple that can in principle travel forever. But this is an idealization: any real particle interacts with other objects, and this means nothing is ever exactly this precise, idealized ripple. So the issue is how close is it to the ideal case. In most physical processes one deals with objects that are clearly either close to the ideal or very far from the ideal. A photon traveling from the Pleiades is clearly about as close as you are going to get to the ideal; its energy and momentum are almost the perfect match that you would expect for a massless particle. The disturbance between [a “virtual photon exchanged”] between an electron and a nucleus in an atom has very little energy and a lot of momentum; it is very far from what you would call a particle.

    • Columbia, your point here about every particle being part of a larger diagram suggests a way to dispel puzzlement about EPR-type experiments. The EPR “paradox” appears, I think, only when there are humans (or other sentient beings) acting as scientists, creating the experimental conditions and collecting the results. We like to think of ourselves as standing outside the experiment, causing photons to become entangled, then sending them off to distant observing stations where randomizing polarizers have been set up in certain ways, such that the results will be automatically recorded at each station by appropriate detectors, then later transmitted from place to place and compared with each other, and so on.

      But we (the scientists) are part of an inconceivably tangled up arrangement of diagrams within diagrams, in which events “just happen” — including all of our own actions. If we could examine all those linked diagrams and the evidence of what the results had been, without ideas about free will and intention, it seems to me that there would be no place in the description of what happened for any paradoxes to be inserted.

  6. If I’m understanding correctly, your saying virtual ‘particles’ arise because of ‘nearby’ real particles disturbing a field, those disturbances being the virtual ‘particles’. That left me wondering what then explains the ‘vacuum energy’ of empty space? I naively thought virtual ‘particles’ where popping in and out of existence with no real particles nearby. I took it that the cosmological constant was somehow ’powered’ by vacuum energy ?

  7. Thanks for the nice article. When reading about Hawking radiation, one is told that when a pair virtual particles is created near the event horizon, one may fall into the black body and the other escape as radiation. Are the virtual particles in this situation somewhat different than the ones you describe? Do they become “real” particles in this case?

    • Great question. If the escaping virtual particle becomes real then there would be an increase in the mass of the observable universe. The virtual particle absorbed by the black hole should also become real and should then increase the mass of the black hole and not reduce its mass. The information regarding the absorbed particle is not lost as the escaping particle reflects the information of the absorbed particle as virtual particles are created in opposite pairs. 17Dec2019

  8. My lay understanding was that virtual particles “challenge” conventional notions of cause and effect, but you use the word “cause” in very conventional ways in this article.

    • Could you try to help me figure out where this notion comes from? Do you know where you read it? I have some guesses as to where this conception comes from, but I wonder whether there are modern books promulgating the idea. While it is true that one has to be careful in general about assuming that all processes can be described in terms of cause and effect (even before accounting for quantum mechanics), and also true that quantum mechanics is weird, no doubt about it , there is no profound challenge to basic causality in this context. Certainly I do not think you will not find any discussion of challenges to causality from “virtual particles” (i.e. generalized disturbances in fields) in any modern quantum field theory book.

  9. Is this “virtual particle=>causality issue” maybe coming from discussions like those in Bjorken and Drell section 12.3 ? My reading of their conclusion is that there isn’t really a problem though.

  10. I’m confused as to what explains the ‘vacuum energy’ where there are no real particles disturbing any fields ? what powers the cosmological constant ?

    • There’s plenty of energy in those disturbances. You seem to be assuming that the only way fields can carry energy is through their particles, but this is not the case. Analogy: one way for a spring to carry energy is to go back and forth at its resonant frequency, but a spring could carry energy even if you pushed it back and forth in an arbitrary way. And a quantum spring, thanks to the uncertainty principle, will move around, in a limited but arbitrary way, and with non-zero energy, even if you just leave it alone. The difference in the math is the same for particles (resonant behavior that can go on its own) versus general disturbances (which require an outside push, or just the jiggling assured by the uncertainty principle.)

  11. As an electrical / electronics engineer with a strong interest in physics (but not great at advanced math) your articles have explained more to me in a few hours than in the several years I spent in secondary and tertiary education. You write and diagram with amazing clarity. I do notice that when questions are asked about speculative physics (such as the possibility of extra dimensions), you confine your responses to answers that can now (or may be in the near future) subject to experiment.

    Your explanation of “virtual particles” here eliminates most of my confusion about articles on the subject I have read elsewhere, but two bits of confusion persists; if “virtual particles” are complex disturbances in a field, then, can the disturbances (through Fourier transforms) be described as an agglomeration of resonances (particles)? also, what did / does Prof. Hawking mean by HIS use of the term in relation to what happens at the event horizon of a black hole? (I know I should ask Prof. Hawking, but he is somewhat less accessible :-))

    • [quote]You [Strassler] write and diagram with amazing clarity. I do notice that when questions are asked about speculative physics (such as the possibility of extra dimensions), you confine your responses to answers that can now (or may be in the near future) subject to experiment.[/quote]

      Well, I am asking, has there been to date [ in my location, April 19, 2013, Monday, 10:48 AM ) experimentation on the reality in observation of virtual particles, or virtual particels are all speculative?

  12. In your article “What’s a proton?” you state that there are “zillions of gluons, antiquarks, and quarks in a proton”. Do most of these qualify as virtual particles as described in this article, i.e. as mere disturbances of their fields that are in many respects quite unlike real particles?

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  14. If a particle is “a nice, regular ripple in a field”, how would you describe a string from string theory? What will they appear like in the field?

    • Well, a string is a ripple in a string-field, something for which we have no daily intuition. We have intuition for fields because we live in a wind field, a temperature field, a air-density field, and so forth, and wind, sound, heat diffusion are all things we can imagine and study rather easily. But a string field actually contains an infinite number of types of ordinary fields — and we don’t encounter one in daily life — so you can imagine building an intuition for that would not be easy. Let me think about how I might explain this one someday — this will not be coming soon.

        • More or less what you’d think: if you strike it, you will find an elementary string can respond in all sorts of ways — by wiggling in all sorts of different configurations — while an elementary particle cannot do that.

  15. If a particle is “a nice, regular ripple in a field” would it be similar to a phonon concept in a virtual-particle “Dirac-sea”?

    • No, what I have in mind is simpler. Think of light — an ordinary ripple in the electric and magnetic field. Now remember that in quantum mechanics that light cannot be arbitrarily dim — there is a dimmest possible flash, a ripple of lowest possible intensity. That dimmest possible flash — the ripple of lowest possible intensity — is a photon.

      Does that help?

      • That helps a lot when discussing things like electrons: since they have the exact same charge, and—ignoring quarks and such—all electrical charge variations come in increments of one electron’s charge, it’s sort of intuitive that “an electron is the smallest possible variation of the charge field”. I can even sort of imagine moving electrons as a kind of moving ripple, and even stationary electrons (my mind throws out the analogy of a spring in a mattress oscillating without affecting its neighbors).

        But I don’t really get the “ripple of lowest possible intensity” analogy for photons. As far as I can tell, you can have photons of pretty much every frequency, from ultra-long-wave radio to ultra-hard gamma rays, and I can’t figure out anything that’s “smallest” and they all share, the way charge is for electrons. Is that spin or something?

        (I get that *specific* interactions, like electron excitation in atoms, produce or absorb photons of a certain energy, but unless I’m very much mistaken that’s quite a different issue.)

      • I get that explanation for electrons, or at least it feels intuitive; you can only have variations of charge in specific units, and those are electrons (and positrons), at least until you start wondering about quarks and why they’re allowed to use thirds. But unless I’m very much mistaken, you can have photons of pretty much every energy, from ultra-long-wavelength radio to hard gamma rays. What exactly is the quantity a photon is “the least intensity ripple” of?

        • A photon with frequency f is the smallest possible intensity of frequency-f light, i.e. the smallest possible frequency-f ripple in the electromagnetic field. “Intensity” here is basically the same as energy: the amount of work your light could do. “Frequency” is basically the same as color.

          • Do we have any indication whether or not real photons can become virtual? I know Chalmers University in 2011 concretized virtual photons into real photons using a SQUID, but I’ve not heard of the opposite occurring.

            Take, for instance, a virtual photon of 1 micron wavelength. It gets red-shifted (say, via universal expansion) to 2 micron wavelength. Since E=hf (E=hc/wavelength) and f has decreased, E has likewise decreased.

            If a real photon is the minimum possible excitation (a single quanta) for a given frequency in the EM field, and E decreases, is it possible for a real photon to become virtual, or is the relationship between E and f such that a concretized photon always remains concretized regardless of blue- or red-shift?

  16. Sorry if this is a double-post. I tried to comment earlier but it didn’t seem to go through (which is hopefully a good thing, because I’ve since edited the post.)

    This is all extremely fascinating—thank you!

    The impression I’m getting about the fundamental nature of matter is as follows, and I’d love to know if I’m more or less on the right track. Please forgive me if I’m way off-base; the last thing I want to do is confuse other lay-readers like myself with falsehoods!

    –Quantized fields that permeate the fabric of space-time—rather than particles—might be thought of as truly “fundamental.”

    –A “fundamental particle” is a stable ripple of contained energy on a field.

    –At least partly because of the quantized nature of fields, stable ripples in a given field (that is, all “real” particles of a given type) can’t just have any old values for their properties. Instead, they must have certain characteristics in common (mass, spin number, etc.) and are essentially indistinguishable from one another.

    –There are plenty of unstable disturbances in a field, too (more of them than stable ripples even?), which can only be very short-lived and need not behave the same way as stable ripples (particles) do in the same field. They are known confusingly as “virtual particles.”

    –Stable ripples (“particles”) and unstable disturbances (“virtual particles”) alike interact with other ripples/disturbances in their own field and/or in (some) other fields (the specifics of which other fields’ disturbances a given field can interact with vary from field to field).

    –The results of these interactions among field ripples/disturbances are matter and forces as we know them.

    If I’m basically on the right track, I have a few questions to throw at you:

    I understand that the Higgs field is thought to pervade all of space-time. Is the same true of other fields associated with elementary particles, such as the “electron field” and “photon field” you’ve mentioned? Is it thought that there is just one “electron” field that exists everywhere?

    When you speak of unstable disturbances (short-lived “virtual particles”) in a field—do these phase in and out everywhere, all the time, in every field, in something like a uniform fashion? Is this what is meant by “quantum fluctuations” in a vacuum, or “vacuum energy”? If so, is there a theory as to what “causes” these disturbances? In other words, are these disturbances always the result of the presence of other nearby particles (real or virtual) interacting with the given field? Or is this just something fields do?

    Am I right to think of a field as something like a fabric of quantized energy?

    I really appreciate what you are doing on this site. Many thanks in advance for any corrective feedback you can provide for my evolving conceptual comprehension of the nature of reality. I know I can never fully understand this stuff without the math, but I really want to try!

    • Remarkable. Almost everything you’ve said is basically right. A small issue:

      “A “fundamental particle” is a stable ripple of contained energy on a field”

      well, the words “contained energy” aren’t really necessary and don’t really have content. Any ripple in any field has some energy. So let’s just say “A “fundamental particle” is a stable ripple on a field” and be done with it…

      … except for one additional subtlety with the word “stable”… it needs to be “relatively stable”, because most particles eventually decay to other particles, though it takes a while.

      Now, to your questions.

      Yes, all fields related to the known elementary particles are believed to exist everywhere in space, and at all times. There is just one electron field that is everywhere in the universe. What makes the Higgs field different from the other known fields is that it is non-zero on average everywhere in the universe, while, say, the photon field [i.e. the electric and magnetic fields treated together] and the electron field are on average essentially zero.

      Quantum fields are constantly fluctuating, and the unstable disturbances that we call “virtual particles” are always there. It is just something that quantum fields do, and the mathematics known as “quantum field theory”, which I teach to first and second year graduate students and which is very well established both theoretically and experimentally, does a great job of predicting the details of these fluctuations/disturbances/virtual particles. No lingering mysteries here, not for many decades.

      I don’t know what a “fabric of quantized energy” is or means. You can’t really explain fields in terms of more fundamental things, at least not at this time; as far as we know, they are the fundamental things. Fields are just the basic ingredients of our universe, in our current view. Of course this picture of the universe is likely to evolve over time as we learn more, and so my point of view may someday have to change. Right now it is consistent with all experiments.

      • Great! Thanks for this. Conceptual explanations of this material are incredibly hard to come by, which is really a shame, since it’s endlessly interesting. Have you ever thought about writing a book on particle/field physics for laypeople? I’m sure you have real science to attend to, but it’s worth keeping in mind that there are probably very few people in the world who possess both your level of expertise in the discipline and your knack for dumbing things down juuust the right amount when explaining mind-blowing and unintuitive quantum truths to the mathematically challenged.

        Here is another one, if you find a few free moments: does QFT have implications for making sense of wave-particle “duality” and wave-function “collapse”? Given your understanding of particles as (relatively stable) ripples in constantly fluctuating fields, how do you wrap your mind around the observed effect of a single electron apparently “interfering” with itself in the double-slit experiment?

        Thanks again,

        • I am writing a book for laypeople. Slowly.

          Quantum field theory does not help make quantum mechanics less weird. It doesn’t make it more so…

          There are reasons I have not discussed the difficulties of making sense of a quantum mechanical world. It’s hard to do it well, and I’m not ready.

          The way I wrapped my mind around the double slit experiment is that I watched the experiment being done (with photons, not electrons, but it’s the same effect.) So then I had no choice in the matter. I’ll write about this someday.

          • What happens if we put a double-slit experiment with an electron in a gas chamber? I assume we shall see the tracks of electrons, but no interference? Or no tracks of electrons, but with interference?

      • Matt Strassler wrote:
        “well, the words “contained energy” aren’t really necessary”

        Are the concretized particles not ‘contained’ in that they are a resonant standing wave in the Higgs field, said resonant standing wave giving the concretized particles their mass and thus inertia? That was my understanding.

        If so, that opens up some pretty interesting possibilities for tearing invariant-mass matter down into its constituent energy…

  17. This is a great article.

    I do have a few questions though. I am studying particle physics as an undergraduate and I am struggling with this concept a bit. After immense amounts of research, I have found no explanation as to why virtual particles are needed to explain forces. What do particles offer that fields do not? Can oscillators in a field not be explained by quanitizing the field? I’ve read most all of Feynman’s lectures and many others and have found no answer.

    Also, I am a confused about the state of the virtual particles before and after the interaction between two field particles. Do they only form when approaching other field particles? Are they emitting these virtual particles at all times? What actually happens to the particle after the interaction?

    Thank you very much for this article. It has helped me very much conceptually.

      • Not exactly. I know Green’s functions are used to solve advanced differential equations to sometime correlate functions but I have a weak background in electrodynamics and have not taken any classes on it yet. Is this where I should look to find my answer?

        • Yes. A virtual particle is to a real particle as a Green’s function is to a wave.

          A wave is a solution to a wave equation, with zero on the right hand side of the equation. Such a wave can propagate on its own. Light is an example; it can travel through space even if there are no electric charges around. Quantum light is made from quanta [i.e. photons] and these are what we call “particles” of light.

          A Green function is a solution to the wave equation in the presence of a point source on the right-hand side. You learn how two electrons affect each other by studying the field at one electron’s location due to an electron at a second point; this involves the Green function with a point source at the location of the second electron. A simple example of a Green function is the 1/r electrostatic potential between two static electrons. The potential would never take this 1/r form on its own, if the charges were not there.

  18. Hey Matt

    Discovered your blog over the weekend am a second year physics student at the university of south australia but all the people here are dopes and not interested in fundamental questions. I’m interested in the background independent aspect of the field theories ie: what if we throw away space time altogether and just haver the fields and their interactions? . Bothered by you’re inclusion of the “muon field” as seperate from the electron field in this discussion tho. The muon and the tau should just be other kind of excitations in the “electron field” right? the question is how many fields and how many ways to fold them? the less the better

    • Your field question is slightly ill-posed, though probably you can refine it. A field in classical physics is a function f(x,t), with a set of differential equations that govern its behavior. If you throw away space and time it becomes a number f with a set of algebraic equations that determine it. Quantum mechanics of such a field is just ordinary integrals. This is probably not what you had in mind, but I’m not sure yet what you really did have in mind. Did you want to remove the *metric* on space and time [i.e. our ability to measure distances?] while keeping the space and the time around?

      There is strong evidence against thinking of the muon and tau as excitations in the electron field. When you excite an atom, the thing you expect is that the excited state can decay to the ground state by the emission of a photon. But muons decay to electrons only via the weak nuclear interaction, during which they spit off a neutrinos and an anti-neutrino. The process muon –> electron + photon has been searched for, but very extensive experiments have never seen this process (or the corresponding ones for taus) and the result so far is that less than 1 in 100,000,000,000 muons decays this way.

      You might still wonder whether that just means there’s something special about the way that a muon and a tau are excited forms of the electron that is different from atoms. Well, here’s more evidence. If the electron is special, in that the muon and tau are excited versions of it, then you would not expect a tau to decay to a muon (plus a neutrino and anti-neutrino) at the same rate that it decays to an electron (plus a neutrino and anti-neutrino). But in fact the rates for these two processes are the same.

      Finally, the electron and muon and tau are in some sense intrinsically massless; they only develop a mass when the Higgs field becomes non-zero (see ). So their masses are determined by how they individually interact with the Higgs field, not by some internal dynamics.

      I guess I should mention that in atomic physics there are many excited states with heavier and heavier masses, but beyond the tau there’s no sign of any fourth lepton even up to masses over 100 times larger than the tau’s mass.

      You may contrast this with the proton, for which there are many excited versions, all of which decay preferentially back to a proton plus some pions (which for proton-like objects, made from quarks, gluons and antiquarks, is an even more efficient process than emitting photons).

      Why should we have three versions of almost the same type of particle? And why would they all interact very differently with the Higgs field? There have been many, many proposals, but so far nothing is yet known about the answers to these questions.

  19. Dear Sir,

    In the vacuum of space, if there are two bodies A and B and if there is absolutely nothing between them they should come together since there is nothing to keep them apart. They must be some form of energy field that creates the space to keep them apart. This energy field which keep the planets and stars apart could have been created during the big bang.

    Gravity could also be explained by assuming that any body with a mass will be capable of absorbing this field and creating a decreasing density of this field as we go nearer and nearer to this body.

    So before the big bang since there is really absolutely nothing, with no time and space, all virtual particles that are being continuously created out of nothing should come together and occupy the same point and as such would ultimately form a singularity with almost infinite density and triggers off the big bang.

    This could happen if there is a mechanism which separate these virtual particles from their anti-particles.
    So has anybody found such a mechanism?

    Dr HW Looi

    • Your first point is correct, but incomplete.

      ” if there are two bodies A and B and if there is absolutely nothing between them they should come together since there is nothing to keep them apart. ”

      Two bodies A and B that are stationary relative to one another will gradually come together under the force of gravity.

      However, if they are moving relative to one another, conservation of angular momentum will drastically slow the rate at which they can come together. That is why the planets can orbit the sun for billions of years under the force of gravity.

      So there is no need for an energy field to keep objects apart and to explain why objects do not come together.

      “before the big bang since there is really absolutely nothing, with no time and space, ”

      We don’t know that.

  20. Dear Sir,

    Thank you for answering my question. But I think you have completely misunderstood what I was trying to say.

    Of course I know very well that the conventional Einstein concept of gravity is that it bends space-time and as such causes two objects to move towards each other. And the Newtonion concept is that it is nothing more than just an attractive force.

    What I am trying to say is that there maybe another more simple concept.
    If there are 2 objects in the vacuum of space, and if there is really absolutely nothing in between, the two objects do not just move towards each other, but rather they should be next to each other!

    Take another analogy. If there are 2 chairs that are 10 feet apart. There is a “space” of 10 ft and if there is absolutely nothing in between, including no space and time, the chairs would be next to each other and they do not need the conventional gravity to get them moving towards each other.

    The fact that objects in the vacuum of space are separate is because there is “space” in between them and this space must have been created by some form of energy field.

    Thanking you especially for you great patience and endurance,

    Dr HW Looi

    • Your statements are correct until the last one.

      “this space must have been created by some form of energy field.”

      This is both a bit illogical and also somewhat confused. A field is one thing; energy is something it can have, but there is no such thing as an “energy field”. There are electric fields; particles that are ripples in these fields are called photons and they can carry energy from one place to another. There are gravitational fields; particles (hypothetical but deeply plausible) that are ripples in these fields, essentially ripples in space itself, are called gravitons, and they too can carry energy from one place to another. But an “energy field” wouldn’t make any sense. You must mean something else.

      In general, we don’t know why there is space, or why there is anything that can be called a “universe”, but in principle it need not be created by some other field, any more than the electron or quark fields that are found throughout space need to be created by some other field. There are many theories as to how space comes to be, including theories that have time but not space at first, and then develop space through a very subtle mechanism that is far too difficult to explain here. But once you have space, you can have objects in it, and they will remain separate.

      Am I right that your real question is “why is there any such thing as space, through which waves and particles can move and in which one can find objects?” If so, the answer is not known, but it does not have anything to do with an energy field.

  21. Dear Sir,

    Thank you very much for your great patient and explaination.
    I really do appreciate it.
    So I will just have to change the last part of my statement to “there is a tiny possibility that this space may be created by some form of matter or energy, but we really don’t know what space is made of.”

    Thanking you,

    Dr HW Looi.

  22. The importance of virtual particles is in whether they have an effect on measurable quantities.. If they had no effect, then studying them is just a mental exercise. Vacuum polarization of virtual particles is a real effect, and in the case of pionic atoms, the atomic energy levels are shifted by a large amount. The first precise measurement of the pion mass was done by measuring the atomic transition energies of pions in pionic atoms, and calculating the level shift due to vacuum polarization. See Appendix B in Robert E. Shafer, “Pion Mass Measurement…”, Phys. Rev. 163, 1451 (1967) The vacuum polarization effect was first calculated by Uehling in Phys Rev (1935).

    This atomic level shift is related to charge renormalization, in that virtual particles in strong Coulomb field partially shield the bare Coulomb field..
    Robert Shafer

  23. Hi, do you know how I found this? At a depression website bulletin board labeled as off topic. Some of the smartest people I know are nuts. And of course, I didn’t get there by accident, even though I got here by accident.

    I love this stuff. Total lay person here. I was a surveyor though and I can use sine, cosine and tangent to lay out the corner of the latest Walmart building to within…well, a thousandth of a foot. Close enough for concrete. And using those 3 functions and a 20 dollar calculator and a hundred foot tape, I can check into known points, inverse some rectangular coordinates into angle and distance, and voila! Attention shoppers, Brian has caused all this.

    You write so well…better than Feynman. That’s right, I said it. Q E D (major and minor premises, with a happy ending type of Q E D)
    Thanks, excellent. The analogies, ie. the spring, the swing, are huge, Feynmanesque. My spatial faculties have grown a lobe.

    layman Brian, eating in a corned beef and cabbage field, interacting with a coffee swallow field. It is almost time for a cigarette field. (Did you ever look at cigarette smoke in a sun ray in a overly windowed room? It is 1.) blue. and 2.) made up of tiny particles.)

    • “layman Brian, eating in a corned beef and cabbage field, interacting with a coffee swallow field. It is almost time for a cigarette field.”

      this made me smile

  24. I love these articles. Like you, I’ve read many books for laypeople on particle physics (and even glanced into a few for experts), and your articles are the first that have given me even a glimmer of understanding of quantum field theory.

    The explanations of virtual particles I’ve read have generally been along the lines of “the uncertainly principle allows conservation of energy and momentum to be violated over very short times, and virtual particles are the result.” How does this relate to what you say here? Or is it another “white lie”?

    • Another white lie, but it gives roughly the right estimates (when you apply the uncertainty relations) for how common are quantum disturbances of a given size. That’s why people talk that way.

      • Could you please explain why it was a white lie? I have been wandering all around the internet and everyone seems to give conflicting views.
        I would be very grateful if you could help.

  25. Prof. Strassler,

    Thank you for this article. I have a few questions:

    1) I always thought that, in the context of two “real” particles interacting with each other, Feynman diagrams were a mathematical convenience, with each diagram representing a term in the perturbation expansion, and virtual particles were nothing more than a pictorial way of representing the propagator. You characterize a virtual particle as a “disturbance” in the field; how does one reconcile the “mathematical convenience” view of virtual particles with the “disturbance in the field” view of it?

    2) I have read the “Schwinger limit” described as the electric field of a laser which is strong enough to pull virtual electron-positron pairs out of the vacuum and make them real. Using your language, the laser field creates disturbances in both the electron and positron fields, i.e. polarizes the vacuum, and if these disturbances are large enough, they become ripples in the fields, i.e. a real electron-positron pair. Is that an accurate description of what happens when a strong laser field interacts with the vacuum and creates electron-positron pairs?

    3) How can the following statement from the Wikipedia page for virtual particles be reconciled with your description of virtual photons as “disturbances” in the photon field:

    “Virtual photons are also a major component of antenna near field phenomena and induction fields, which have shorter-range effects, and do not radiate through space with the same range-properties as do electromagnetic wave photons. For example, the energy carried from one winding of a transformer to another, or to and from a patient in an MRI scanner, in quantum terms is carried by virtual photons, not real photons.”

    4) At one point you said, “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.” Could you be more specific? I am trying to relate what you said here to what I have read in QFT books. How does your description relate to the S matrix, propagators, and perturbation expansion? I have seen the QFT formulation of electron-electron scattering which leads to a scattering cross section, but how does the repulsive force follow from that?


    • 1) propagator = Green function = off-resonance disturbance in the field caused by a source. Example: 1/r electric potential between charges.

      singularity in the propagator = resonance = ripple in the field that can travel indefinitely without a source. Example: photon

      2) Yes. If the energy is large enough the singularities in the propagators can be accessed and there is a non-analytic change in the response of the vacuum. This also happens for quarks and antiquarks in a strong gluon field, in the context of jet formation; see

      3) See (1); the near-field effects are off-resonance. Photons are on-resonance.

      4) See (1): the equation for a Green function G for a field phi is O(G) = J, where O is some differential operator and J is a source; the equation for a resonance is O(phi) = 0, for the same operator O.

      Said differently: the “virtual particle” i.e. Green function i.e. propagator satisfies an inhomogeneous linear differential equation, while the real particle satisfies the homogeneous version of the same equation.

  26. Dear professor Strassler

    I am so happy to have found your website. It has been extremely educating. thank you.  I hope you write the book(s). There at least two books: the perspective for the layperson; an undergraduate level for budding physicists. 

    I finished my doctorate in physics back in 1995 and became a patent consultant. My doctorate thesis was on magnetic thin films. I did some modelling work on the experimental results. The model explained a number of things especially interlayer magnetic spin coupling and it made some predictions that could be tested. After Presenting the model at a conference, a friend asked me a profound question: Abu is this what is really happening at the spin level in the thin films? I replied that the model fitted the data well and made predictions that could be tested and where tested. And so based on that it was a valid model. However, regarding his question in the final analysis I have to be honest and say I don’t know.

    Now coming to ‘virtual particles’, ‘quantum fields’, ( quantum mechanics) etc and their underlying models  they are indeed useful, powerful but in the final analysis do they describe reality that actually exists?

    Regarding quantum fields for some reason I always imagined them to be one-dimensional lines: is it better to think of them as volumes – since they fill all space? And is regarding the different (particle, force) fields as being intertwined a useful analogy when thinking about particle decay?
     Many thanks

    • In the case of the thin films, we do understand that there is another layer of reality below the layer that you were using to describe the phenomenon — so the question you were asked was well-posed.

      But when you ask “in the final analysis do they describe reality that actually exists?”, the answer has two parts. First, how do we know we are anywhere near a final analysis? There could certainly be more layers of reality beyond the ones we’ve encountered so far. What experiment can you imagine doing that could ever answer your question with finality? And if no experiment exists, is your question a scientific question, in the end?

      Furthermore, what does “actually exist” mean? can you imagine an experiment that tells you whether something really exists or whether it is just a useful tool for describing and predicting the world? Again, if there is no experiment, can this question be answered scientifically?

      As far as we know, the description of the world using quantum fields and so forth is an excellent way to think about the world that allows for a vast array of measurements to be predicted in advance. But we neither know this is a unique nor a final way to think about reality.

      Probably the reason you think of fields in terms of one-dimensional lines is because of what you know about the electric field, which is indeed drawn as field lines. But that does not work for all types of fields. Generally, a field is a function of space and time — start with that. It might just be a number at every point: F(x,y,z,t). In the case of an electric field, it would be a vector at every point: E_x(x,y,z,t), E_y(x,y,z,t), E_z(x,y,z,t); in fact you need to generalize this to include also the magnetic field to make it consistent with relativity, but this isn’t so important here. After Einstein, the gravitational field is a function with even more indices on it. For an electron field, you need a function that is a one-by-four matrix — etc. So this is to say that all fields are functions of space and time, but different types of fields, depending on their spin and perhaps on other properties, will actually be collections of functions, ones that can only be thought of in terms of field lines in the special case that the functions form a vector.

  27. I think you’re selling virtual particles short here.
    One way to think of Compton scattering is that the photon forms a virtual e^-e^+ pair, the virtual positron annihilates the original “real” electron giving off a photon and the “virtual” electron continues out of the Feynman diagram as the scattered “real” electron.
    So we can talk about things being on-shell and off-shell, but to say virtual particles aren’t real is, I think, too simplistic a view.

    • For some reason you misunderstood me; perhaps you can direct me to the point in the article where my meaning became confusing?

      I did not say (or at least, mean to say) that virtual particles aren’t real.

      What I said is that virtual particles are not particles — they are more generalized disturbances in fields. However, they are very real; they are responsible for all of the basic forces of nature.

      The example you gave (Compton scattering) is completely consistent with this. The “off-shell particle” is most definitely real, but it is not a one-particle state of the Hamiltonian. In fact it only looks like a single particle in first-order perturbation theory. That is to be contrasted with the photon and the electron in the initial and final state, which are one-particle states of the (all-orders) Hamiltonian.

    • Including a virtual electron-positron pair in Compton scattering makes the total cross section too small, and also does not match well to the Thomson scattering cross section (= 2/3 barn) at very low energies.

  28. The total cross section for Compton scattering in the non-relativistic limit is σ = (8 pi/3)(r_e)^2 = 0.66 barns. This is also the total cross section for classical Thomson scattering. If the total cross section for Compton and Thomson scattering included virtual pair production and annihilation, wouldn’t the cross section include a factor.α= e^2/h-bar c ?

    • No. First of all, r_e is not a real radius of anything; after quantum mechanics we understand that r_e = 4 pi alpha / m_e c^2 . So there is already an alpha^2 in the cross-sections. Second, the scattering process in Compton scattering is described in quantum field theory as

      photon + electron –> virtual electron –> scattered photon + scattered electron

      In an ancient notation (which is what the previous commenter was referring to) you could write this as

      photon –> scattered electron + virtual positron

      followed by

      electron + virtual positron –> scattered photon

      which has the same effect.

      Either way you need a virtual fermion somewhere. (Actually, depending on what frame you use, there’s another quantum contribution; but that too has a virtual fermion.)

      In all of these leading-order processes (to which there are additional quantum corrections) you get a factor of “e” at each “–>”, so that gives you e^2 in the amplitude, and thus e^4 ~ alpha^2 for the probability and the cross-section.

  29. I agree that there are two electron-photon vertices in Compton scattering, each with one real photon, and one real electron, and one off-the-mass-shell (virtual) electron or positron. However there is never a virtual electron-positron pair (bubble diagram) in Compton scattering, as suggested by Jack H above.

    • You are right that there is never a pair of virtual particles; at each step at most one is virtual, at leading order in perturbation theory. But I’m not sure Jack H really meant there was a bubble; I think he meant what I described in my answer. However, I agree his wording was ambiguous.

  30. Here is the definition of virtual particles by

    “Virtual particles are a mathematical device used in perturbation expansions of the S-operator (transition matrix) of an interaction in quantum field theory.

    No virtual particle physically appears in the interaction: all possible virtual particles, and their antiparticles, occur equally and together in the mathematics, and must be removed by integration over the values of their momenta.

    In the coordinate-space representation of a Feynman diagram, the virtual particles are on-mass-shell (realistic), but only 3-momentum is conserved at each vertex, not 4-momentum, so there is no immediate way of obtaining 4-momentum-conserving delta functions.

    In the momentum-space representation, the virtual particles are both on- and off-mass-shell (unrealistic), but 4-momentum is conserved at each vertex, and also round each loop (as shown by a delta function for each).

    In the coordinate-space representation, each virtual particle appears “as itself”, but in the momentum-space representation, it is represented by a “propagator” (a function of its 4-momentum).”

    The statement that virtual particles occur “equally and together” excludes the single off-the-mass-shell electron or positron in the Feynman diagram for Compton scattering.

    • Your point being?

      This definition is technically correct.

      What it doesn’t do is serve any deeper pedagogical purpose. And it leaves off the physics.

      There are real physical effects from non-resonant phenomena in field theory. Choosing to write those in Fourier notation so that you express them using the “mathematical device used in perturbation expansion” is the technical aspect of how you calculate their effects. But this entirely ignores the physics part.

      The physics part is that these non-resonant phenomena are responsible for:

      electrical and magnetic forces
      scattering of particles off one another
      all sorts of particle production processes
      the shifts in the strengths of forces as a function of distance (beyond the 1/r^2 force law)
      the shifts in the strengths of the electron and muon magnetic moments
      the interaction of the Higgs particle with photons
      and on and on and on…

      So to view these purely as a technical device is not complete; there is an enormous amount of physics here. But to view them as particles is also deeply misleading; particles are a resonant phenomenon. The non-resonant phenomena, for technical and historical reasons, tend all to be called “virtual particles” even though they aren’t particles at all.

  31. Prof. Strassler,

    I’m a little confused here. Doing a perturbation expansion is a purely mathematical procedure. But you seem to be saying that the individual terms in the expansion correspond to non-resonant phenomena, with real physical consequences. How do you make this leap?

    • Well — I see your point. There is a slipperiness here that I’m in danger of letting into my language… there are non-resonant phenomena (start with that) and now you have to figure out how to calculate them. Only at that point do you introduce a mathematical procedure and start drawing diagrams, and in particular expressing things in terms of propagators etc.

      Let me think about what has to be done here, pedagogically.

  32. I have a quick question: does the “electron field” have anything to do with the probabilistic distribution of the electron…or is this something completely different? I have a certain understanding of what an EM field is, but an electron field?

  33. Following on from Neil Fazel’s point: Do you think that the physics behind quantum electrodynamics is *fundamentally* perturbative i.e. there’s no way even in principle to formulate it “exactly”? My point being that, if you *could* formulate it non perturbatively, then the virtual particle question would never come up. You would have some other way to compute the effects that are currently computed using virtual particle contributions.

  34. Hi, I recently turned sixteen, so when you spoke about reading of virtual particles and not understanding them at the age of sixteen, my interest was piqued. This article helped solve my curiosity about virtual particles, although I do feel as though I still have a whole lot to learn. Everywhere else I looked didn’t really make any sense, but this did. I just wanted to say thank you. My knowledge is pretty limited, and I was wondering if you could give me links or ideas as to where I could learn more.

    • Hmmm. Beyond what I’ve told you, I think one has to start getting into the math. If you’re really interested in learning much more, it may be time to sit down and learn some real physics … especially about the phenomena of resonance, and about waves. And probably also about energy and momentum. A freshman physics course is probably what you need (and you can find on-line resources from major universities such as MIT if you’re impatient.)

  35. Hello there. A theoretical physics website has this to say about virtual particles:
    “If virtual particles were real, they would leave their trace in all methods of predicting certain phenomena, and they would assign the same properties to the virtual particles no matter which approximation method is used.

    However, the literature readily shows that the details of Feynman diagrams strongly depend on the perturbation scheme used: In light front calculations, one gets a completely different set of diagrams than in the more traditional covariant form. And in nonperturbative approaches such as lattice gauge theory or conformal field theory, the predictions do not involve virtual particles at all.
    The nonexistence of virtual particles in nonperturbative calculations (whether conformal field theory or lattice gauge theory) is proof that the virtual particle concept is an artifact of perturbation theory. Something whose existence depends on the method of calculation cannot exist in a strong sense of the

    What do you think of this?

    • From A.J. ““If virtual particles were real, they would leave their trace in all methods of predicting certain phenomena, and they would assign the same properties to the virtual particles no matter which approximation method is used.”
      Pair production of electrons and positrons is a well-known component of gamma-ray attenuation (in addition to Compton scattering) above 1.02 MeV, and has been used to produce positron beams from high energy bremsstrahlung since the late 1950’s. Since 1965, the best estimate of the pion mass has been based on measurement of the x-ray transition energies of negative pions bound in atomic levels of various elements (Prior to this, the pion mass was estimated by measuring lengths of tracks in nuclear emulsions). Is the i/r-squared radial dependence of the Coulomb field assumption valid in pionic atoms, when the pion is so close to the nucleus?

      In 1935, Uehling (Phys Rev Vol 48, page 55) showed that the Coulomb field near a nucleus varied from the expected 1/r-squared radial dependence by a new term which he called “vacuum polarization”. Certainly in pionic atoms, there is not enough energy in the atomic binding energies to create electron positron pairs, so what is this “vacuum polarization” term proposed by Uehling? Uehling states;
      “According to Dirac’s theory of the positron, an electromagnetic field will, in general, induce a charge and current distribution due to the creation and annihilation of electron-positron pairs. The induced fields produced by the electron-positron distribution may be regarded phenomenologically as corresponding to supplementary terms in Maxwell’s equations. Since one must demand the validity of [Maxwell’s] equations in sufficiently weak and slowly varying fields, ………. these these [supplementary] terms must depend on higher powers of the field intensities, …….. whenever the fields vary appreciably in a distance of the order of h-bar/mc [electron Compton wavelength], under which circumstances an appreciable polarization electron-positron distribution can exist.” Uehling refers to this as “vacuum polarization”.

      This vacuum polarization proposed by Uehling is a very large correction to the atomic energy levels in pionic atoms, and represents a many standard deviation effect in the pion mass measurement. The pion mass can also be measured by looking at the kinematics of pi-plus 2-body decay into a muon and neutrino, and this confirms the presence of the vacuum polarization term in the Coulomb field at small distances.

      So the vacuum polarization correction to the 1/r-squared law is real, and can be accurately phenomenologically represented by induced creation and annihilation of electron-positron pairs. Is it just an accident that this correction to the Coulomb field is accurately represented by a pair of induced charged particles that have both the charge and mass of electrons and positrons? Is this “vacuum polarization” just an artifact of perturbation theory? Is there another non-perturbative scheme, as proposed by A.J., that yields the same result? i think not. If it looks like a duck, and quacks like a duck, then what should we call it?

      • I think you need to distinguish between virtual particles which show up as internal states of Feynman diagrams (i.e. in perturbation theory), and virtual particles as “disturbances in a field” (e.g. in vacuum polarization). The virtual particles in the latter category are very much real. The virtual particles in Feynman diagrams are mathematical constructs.

        I think the confusion arises when people draw a particle interaction diagram showing production of outgoing particles from incoming particle via intermediate disturbances in the fields, and call that a Feynman diagram. First of all, the interaction may not even be perturbative, so talking about Feynman diagrams is not valid; and even if it were perturbative, there are an infinite number of Feynman diagrams in the perturbation expansion corresponding to that single interaction diagram.

    • This is basically right, yes. though it does leave one thing out; see below.

      My statement that virtual particles aren’t particles at all, but are disturbances in fields, is designed to be as consistent as possible with these statements. Those disturbances are very complex. Only in perturbation theory do we have a way of talking about them in a simple way — and indeed, as the author says, there are multiple ways of talking about what they are and how they work.

      Real particles are things you can hold, kick, absorb and study. Virtual particles cannot be isolated and studied — only more general effects of these general disturbances can be studied. What the author leaves out is that those general effects ARE measured and studied, and in fact are hugely important — Casimir effect, changing of the strengths of forces away from the 1/r^2 approximation, scattering of photons off each other, etc. I’m sure he would agree, he just was making a different point… which is that when you express those general effects using nice pictures of particles running around inside of Feynman diagrams, you’re using a particular calculational technique, and not making a statement about the “true nature” of those generalized disturbances. You could have used an entirely different calculational technique and gotten the same answer without ever drawing diagrams of virtual particles running around.

  36. Hello Professon Strassler,
    Thank you for a great article. I have a question if these messy disturbances (formerly known as “virtual particles”) can be weaker than real particles. In the text about Higgs boson decay into 2 Z bosons I found that one of the Z particles must be virtual (because 2 real Zs are heavier than 1 Higgs). But the “virtual” Z is still somehow there: it is a disturbance in the Z field. So the Z field is disturbed and there is something like a “fraction” of Z boson? Something lighter than a real Z? That would imply that elementary particles are not the dimmest possible waves in the field. But I’m probably misunderstanding something.

    My second question is about the statement that electron spends part of its time as a combination of photon and electron disturbance. Are there some clearly definite separate times when the electron is only electron and then for a nanosecond it is a combination of disturbances? Or the electron is somehow always someting like a quantun superposition of all these variants (i.e. pure electron, combination of electron and photon, combination of other things disturbed by various fields)?

    • For quanta (i.e. the things we somewhat misleadingly call “particles”) you should not confuse “lower in energy” with “weaker” or “dimmer”. There’s no connection.

      A wave has a frequency (how often does it wiggle) and an amplitude (how far does it wiggle.)

      Particles are lower in energy if they have lower frequency.

      A real particle is the wave of lowest possible amplitude (in a corresponding field). If it is at rest, it has its minimum frequency and energy, corresponding to its mass. If it is moving in some direction, it has a higher frequency and energy. No matter what, its amplitude is the smallest allowed.

      Understanding this is key to understanding Einstein’s insight that led to his explanation of the photo-electric effect.

      A generalized disturbance (corresponding to one or more virtual particles) doesn’t have to satisfy any of these conditions.

      In the end, the electron is the electron. You can write it as a quantum superposition of a free non-interacting electron, a free non-interacting virtual electron along with a virtual photon, a free non-interacting virtual electron along with two virtual photons, a free non-interacting electron along with a virtual muon-antimuon pair, etc. So the electron is always partly all of these things, and no, there aren’t special times when it is one thing rather than the other.

      • Thank you very much for the response. So the virtual Z in Higgs decay has lower mass (energy, related to its frequency) than real Z (when being at rest). But the virtual Z does not have smaller amplitude than real Z.

  37. Professor Strassler-
    Thank you for this illuminating reply. I do have a question about your statement concerning the relationship between a free electron, and a virtual electron and a virtual photon, as shown in your Figure 4 on the Feynman diagram in your original post. A real electron, regardless on how fast it is moving, has an invariant mass (squared) of E^2 – (pc)^2 = (mc^2)^2 = (0.511 MeV)^2. Similarly, a photon has an invariant mass of zero. Do the real electrons on both sides of the virtual particles in Figure 4 both have an invariant mass of 0.511 MeV? What about the invariant masses of the virtual electron and photon in Figure 4? Are they still 0.511 and zero MeV respectively, or does the combination of the virtual electron and virtual photon preserve the invariant mass of the free electron? Thank you.

    • Virtual particles do not have the mass of the corresponding real particle. A virtual particle can have any mass, including a negative mass-squared (i.e. a mass that is imaginary) by having more momentum than energy instead of the other way round.) It’s a very bad idea to think about a virtual particle as being something like a particle; it’s not a particle, it’s a generalized disturbance in a field, and it doesn’t obey the rules particles obey. Energy and momentum are conserved in Feynman diagrams at each vertex in the diagram, so the combination of the virtual photon and virtual electron into which the real electron has dissociated has the same energy, momentum and invariant mass of the real electron that entered and exited the diagram.

  38. Professor Strassler. Thank you very much for your reply.
    So could I then say that a particle is a real particle only if its invariant mass (E^2 – (pc)^2) is its real mass^2, and a virtual particle if its invariant mass is not its real mass.
    Earlier, Neil Fazel | July 15, 2012 at 12:03 PM | replied:
    “I think you need to distinguish between virtual particles which show up as internal states of Feynman diagrams (i.e. in perturbation theory), and virtual particles as “disturbances in a field” (e.g. in vacuum polarization). The virtual particles in the latter category are very much real. The virtual particles in Feynman diagrams are mathematical constructs.”
    With respect to the electron – positron loop (vacuum polarization) in the external Coulomb field (the Uehling correction), are the electron and positron in the loop both real particles as Neil Fazel states, in the sense that their individual invariant masses are both 0.511 MeV? If so, wouldn’t they be free particles, like in pair production? Thank you.

    • To pre-empt any confusion, I used the term “real” to mean that it is something more than a mathematical construct. If I understood the Professor correctly, the electron and positron in vacuum polarization represent (real) “disturbances in a field”, but not particles. But if, somehow, the disturbances acquire enough amplitude in a short enough time, they could become real particles.

      • Does it mean that the virtual particles in Feynman diagrams do not represent any disturbances in a field? From what I understand, they represent mathematical terms in “perturbation expansion”. But it should be an expansion of something. For example the terms in Fourier expansion, when added together, they form a function. So there should still be some “disturbance in a field”, even in the case of the Feynman diagrams. However I have never seen these things really written down mathematically, so I don’t know. Is my understanding confused?

  39. Dear Professor Strassler,

    I was reading on virtual particles, and came across an interesting thought. There is this “sea” of virtual particles at any given point in the vacuum. While I understand the concept that really the only difference between real and virtual is a very subtle one, on whether we can “see” it or not, and if it does or doesn’t violate the conservation laws. From this idea I have four questions- If an electron spits out any virtual particle of sorts, wouldn’t that electron itself become virtual momentarily because two objects bound together cannot split apart without energy from outside the system, even if this effect is immeasurable? Secondly, Dirac predicted the positron with these concepts, virtual particles as pairs. Is this pair of particles actually a pair, or is one merely the appearance of existence of the newly turned “real” particle’s anti-particle, because, when observing a system of, say electrons, if one electron leaves it appears a positive charge is now present? Thirdly, For these virtual particles to become “real” a transfer of energy must occur from a real particle to the virtual particle, so is it possible that a real particle that hit a virtual particle and gave sufficient energy to make them now both real, could lose energy as it travels through the vacuum of space? Is this possibly what we observe as mass, with particles interacting with the higgs field? I also read about how real particles can condense in a vacuum from virtual particles if arranged just right. What does that mean, how do they have to be arranged? If this is true, is it because of Einstein’s binding energy concept? Thank you very much for your time. It is very much appreciated.

    Sincerely, Stone Oliver

  40. Hi,
    You say “forget about the virtual particles, it`s just that the particle disturbs the field”. My simple question: HOW?

    • The way nature works is that fields interact with each other; a particle is a ripple in one of the fields, and the interaction of that field with other fields disturbs them. There’s no “how” to that — it’s simply what nature does. You’re asking me to define the fundamental processes of nature in terms of even more fundamental things — well, as far as I know, there’s nothing more fundamental than this.

      I can write some equations that show you how this works. But I can’t tell you something more basic than the interactions of fields with one another.

  41. Hi Matt,

    I am glad you think that virtual “particles” are real. There seems to be a movement in some European circles that they are not real. For example, I got booted off for arguing that they are real and you can see the link above to Arnold Neumaier’s FAQ (a advisor). I sort of get your drift that you want to call them disturbances but my particle physics instructor, Dr. Andy Inopin, taught me that they have all the same exact properties as their “real” counterparts except they are simply “off mass shell” and can’t be detected. Well.. of course if they are detected, they become “real”.

    Take muon decay as an example. If there isn’t a real virtual W boson involved, the muon could never decay. That virtual W boson has all the same properties as a “real” W boson except for it is “off mass shell”. So your “disturbance” here sure smells like a W boson particle. 🙂 Now, I think that with lower energy Coulomb type interactions, the “disturbance” connotation could be appropriate. Perhaps you mentioned that above as I did not read all of the preceding comments.



    • You are putting huge numbers of words in my mouth here. Your example of the W boson in the case of muon decay is exactly opposite to what I said. You say “your disturbance sure smells like a W boson particle”. Obviously you have a serious problem with your nose. I said very specifically: “`virtual particles’ are NOT particles”; particles are resonances, virtual particles are not. They can even have negative mass-squared (does this not bother you?)

      • I know it is opposite of what you said. I suspect most particle physicists would disagree with you about the example of muon decay with the virtual W boson being just a “disturbance”. I would think it is in fact a temporary resonance that has all the properties of of a real W boson except for its mass. So there is a possible counter-example to your “disturbance” hypothesis. There are of course many others. In particle physics, the term “virtual particle” has a very specific meaning. It simply means a particle that is “off mass shell”. Griffiths’ says in “Intro. to Elementary Particles”, “Actually, the _physical_ distinction between real and virtual particles is not quite as sharp as I have implied. If a photon is emitted on Alpha Centauri, and absorbed in your eye, it is technically a virtual photon. However, in general, the farther a virtual particle is from its mass shell the shorter it lives, so a photon from a distant star would have to be extremely close to its ‘correct’ mass — it would have to be _almost_ ‘real’.”

        What is an example of a virtual particle that has “negative mass squared”? I would suspect it may be related to momentum. Thanks.

        • Your suspicion is wrong. And the fact that you have never heard of a virtual particle with negative mass-squared puts a knife into your credibility. [Check: what is the mass-squared of a photon exchanged between an electron and a nucleus?]

          Go learn some quantum field theory, and don’t bother me with irrelevant statements [such as Griffiths’ correct, but obvious, point] until you understand the main difference between a propagator (which can have any mass and a relatively arbitrary functional form) and a particle (which is a pole in that propagator, has a definite mass [possibly with a non-zero width] and is controlled by theorems that do not apply to the propagator.) The fact that two things are continuously connected does not make them equal; yes, the distinction between a virtual particle and a real particle is only sharp if the particle has an infinite lifetime, and even then, there is a limit you can take where one resembles the other (as in Griffiths’ example) and that’s even critical in doing calculations; but no, that doesn’t mean you should view them as simply equivalent. And I’m trying to explain physics to the public on this site, not to experts, for whom this subtlety would need to be properly explored.

          On the example of muon decay; let’s take, instead, the scattering of an electron off a positron to make a W+ and W-. There are three interfering processes, one with a virtual photon of positive mass-squared, one with a virtual Z of positive mass-squared, one with a virtual neutrino of negative mass-squared. Are they all particles? Or are some more “particle” than others? Oh, and that’s only at lowest-order in the quantum field theory. There are also processes where the electron and positron turn into multiple virtual particles with all sorts of different mass-squareds that we have to integrate over. Are these all to be thought of as particles, even though within the integration the mass-squared will vary from negative across zero to positive? And there are several interfering processes, while we’re at it; how are you thinking about these?

          It’s a mistake to view these things as particles. A fundamental mistake. The W particle that appears in top quark decay is different from the W virtual particle that appears in muon decay, or that allows a neutrino to scatter off a nucleus and turn into an electron. The issue is the lifetime. A W particle has a lifetime that corresponds to a width of about 2 GeV. A W particle that is much further off-shell than 2 GeV decays away not because of damping but because it is non-resonant; a W particle that is much less off-shell than 2 GeV decays away due to damping, not due to being off-resonance. Again, these are continuously connected, but so is a young man and an old man; so are red and yellow; that does not make them equivalent.

          I trained under Peskin, Susskind, Banks, Seiberg, Witten, Shenker, and Wilczek, and my research in quantum field theory and my teaching of quantum field theory’s many subtleties is well-known. My readers don’t need your advice.

      • Apparently Fred D. would prefer to jump to the conclusion that he was censored rather than investigate the comments section of this site a bit to test his hypothesis. Had he put in the time and effort to follow the scientific method and inform himself of the evidence at hand, instead of skipping the data-gathering process altogether and mistaking his layperson’s ignorance for expertise in the field of site moderation, he’d have discovered that all nested replies here (not just his) go only two layers deep. If the work required to become an expert in this area is too daunting for him, he’d do well to listen to those who’ve devoted their careers to doing just that.

      • @Matt,

        Yes, sorry about that as I realized WordPress has a defect in the way their thread reply works after I posted my reply on SPF. I am used to the FQXi blogs that have the reply link properly at the end of the thread you want to reply to. I have posted a correction to SPF.

  42. Dear Mr Strassler,
    1st THANK YOU! I love this explanation, I got the whole fritjof capra’s “tao of physics” wrong and you explained me a fundamental bit of information that helped me realizing this.
    2nd I still need a bit of information to understand what you explained: what you mean by “ripple” and “disturbance” in a field? What makes a “ripple” in a field a particle that does not the same of a “disturbance”?
    3rd A topic-related question: How decay processes can be described in terms of field disturbances?
    4th I just read “particles are resonances” in the comment above, what does it means?

    Please notice, if you are going to answer (in which case I thank you again), keep in mind that I’m not familiar with the math behind quantum physics, I studied only basic physics in a computer science bachelor. In other words I do not speak FourierTransformish nor DoubleIntegralese and know only some words of Derivish 😉

    • Derivish! My favorite.

      Roughly: a ripple is a sine wave, a solution to some form of wave equation. A disturbance is not a solution to the wave equation; it is a solution to an equation which has the same form on the left-hand side of the equation but has something non-zero on the right-hand side.

      A resonance is something that is easy to make: you know that no matter how you hit a tuning fork or bell, it will always ring with the same tone, i.e. vibrate with its resonant frequency. A disturbance, in my language, is a non-resonant process; for instance, if you try to make a tuning fork or bell vibrate at a frequency which it doesn’t prefer, or make it shake in some non-repetitive way, you can do it, but you have to work hard. If you do anything particularly energetic in the universe — say, set off a supernova — you will make lots of particles; you will be much less likely to make all of the more general types of disturbances, and to the extent you do, they will turn into particles very quickly.

      Decay processes are not necessarily related to field disturbances — can you clarify your question? What example are you thinking of?

  43. so, if I got it right, by ripple you mean a specific kind of oscillation in the field, with values that come out of a set of equations, a stable one; while by disturbance you mean another kind of oscillation, that has different values and is not stable. Are there other peculiar properties that are different between particles and virtual particles besides stability?

    As for the Decay process, I was thinking of something like W boson in muon decay , what I’d like to know is how the resonant ripple turns to other things in this view. By “how” I mean how you describe the process, what does it mean that a particle can turn in other particles in terms of a wave turning into other waves or combinations of waves.

    • You’ve only partly got it right; but to really get it right we do need to do math. It would be very easy to explain with equations.

      “Virtual particles” is really a term that has multiple meanings capturing many non-particle processes in quantum field theory, and even if I used math I’d have to give you quite a few examples. Particles, on the other hand, are very easy to describe. I simply would not ask your question “are there other peculiar properties that are different between particles and virtual particles”; there’s almost nothing about “virtual particles”, viewed in general, that is similar to the corresponding particle, other than that they carry the same electric charge and other similar conserved quantities [but that’s just because the charge is something the field has, and the particle, as a ripple in the field, inherits it.]

      Do you understand my example of the swing, and the difference between a resonant and non-resonant process?

      The W boson in muon decay is not a particle; it is “off-shell”, which is technical jargon for the statement that it is representing a non-particle disturbance in the W field. So there is no resonance in the W field in this case.

      How one wave (resonant or not) can turn into other waves is something I plan to explain in the coming weeks, in my series on how the Higgs field works. Please stay tuned for that.

      • “Do you understand my example of the swing, and the difference between a resonant and non-resonant process?”
        I think so! the resonant process should be (like?) a stationary wave, right? While the non-resonant is a wave that is not stable in the medium it travels in and will rapidly degenerate, eventually leaving a static wave behind.

        “How one wave (resonant or not) can turn into other waves is something I plan to explain in the coming weeks, in my series on how the Higgs field works. Please stay tuned for that.”
        I’ll try, if I remember of anything when back from holydays 😉

  44. You write: ”But there is so much energy trapped inside a proton that there is enough to make those virtual quarks and anti-quarks almost real”. You also write that energy does not make the ripples or disturbances (of fields), but that the fields (which are fundamental) contain energy: “A field is one thing; energy is something it can have, but there is no such thing as an energy field”. “Can have”; so are there fields containing no field energy? Or are these two things always married? “A particle has energy through its mass and through its motion”. How about a field containing no particles and not moving? I do understand there is no such thing as “pure energy”.

    Or did I get it right? Does energy make the ripples (and disturbances)? If not, who does? Who creates the sine (or not-sine in disturbance)?

  45. You write: “Yes, all fields related to the known elementary particles are believed to exist everywhere in space, and at all times. There is just one electron field that is everywhere in the universe. What makes the Higgs field different from the other known fields is that it is non-zero on average everywhere in the universe, while, say, the photon field [i.e. the electric and magnetic fields treated together] and the electron field are on average essentially zero”.

    Question: take for ex. the Z-field (or other weak force bosons or quarks and gluons). They do not exist “everywhere in space and at all times”. Their range is very limited. Or did I get it wrong (again)?

    • You are probably confusing fields with particles. The fields exist all the time everywhere. Particles are something that may or may not appear in a field and may have limited range or life time. But the background field is always there. No matter if any particles run through them. I hope I got it right.

  46. So fields exist everywhere all the time. These fields have to be Lorentz-invariant, so any observer in any inertial (non-accelerating) Lorentz frame would always see the same field. This would not be true of either individual electric or magnetic fields because an E field Lorentz-transforms to a B field, and vice-versa. So how can these fields be Lorentz-invariant?

    • Because in vacuum, the electric and magnetic fields are zero. And zero is Lorentz invariant.

      Only the vacuum, and the laws of nature in vacuum (in regions that are relatively small compared to the universe as a whole) are Lorentz invariant.

      Indeed, if there is a magnetic field in your vicinity, Lorentz invariance is locally broken. However, then you have to look at physics more carefully, because the effect of Lorentz violation may or may not be important on experiments that you are doing. For example, there are magnetic fields inside the Large Hadron Collider [LHC] experiments, and those break Lorentz invariance. However, they are so (relatively) small that they have only a very tiny effect on the particle-particle collisions that occur inside the LHC, so Lorentz invariance is still true to very high accuracy in those collisions.

  47. Agreed. The laws of nature are Lorentz invariant, and there is no preferred inertial frame. But previous posts state that “[These] fields exist all the time everywhere.”

    So what kind of fields can be Lorentz-invariant? Can a Higgs field, for example, be Lorentz invariant?

  48. Strassler: “Yes, all fields related to the known ELEMENTARY PARTICLES are believed to exist everywhere in space, and at all times.”

    Martin: “You are probably confusing fields with particles. The fields exist all the time everywhere. Particles are something that may or may not appear in a field and may have limited range or life time. But the background field is always there. No matter if any particles run through them. I hope I got it right”.

    So,sorry I am milking (don´t get nervous): does for ex the Z-field exist ” everywhere in space, and at all times”, although there are no Z-particles in the vicinity? Or the gluon field? If the answer is, that in spite of the range all fields always exist everywhere in space, so why do the different particles (“forces”,fields?) have different ranges? The answer can not be mass of the interaction particles, because gluons are massless. I can understand why weak force is weak (and has short range); the Z and W particles have big mass, they are lazy.

    • I’m no expert, so I’m just telling you what I understood from Professor’s explanation: yes, the Z-field exists everywhere in space at all times, although there are no Z particles anywhere. The only important thing: the value of the field is zero (on average). The field does exist, but is zero, until you disturb the field somehow (through a disturbance in another field that interacts with the Z-field).

      Why the different particles have different ranges? In this matter I’m not 100% sure, but in case of the gluons (which are massless) it is probably due to the confinement because of the color charge. Weak force has limited range probably because its bosons are very massive and they decay quickly into other particles. Photon does not have any such constraints, so it can get to great distances.

  49. Hi, Mr. Strassler! I feel so fortunate to have found your website–in particular your posts on the composition of protons and explanation of virtual particles. I have a question regarding virtual particles: Do you know, or can you guess why some people have written that virtual particles (VP) are merely mathematical artifacts of perturbative quantum field theory, and thus VP have no ontological basis? Should I just ignore those people (I’m being sort of glib)? By the way, I’ve also read articles by Frank Wilczek which generally correspond to what you have written about VP. Can you set me straight? Thanks!


  50. Hi Matt, I’m a theoretical particle physicist PhD that ended up in biophysics for 20 years. What’s your thoughts on these virtual particle conundrums:
    1. If virtual particles aren’t real (in some sense) why do calculated probabilities depend on properties of virtual particles (eg B0-B0bar mixing box diagrams depend on top quark mass etc)? Although one can say they are ‘integrated out’ that’s not entirely true, the processes depend on virtual particle properties like mt. And, forgive me, I have not been able to read all of the above entries. Related, how would a non-perturbative treatment of B0-B0bar mixing hope to involve the top quark mass? If virtual particles are in some sense real, what sense and what do they mean non-perturbatively?
    2. A fun one here re-quantum gravity. I’ve never had enough time to get into this. Would quantum gravity do away with curved space time or simply account for it?
    3. How would virtual gravitons (in a calculation) escape from a black hole so that the black hole could, act like a black hole, and suck things in? Presumably their virtualness . .
    Regards – Paul

  51. Martin: “Why the different particles have different ranges? In this matter I’m not 100% sure, but in case of the gluons (which are massless) it is probably due to the confinement because of the color charge.”

    I do know what confinement means. But that is just a word. It does not give an answer to my question. If the fields are around everywhere and all the time, what determines (and why) the different ranges? Weak force is weak and has a short range because of massive bosons (that´s easy), but why is strong force strong and has a short range although gluons are not weak and massless. So how does the “confinement” do the trick?

  52. Hi, Professor Strassler! I’m with Kevin (August 14, 2012), I feel so fortunate to have found your website–in particular your posts on virtual particles. I have the same basic question as Kevin’s regarding virtual particles: Do you know, or can you guess why some people (Physicist Arnold Neumaier, have written that virtual particles (VP) are merely mathematical artifacts of perturbative quantum field theory, and thus VP have no ontological basis? Should I just ignore those people (I’m being sort of glib)”

    Some quotes from Professor Neumaier:

    “Virtual particles are part of the imagery of quantum field theory. They are figurative language for abstract mathematics, used by experts and laymen as imagery for giving abstract recipes for calculating scattering amplitudes an appearance of intuitive meaning. However, any attempt to take this language literally gives a very misleading and unscientific view of the microscopic world …
    Therefore virtual particles ”exist” as lines on paper, as intuition in people’s minds, as superficial but catchy allusions to images that make abstract things concrete, but not as tangible, verifiable entities. On the level of physics, virtual particles are quite similar to what ghosts are on the level of ordinary experience. One cannot ascribe to them most properties that real things have. One can only ascribe to them the properties of internal lines in diagrams and multidimensional integrals in perturbative computations. Once one attempts to ascribe to them more, one gets nonsense.
    Since virtual particles are defined only in terms of the Feynman diagrams, they describe asymptotic properties
    of the scattering, not an actual motion (which would be described by some process at finite times). Thus virtual particles don’t ”move”. They are ”exchanged”, but it makes no scientific sense sense to talk about their motion, their speed, or about the direction they travel, This is meaningless talk, and asking about such properties is like asking for the speed of a ghost.
    Thus it seems impossible to place the superficial virtual particle picture on a sound scientific footing. It is a picture valid only if restricted to the superficial level where no detailed inquiries are made. It is like ordinary people using the word ghost to describe a fleeting but fear-provoking experience. It makes sense only as long as you don’t ask about their precise properties. But once you start asking how fast a ghost is traveling, things no longer make sense, since the concept of a ghost is not intended to be applied literally.”

    In response to A.J | July 13, 2012 at 9:18 PM | You reply, “What the author (Professor Neumaier) leaves out is that those general effects ARE measured and studied, and in fact are hugely important — Casimir effect, changing of the strengths of forces away from the 1/r^2 approximation, scattering of photons off each other, etc. I’m sure he would agree, he just was making a different point…”

    However, Professor Neumaier writes, “How can anything be real if its existence depends on a particular way of viewing the world? How can an experiment (verifying the Casimir effect, say) can be said to prove the existence of virtual particles if the same experiment can be explained by a method of calculation not involving virtual particles at all?”

    You make virtual particles sound influential and at least potentially real, “a disturbance in a field can become a “real” particle with the addition of more energy.” This had always been my assumption about virtual particles but Professor Neumaeir’s posting thru me into confusion.

    Please help me understand any differences, if any, between your view of Virtual Particles and Professor Neumaeir’s.

    Joe S.

    • Hmm… The main difference between me and Neumaier seems to be one of definitions, not substance. At least I think so. [I was quite wrong — see Fred’s comment below. Neumaier and I agree virtual particles as lines in Feynman diagrams are fictions, but the conclusion that he draws, which is inconsistent with quantum field theory, I completely disagree with. And so does data from lattice simulations of quantum field theory, which makes no reference to virtual particles, gets the right answer for ratios of hadron masses, but certainly disagrees with Neumaier’s conclusion.]

      Disturbances in fields are real. I *think* Neumaier would agree. The Casimir effect proves the existence of quantum disturbances of fields that are not particles. So do atoms and other bound states, through both their existence and the subtle effects that one must account for to get their binding energies correct.

      Now the question is: do you call those “disturbances in fields” by the name “virtual particles” or not? I think Neumaier is taking a strict perturbative Quantum Field Theory definition of what a virtual particle is (a line in a Feynman diagram) and so he would say (I think) that disturbances in fields may be real, but expressing those disturbances in terms of lines in Feynman diagrams (which is a *calculational technique*, and not necessary) involves introducing non-real artifacts. I agree with that statement. He happens to call the “lines in Feynman diagrams” by the name “virtual particles”. Strictly speaking that’s what one should do in a technically accurate and precise context. So I don’t disagree with his approach.

      I took a different line of approach. I said: Feynman diagrams (and the lines in them) are a calculational approach, but disturbances in fields are real. Since the name most non-experts know for “disturbances in fields” is “virtual particles”, I decided to stick with the name “virtual particles” but redefine it slightly so that it actually does mean something physically real.

      The merit of Neumaier’s approach is philosophical precision with very clear definitions. The merit of my approach is that the words “virtual particles” are widely known among non-experts (and widely used in the field and when talking to the public) and they aren’t going away. But the two approaches agree that the calculational tool known as Feynman diagrams — and the specific way that virtual particles appear there — are not representative of something real, because the calculation can be done in other ways.

      I think the two approaches also agree that in a physical process, certain fields are disturbed a lot more than others — and that this statement can be assigned reality because no matter how you do the calculation you’d come to that conclusion. For example, we may or may not choose to calculate the shift of the magnetic moment of the electron using Feynman diagrams and the specific way that virtual particles appear there. But I think we’d agree that a disturbance in the electromagnetic field is responsible, because the result of the calculation (no matter how you carry it out) is proportional to the strength of the electromagnetic force.

      Amusingly, the title of the paper that became my Ph.D. thesis was “Field Theory Without Feynman Diagrams.”

  53. Thanks for your thoughtful response to my September 2, 2012 posting. Your explanation preserves the “reality” of virtual particles with the understanding that the physical effects of their reality can be calculated with or without the use of Feynman Diagrams. In the context of this discussion, the title of you thesis is truly funny. Again thanks for your time.

    Joe S.

    • Hi Joe,

      Neumaier’s position is from the notion that he believes the Coulomb field of an elementary charged particle is not quantized but remains as a pure classical field. There was a substantial discussion on sci.physics.research with him about this if you are interested.!topic/sci.physics.research/c-hWst9vu68/discussion

      Of course if you take that particular position, you will have to reject the notion that virtual particles are real. In Matt’s language then the Coulomb field of an elementary charged particle is just one big disturbance. But I suspect that Matt would have it as a disturbance of a quantum field whereas Neumaier has it as a disturbance of a classical field.

      As I mentioned previously in this thread, I was taught that the only difference between a real and virtual particle is that the word “virtual” simply means “off mass shell” and all other quantum properties of the particle remain the same. Though quantizing the Coulomb field is a bit of a tough nut to crack, I simply think of it as the quantum vacuum is a polarizable medium and the Coulomb field (and magnetic fields) are a “tilt” of virtual fermionic pairs due to the presence of the elementary charged particle. In that viewpoint, the Coulomb field is quantized and I think agrees with Matt’s “disturbance”. A problem with keeping the Coulomb field as a classical field is instantaneous action at a distance. So I have to reject Neumaier’s position. Besides all that, if you reject that quantum particles can’t be momentarily “off mass shell” you are rejecting the uncertainty principle.


      • Wow. If that’s Neumaier’s conclusion, then indeed, as Fred suggests, I completely disagree with that!!!!! There is no consistent theory of an electron coupled to a classical electromagnetic field in which the electron can also emit discrete photons in scattering processes, as real electrons in our world do. That’s a physics fact that has nothing to do with whether or not you choose to calculate using Feynman diagrams.

        However, Fred, your notion of virtual particles being the same as real particles but “off-mass-shell” is a perturbative notion that does not survive to the fully non-perturbative theory.

        At best, real particles are poles in propagators (possibly off the real axis) and they satisfy various theorems. The virtual particles do not satisfy these theorems. Another way to say this is that the propagators can take a wide variety of functional forms, depending on how the interactions in the field theory work; but a pole in a propagator has universal properties.

        And even this statement isn’t correct. Most propagators that have the relevant poles aren’t even gauge invariant [for example, the electron propagator isn’t.] You really have to look at asymptotic states of the theory and their scattering amplitudes, very carefully defined. In the end the whole relation between real particles (which are things that really exist and are, for instance, gauge invariant) and any notion of virtual particles (which aren’t in general gauge invariant) completely falls apart.

  54. Hi Fred D.
    Thanks for looking more deeply into this. I tried reading the forum you suggested but the format is too hard to follow. I thought Professor Neumaier’s position on virtual particles was odd and I’m glad you flushed it out more explicitly.
    Joe S.

    • See my answer above. It seems Neumaier has some correct things to say about virtual particles, but then leaps to a conclusion that isn’t at all justified (and is surely contradicted by the successful numerical simulations of quantum field theory, where one does not use virtual particles in the calculational technique but certainly treats the fields around particles as fully quantum mechanical, not classical as Neumaier suggests.)

      • I sure would like to see a calculational technique that could get the correct lifetime for muon decay without a virtual W boson involved in the procedure. You are screwed right out of the gate since you have to have an outgoing muon neutrino that carries off the quantum number for muon-ness and another charged particle with spin 1 or 0 that carries off the charge and can decay to an electron and an electron anti-neutrino. There is only one particle that we know of that fits the bill. A W boson with spin 1 since there are no charged elementary particles with know of with spin 0. And has to be way off mass shell. But it still has all the other quantum properties necessary for the decay to happen.

        • At leading order in perturbation theory, the case of muon decay is especially and misleadingly simple, since there is no interference in the amplitude. The amplitude contains one and only one pole, so all calculational techniques look the same; the amplitude-squared is given by the square of a single propagator, and no matter how someone obtains the answer you can call it a virtual particle if you want.

          So let’s instead consider something a little more complicated: e+ e- –> photon photon . There are two Feynman diagrams, each with a virtual electron; of course the virtual electron is different in the two cases. Now the final answer for the amplitude-squared does NOT take the form of a single propagator-squared. So if I can write down the amplitude using other techniques, I never have to see the two propagators, and there is no sense in which the result is obtained by summing up two diagrams with virtual electrons.

          Well, in fact those techniques exist. They go back a long way, decades in fact.

          For more complicated processes, for instance e+ e- –> 4 photons, the number of graphs explodes, but the amplitudes do not become wildly more complicated. Rather than cope with all the cancellations that have to happen in Feynman diagrams, you may be better off doing the calculation another way.

          For instance, at tree level you can use something like

          Recursive Calculations for Processes with n Gluons.
          Frits A. Berends, W.T. Giele (Leiden U.). Dec 1987. 41 pp.
          Published in Nucl.Phys. B306 (1988) 759

          In fact this technique is always incorporated in the faster computer calculations of scattering amplitudes, see for instance .

          At loop level you could use Bern-Kosower from 1991 , though there are more powerful techniques now that build the loop amplitudes from tree amplitudes using unitarity, such as

          One loop n point gauge theory amplitudes, unitarity and collinear limits.
          Zvi Bern (UCLA), Lance J. Dixon (SLAC), David C. Dunbar (UCLA), David A. Kosower (Saclay). Mar 7, 1994. 53 pp.
          Published in Nucl.Phys. B425 (1994) 217-260
          e-Print: hep-ph/9403226

          And more recent breakthroughs have helped a lot:

          Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills.
          Ruth Britto, Freddy Cachazo, Bo Feng (Princeton, Inst. Advanced Study). Dec 2004. 35 pp.
          Published in Nucl.Phys. B725 (2005) 275-305

          One-Loop Calculations with BlackHat.
          C.F. Berger, Z. Bern, Lance J. Dixon, F. Febres Cordero, D. Forde, H. Ita, D.A. Kosower, D. Maitre (MIT, LNS & UCLA & SLAC & Saclay). Jul 2008. 7 pp.
          Published in Nucl.Phys.Proc.Suppl. 183 (2008) 313-319
          e-Print: arXiv:0807.3705

          None of these techniques require discussion of virtual particles in any strict Feynman Diagram sense; they really use complex analysis, fact about quantum field theory, and combinations of tree-level amplitudes.

          What’s the point? Virtual particles as they appear as lines in Feynman diagrams are unnecessary. What we want is answers for scattering amplitude calculations. If Feynman diagrams, with their virtual particle lines, will work, great. Often they’re too slow and cumbersome, and other methods exist that make no reference to those virtual particles.

          That does not mean, of course, that there aren’t disturbances in fields (as I’ve defined “virtual particles” to be, in order to make them meaningful) that are responsible for the scattering occurring at all. It just means that trying to give meaning to exactly what the virtual particles were and exactly what they were doing involves confusing a crutch for a leg.

          All of this leaves out the great deal of additional subtlety that arises when you remember that nature does not live by perturbation theory; real scattering amplitudes are all-orders results, not tree-level or one-loop-level results. Put that in, along with gauge invariance, and you will soon find yourself unable to define virtual particles as lines in Feynman diagrams… try drawing the more complicated graphs in muon decay, with virtual photons and virtual Zs running between the muon line, electron line, neutrinos and the W, and then put in some lepton loops that split the Z W W or photon W W vertices, and you will already see trouble.

  55. There are many senses in which it does not make sense to treat the electromagnetic field around the electron as classical, but one of the worst arises in the context of the gluon. The gluon is a particle, like the electron. But gluons interact with gluons; the gluon has a chromoelectric field, like the electron’s electric field. And the chromoelectric field is another word for the gluon field, just as the electric field is another word for the photon field. There is no theory where you somehow treat the gluon particle as quantum mechanical and treat its field as classical — this is a completely inconsistent thing to do.

  56. Professor Strassler, could you explain Hawking radiation from your perspective? Or, do you feel that it is not a correct theory?

    • You mention that spontaneous disturbances (quantum fluctuations) usually reconnect. I always wondered how they meet again? (Regardless of discussions about black holes.)

      If these disturbances, for instance, start off in opposite directions, would they not need to turn around exactly 180 degrees at some point, and go back to reach each other again? That sounds like a fairly improbable event. (Even without a black hole close by.) What is wrong with this picture?

      • This is another reason why it is a bad idea to think of these disturbances as “particles”; if you created a pair of particles traveling in opposite directions, why would they ever turn around and annihilate again? This is just the wrong intuition; it just doesn’t work that way. The disturbances can do all sorts of things particles can’t do, such as appear without the input of any energy at all. I take the point of view that one is better off thinking of a quantum field as a seething, complex object, rather than thinking about particle pairs appearing and disappearing in processes that do indeed sound like they violate conservation laws.

    • I’ve tried to imagine the quantum field as a “seething, complex object” too, like an ocean surface with just random waves going everywhere, that just average out all together, rather than having to pair up the same way they appeared.

      But with that picture, on the other hand, it is not clear how it would make any difference for one “part” of a disturbance if another random “part” would become trapped inside a black hole so they can’t “reconnect”. It also
      becomes less clear how some “part” of a disturbance then can start traveling far away. Maybe something is still missing in this intuition? (Too much of the opposite intuition?)

      (And what are these “parts” you talk about in a disturbance, really? You still seem to talk about them yourself like objects of their own, and not just as one big complex field…)

  57. That was very illuminating professor. Thank you for your quick response. I have a few follow up questions.

    1. Your very last statement. “for most disturbances that happen to sit on top of the horizon, their outside-parts are not made from real particles and will not escape the black hole.”…do you mean that most disturbances that happen to sit on the top of the horizon have a virtual particle form and an anti-virtual particle form that quickly annihilate each other without entering the event horizon. Or, that both the virtual particle form and ant-virtual particle form will both fall into the event horizon? I cling to the former.

    2. Regarding “the very rare thing”. At the event horizon, “the continual spontaneous disturbance”, is usually “white noise” (my term), or a virtual particle and anti-virtual particle that quickly annihilate each other without falling into the event horizon. Can it be assumed, that in very rare events, the virtual particle and anti-virtual particle or “white noise” somehow achieve a “harmonic” (my term) and in essence become a real particle and real anti-particle, where the newly formed, anti-particle falls into the event horizon, shrinking the mass of the black hole, while the newly formed, real particle escapes the event horizon?

    I have a flurry of other questions on the subject…but for another time.

    • 1. This is an observer-dependent statement, and that’s why I was nervous about giving you the answer I did. I am thinking I should revise it, because there are actually two cases, and I didn’t state them both…

      In any case, the latter is more accurate in one of the cases; from the outside observer’s point of view, the disturbance falls into the horizon; from the point of view of an observer falling into the horizon, it’s just an ordinary disturbance like any other. The former happens too, but those aren’t the interesting disturbances that have something to do with the black hole’s hot atmosphere.

      2. The process is Black Hole –> Smaller Black Hole + real particle. Whether the anti-particle was real cannot be ascertained by any experiment; it’s just a more general disturbance falling into the black hole.

      I’m really not prepared to do this subject justice without pictures and careful thought about how to explain this clearly. It needs articles, not ad hoc answers, I’m afraid. And I certainly have to keep focused on other things for now. But I understand the interest in clear exposition of the subject. Most of what I know I learned from Lenny Susskind himself, so you might look at videos he’s made to explain black holes to the public. But I don’t know how thorough he was.

  58. Professor Strassler,
    In your opinion are “continual spontaneous quantum field disturbances,” “quantum fluctuations,” “zero-point energy,” and “virtual particle/antiparticle annihilation,” different words for the same phenomena or are they different phenomena? If they are different what are the differences?

  59. Can the figure 3 be developed even further? Could the virtual photon there be considered also as a disturbance in a quark-field? If so, could it mean that every particle/wave contains virtually all other particles/waves, in a row of infinite implication?

    • The virtual photon is a disturbance in the electromagnetic field (i.e. the photon field). That’s always true, by definition: a virtual particle of any type is a disturbance in its corresponding field, not in some other field.

      But it is true that all fields affect each other to a greater or lesser degree, so a particle — naively a ripple in its corresponding field — is also made partly from disturbances, to a greater or lesser degree, in other fields.

  60. Hi Dr. Strassler,
    I’m very happy I found this website! I don’t have any professional education when it comes to physics, but I enjoy learning about various parts of physics on my own. I think your explanations are great!

    In my “study” of virtual particles, this article helped me understand a lot of things. Assuming I understand correctly, it seems physicists used the energy-time uncertainty relation (derived from the uncertainty principle), to predict that virtual particles of a certain energy could come into existence for a time proportional to that energy, and thereby act as force carriers. The range of the nuclear interaction was already known, and from this range physicists (Yukawa, was it?) were able to calculate what the mass of the associated virtual particle should be. Later on, a particle with close to the predicted mass was discovered (the pion).

    This made sense to me when I read it. Your explanation here of virtual particles (field disturbances) also makes sense, but at this point I can’t see how it would be used to predict or explain specific phenomena (such as pions). Can you write a bit about this?

  61. dear sir
    thank you for this enteresting article, and i have some equestions
    1-after years of discovering the photon, do you think that it is a well known concept in physics.
    2-if we have experiment and we succeed to explane it by mathematical equations, is it nesessary that our explanation is correct.
    3-when a photon interacts with electron, is the direction of every one before and after the interaction is taken in acount in our calculations, for example: compton effect and photoelectric effect.
    thank you.

    • 1- 100% well-known. Photons are used daily; they’re part of modern technology. The CCDs in digital cameras, for instance, absorb them. Lasers only work because one can make photons behave in lock-step, giving a beam of light that’s narrow and has a single color.

      2- generally multiple types of explanations give the same equations; even if the equations are right that does not mean that the conceptual explanation is unique. Newton’s laws are different in word form from the Hamilton-Jacobi equations and from the minimum action principle, but they lead to the same equations.

      3- everything is taken into account; the predictions of compton and photoelectric effects are extraordinarily precise, to better than one part in 10,000.

  62. dear sir
    thank you for your answer,but i have equestion if you please
    in compton effect we have an elasticcollission, and we know very well the laws which govern it, but in photoelectric case the electron absorb the photon, what kind of interaction is the absorbtion, and in the laser case the photon stimulate the electron to emit a photon, what kind of interaction is the stimulation, in the three cases the interaction is between electron and photon, which must be the same in the three cases, but every case has different interpretation, do you think this is acceptable.
    hosam otaibi.

  63. Dear Professor Strassler,

    I have thought of an analogy regarding the virtual particles and Higgs field. But I would like to know if it is valid or lacking. As I understand it, the Higgs field is a condensate of virtual particles that have become real. These virtual particles, known as the “Dirac sea”, have a negative energy (relative to the vacuum of space) and became real because it was energetically favorable to do so (similar to how electrons act in super conductors?) due to spontaneous symmetry breaking of the vacuum (I do not entirely understand this concept.)
    Every day we go outside, and know there is water vapor in the air. But without our senses to feel this on a humid day, we would be none the wiser to this water vapor. But as the sun sets (spontaneous symmetry breaking of the vacuum) and the next morning we wake to find dew on the grass. The water vapor represents the virtual particle sea and the dew, the Higgs field. At which point, the weak force bosons and other particles affected by the Higgs field are observed to have their mass due to interaction with the “dew”.
    Finally, thank you. This site is incredibly helpful and I have recommended it to several friends, all of whom have enjoyed your writing. We all give our thanks to your work.

    Sincerely, S.B.O.

  64. Professor Strassler
    I have been reading up on virtual particles lately and have found your article and one by John Baez particularly (no pun intended) illuminating. I have also been reading related articles in Wikipedia. One of these is entitled “Static forces and virtual-particle exchange”. In it I found the the following statement:

    “The virtual-particle formulation is derived from a method known as perturbation theory which is an approximation assuming interactions are not too strong, and was intended for scattering problems, not bound states such as atoms. For the strong force binding quarks into nucleons at low energies, perturbation theory has never been shown to yield results in accord with experiments[2], thus, the validity of the “force-mediating particle” picture is questionable. Similarly, for bound states the method fails[3]. In these cases the physical interpretation must be re-examined.”

    Is this at all accurate, do you think? I was very surprised to read it, because it seems it is questioning the entire Standard Model with the exception of its applicability to scattering experiments. Questionably applicable to the strong force, the weak force, or bound states generally? Wow.

    Also, this question of what is real and what is virtual (the same thing as “not real”?) has been puzzling me, especially because both your article and Baez’s both end up saying something like even real particles are sort of virtual. I had the idea, perhaps influenced by reading parts of John Bell’s book “The Speakable and Unspeakable in Quantum Mechanics”, that photons that enter my eyes and help create the internal image in my head are definitely real and, beyond this, the particle interactions that leave potentially measurable traces are also quite real, but do not require an actual attempt at measurement. Thus, a meteor impact on the far side of the moon leaves a crater even though my current means of transportation will not get me there to inspect it. The virtual interactions and quantum theory more generally are then just some mathematics you apply to estimate the probabilities of these kinds of real events occurring. Wave collapse is associated with such real interactions, but is itself not real, because the wave function itself is just the mathematics too. Therefore, I think there is clear distinction between real and virtual particles, but you and Baez seem to disagree. Where am I wrong?

    • The article on virtual particles you reference to Baez was not written by him. He merely hosts the article on his website and it is part of a Physics FAQ for the UseNet sci.physics.* groups.

      Unfortunately the term “virtual” is a poor term for what virtual means in this context. It does not mean “not real”. Even Matt’s description as “disturbances” is a real physical phenomenum. In particle physics, “virtual” simply means “off mass shell” when used in conjunction with specific particles.

      PS. Be careful about Wikipedia articles; most anyone can edit them at any time.

  65. Hi Fred: I am trying to reconcile your answer with the one given by Matt, “A photon traveling from the Pleiades is clearly about as close as you are going to get to the ideal; its energy and momentum are almost the perfect match that you would expect for a massless particle.” Should your definition be rephrased as “virtual” means significantly far from being “on mass shell” and real/non-virtual means insignificantly far from being “on mass shell”, because nothing is ideal so that nothing is really on mass shell?

    Also, your point about Wikipedia articles is true, but I’m still interested in whether the opinion expressed by the writer is to be taken at all seriously. I don’t know how well the theory of quantum chromodynamics agrees with the data or whether QED doesn’t work so well in explaining the behavior of bound states. I was hoping a theoretical physicist working in this area could give me a response based on his far better acquaintance with the empirical tests, etc.

  66. Hi Professor,

    Your article, and the comments are especially helpful. I am still confused however, and I think that this confusion has to do with my attempts at understanding other descriptions of what virtual particles are. Prior to all of this I was under the impression that virtual particles are particle pairs that instantly pop and in and out of existence in empty space. And I though that they were also called quantum fluctuations, or quantum energy. But when I read your description, I am imagining them as ripples in this quantum foam. Stable ripples are what we understand as particles and the unstable ripples are known as virtual particles.

    What is the difference between a particle and a ripple or disturbance in the foam? When people say “particle” I think of an atom, or a subatomic particle. And this cosmic foam, is it the Higgs field? From my understanding, it is the Higgs field that gives particles their mass based on their movement through the field. If you could clarify these points for me that would be much appreciated. Thank you.

    • A particle is a ripple in a quantum field. I never used the term quantum foam, I believe. Nor is anyone’s use of the term “foam” to be confused with the Higgs field; there is no relation whatsoever. Let’s back up.

      There are fields in nature. These fluctuate randomly — these quantum fluctuations are often described as virtual particle pairs, but this is not entirely accurate which is why I avoid doing so explicitly. In addition to these random fluctuations, the fields can also have nicely behaved waves on top of those fluctuations. That’s what I call a ripple. The ripple with smallest allowed height is called a “quantum”, and also called a “particle” in modern parlance. If you think of particles as little dots, like dust specks, then you are not understanding what the modern conception of a particle is. A particle is a quantum — a nicely behaved ripple in a quantum field.

      More general disturbances in quantum fields include the things we call “virtual particles”, but those things really are not particles at all. To understand all the different things that quantum fields can do, you really need a course on the subject.

      It is not correct that the Higgs field gives particles their mass based on their *movement*. Many people use analogies that suggest this, but the analogies are inaccurate. The Higgs field gives mass to particles even when they are standing still.

      I have explained much of this at a level appropriate for people with a little math background in a sequence of articles, and . If these are too advanced, stay tuned; I will eventually write less advanced articles on the same subjects… but that’s not easy.

  67. Dear Professor Strassler, Tim Martin asked: Also, why do you answer some people’s questions, but not other’s?.
    You responded: do you really want me to answer that?
    Tim said: But also, I have questions I’d like to ask on other posts of yours, as well, and if certain questions are more likely to get answered than others, I’d sincerely like to know what those criteria are!

    Like Tim, I have also noticed that some (reasonable?) questions don’t get answered. I exclude the questions from obvious trolls, or arguments on topics outside of physics. Some kinds of questions *are* more likely to be answered than others, and we aren’t sure that if we ask a question, it will be answered. So, we would like to know:

    – which kinds of questions are likely to be answered?
    – which kinds of questions are NOT likely to be answered?

    We do understand that you retain the right to decide whether or not to answer any question; all we are looking for is some guidelines.


  68. Professor, please tell me if this makes sense to you:

    Even on its own internal logic, Feynman diagrams do not imply the real existence of virtual particles. This is because each virtual particle is associated with with a single line in a Feynman diagram but we do not get an end calculation of anything except by summing over diagrams, (or “histories”). I am not familiar with the calculation itself but I suspect that the intermediate values associated with the virtual particles cancel out in the end and do you even get a specific numerical result but rather a probability distribution. Feynman diagrams work only because the lines correspond to, (probabilistically), real component waves, (disturbances), in a quantum field. You are actually just using the diagrams as a tool for deciding on terms to include in a perturbation calculation. The virtual particles then are just mathematical fiction.

  69. I think you should consider a full fledged book with all the required math and your exceptional interpretations of equations in terms of physics.

    It is probably too much to clarify each and everyone’s confusion without the necessary math. In the language of the Chinese proverb , teach us to fish rather than providing a piece meal.

  70. Hi Matt, thanks for your explanations, they really help people like me who are interested in the concepts of physics but are useless at maths.

    I think i have a simple understanding now of what virtual particles are. Here is my explanation..

    So a photon is a ripple or excitation in the electromagnetic field or an electron is a ripple in the electron field. I like the word ripple so we use that from now on ! When these particles travel through there respective fields they can interact with other fields causing disturbances in them. These disturbances are what we call virtual particles.

    But also, when there are no particles, the fields interact with each other causing disturbances which we call virtual particles. The difference is, a normal particle is a ripple in the field that can travel through it. But a virtual particle is not, it is a disturbance in the field which is a totally different thing.

  71. Hi Professor, I am hoping you could help me understand what quantum fields are. As i understand it, the Electromagnetic field purveys the whole of space but what is the field made of ?


    • As far as we know today (though you must remember that in the future we might learn more about the universe that would change this viewpoint), everything in the universe is made from fields. The fields are the fundamental ingredients in the universe, according to current views. They aren’t made from anything else. Everything else is made from them, and their ripples.

      • Hello, along a similar line of Kevin’s question, where do the fields “come” from? Or I guess originate might be a better choice of words. Also, I’m curious, if I understand your explanation of virtual particles, then what causes these fields to “interact” or “disturb” when there aren’t any particles around? I think I read somewhere above in the comments where someone used the waves of the ocean as an example, but even then, are not the waves of the ocean caused by a variety of factors?

  72. This is great stuff! I actually came here because of trying to understand something about classical fields and got sidetracked into virtual particles.

    Something I was wondering:

    (slight diversion) You know the classic situation of a current going through a wire, with a static magnetic field around it that radiates out a certain distance? People used to say some bizarre things to me about current putting it’s energy into sustaining that magnetic field when accelerated, and then drawing it out again to resist deceleration, and that that was basically what impedance was. At the time it seemed bizarre that the current should have the energy I was told about, and then have all this extra energy as well in the magnetic field. To explain this, I assumed that energy transmitted by the current was both the energy in the electrical motion and in the associated magnetic field, which combined added up to the normal momentum and energy transfer I was told about.

    Are the normal virtual particles basically the same thing? Where we say an electron has these properties, but any real electron’s properties are also given by how it “blurs” into these other fields, existing maybe as a comparatively more localised electron and a halo of these other interactions? If so, do you have to change loads of things about the properties of a “naked” electron to get the same thing when you add in all the effects of the fields it’s interacting with?

    • I’m having a little trouble understanding your question. This is probably partly the way you’ve phrased it and partly that it has been ten years since I taught freshman physics on impedance etc., so I’m probably forgetting the cause of the common confusion that I think you’re expressing.

      Classical fields are related to certain aspects of “virtual particles”. But virtual particles represent a much more general class of phenomena.

      How energy is stored in currents of moving electrons and in the fields that they carry with them is a tricky business. But I’m not sure exactly what I could say that would clarify your question.

      But I can answer this. Yes, a “naked” electron is quite different from the real, physical electron. In fact it’s not unique what “naked” means because you can’t actually ever strip away all the junk that the electron carries with it, so it’s really just a figment of our imaginations to think of it naked. However, there are different classes of things inside that halo, and some of them fall away with distance much faster than the classical electric field, which is the thing that drops away slowest with distance [like 1/(distance)^2]. That’s why in most of undergraduate physics, we only have to deal with the real electron and its electric field; all the complexities of the real electron are typically important only for measurements which take place at subatomic distances.

      I hope that helps a little.

  73. So virtual “particles” are short-lived disturbances which occur within fields. Is that a correct enough summary?

    If so, I have another question in regards to the Casimir Effect. I understand that the experiment is run with super-thin plates which have all electrical charge removed, in a vacuum. A few places online, I have seen the claim that the virtual “particles,” the effects of which are observable in the experiment, are literally generated from nothing. But if virtual “particles” are short-lived disturbances which occur within fields, then it seems they are making the claim that a disturbance in the field can occur without a field. What am I to make of this?

    • Zia, I would say a quantum field is a mathematical concept for each point in Space. The field is not a real structure but the virtual particles popping in and out of existence are. The reason the virtual particles can come from nothing is because, for a very short time, they can borrow energy from the universe as long as they give that energy back very quickly, which they do, due to pair annihilation. If i am wrong then please, Professor, correct me !

      • Thanks, but I’m having a hard time seeing how “energy borrowed/obtained from the universe” is “nothing.”

        • These particles are not really coming from “nothing” as the universe they are borrowing energy from is not nothing at all. However, if the universe didn’t exist, would virtual particles still be able to “borrow energy”? I mean start with the initial state of there being no particles whether real or virtual… would virtual particles still blink in and out?

          I’ll add my $0.02 here, as I’ve thought about this some — please go easy on me as I’m somewhat of a mathematician and only read physics for personal interest.

          It’s not that the field is “nothing” in some philosophical sense, like it is absolute void (no space, no time, no things). The scientific theory doesn’t really say what a field is or isn’t (in terms of some ontological reality). What the theory says, is that “this particular mathematical equation describes our observations of ‘things'”. People will argue endlessly on what ‘nothing’ means. But that is a question for philosophers, the science is simply meant to take in observations and predict future observations… observations of “things” (electrons, photons, etc.).

          It is a highly significant fact that the equations that describe our observations predict that particles pop out of “nothing”, but it doesn’t prove that in a “true void of nothingness” this would happen, as that entails the assumption that there would have to be no observers around to make the observation and confirm that the observation fits with the equations. So we just fall into a trap in not doing science by attempting to answer that question, but discussing philosophy instead. However, I still think it is an important endeavor to do both.

          In terms of a scientific realist perspective, an equation isn’t a “thing” at all… the ink particles it is written in or the electrons representing it as digital bits are real observable physical things. In other words, equations don’t have any “real” existence to them. “Real physical existence” is limited to those physical things that we can observe. Of course, that begs all sorts of other questions, and scientists will argue endlessly on what “physical things” actually “exist”. There’s a bit of circular logic going on here in all perspectives, really… something exists because we observe it and we observe it because it exists.

          I have satisfied myself somewhat on these issues by clarifying what science actually is, and that is, making observations and formulating models/theories/etc in order to predict future observations. That is science. Any discussion of what “things actually are” is philosophy, not science. Of course, scientists should be free to discuss philosophy openly, however, one may risk bogging down the progress of their scientific work by getting sidetracked too much by the philosophy — of course the opposite can happen too, that the philosophy can spawn new insights and contribute to new scientific theories.

          An obvious question hanging over all this is: What does it mean to observe a thing? Does observing an electron count as observing the electron field and prove the existence of the field? Does observing patterns of clicks in a machine count as observing the particles themselves (in a philosophical sense, not in a scientific-theoretic sense)? Other than DIRECT observation with the human senses, it gets philosophically jumbled somewhat. Personally, I tend to side with the perspective that “no thing actually exists” — in the sense that if a field is actually nothing (not really a solid physical thing in the sense that we think of solidity and nothingness as being distinct concepts), then every thing that is derived from that field of nothingness is actually still nothing as well (emptiness, void, not actually solid in the sense that it isn’t distinct from empty space/void/nothingness). That physical reality is only observation/perception is the inevitable conclusion. Of course, that begs a whole host of philosophical musings. Either way, it does not diminish the success of the scientific method at predicting future observations from past observations.

          Ok, end rant, sorry if this is seen way off topic, but these questions seem relevant and natural to the topic of virtual particles. I’d be really surprised if there are any physicists out there who do not ponder these things and have their own opinions!

  74. Dear Prof,

    Since you are the foremost authority in virtual particles with superb mathematical skills, I wonder if you would be kind enough to point out to me what is wrong with the equations below because the result does not make sense. I am sure there is an error somewhere.


    sqrt = square root

    10 = 3.1623^2

    i = imaginary number = sqrt (-1)

    i ^ 4 = +1


    E = mc ^2 {(1-v^2/c^2)}^(-1/2)

    If an imaginary particle is travelling at 3.1623 x C,

    E = mc ^2 [{(1-(3.1623c)^2)} / c^2]^(-1/2)

    E = mc ^2 {(1-10)} ^ (-1/2)

    …. = mc ^2 / square root (- 9)

    …. = mc ^2 / 3i

    If we raise E to the power of 4,

    E^4 = (mc ^2)^4 / 81i^4

    Since i^4 = +1,

    E = 1/3 x mc^2 when an imaginary particle is travelling 3.1623 times the speed of light in a vacuum ! ! !


    OR TO PUT IT IN ANOTHER WAY, IF A PARTICLE MOVES FASTER THAN THE SPEED OF LIGHT, IT’S ENERGY DECREASES AND IF IT’S SPEED REACHES INFINITY, IT’S ENERGY AND HENCE IT’S MASS BECOMES ZERO !…….. unless it’s energy is compensated by it’s increase in it’s Newtonian Kinetic Energy (which may not work either as the mass becomes zero, the Newtonian kinetic energy will also become zero);

    E = mc^2 + 1/2 x mv^2,

    The only time when matter moves “faster (though not strictly true)” than light is during the period of inflation at the time of the Big Bang.

    At this time the total energy and mass of the universe may be small (and not infinitely large) but as the inflation decreases towards the speed of light C, the total energy and hence the total mass may be at it’s maximum at C.

    From then on decreases exponentially to the total energy and mass of today i.e. at rest of E = mc^2.

    To put it in another “nonsensical” way, it appears that the Big Bang at the beginning of time comes from a singularity that do not have an infinite density but rather a singularity with almost zero mass but with infinite velocity!

    Thanking you,

    Warmest regards,

    Dr Looi


    • Quantum field theory requires there be disturbances of this type, and quantum field theory agrees with data. So we have to have these disturbances.

      Why call them “virtual particles”? Because it proved useful for certain types of calculations to organize the disturbances mathematically as though they were made from a sum of many fictional particles. [If you know some math, this has to do with the usefulness of Fourier transforms.] But that’s a math issue, not a physics issue. Unfortunately, in hindsight, this math fact got taken a little too seriously… its limitations are much better understood today than was the case when the notion was introduced.

  75. As a nascent grad student in theoretical particle physics most of this information isn’t new for me, but it is always great to hear another person explain it. Thank you for the clear and interesting explanation!

  76. Dear Mr. Strassler
    If a photon meets a photon they may sire a particle-antiparticle pair of some kind – if their energy is high enough. But photons do not interact accoding to the linear electromagnetic theory. Is it a second order process then in QFT, “pro- ducing” virtual pairs?
    In the (very) early universe for a brief, brief moment, I understand, there was equilibrium between radiation and matter before expansion cooled it to a one way street leaving precious little matter and a quite bunch of entropy in the form of photons. But what are these very very early interacting photons and how do they do it? Virtual second order proces-ses?
    It all comes from me contemplating the symbolic equation : gamma + gamma electron + positrion (or some other pair of particles) which I remember having seen in porpular science books or met on the net.
    Does it make sense?

    Yours sincerely

  77. Come to think of it: In the early universe the gammas may not represent photons but some other bosons, maybe gravitons. And general relativity is non-linear, where energy can be converted into mass(at enormous temperatures total particle energy is mostly kinetic), and so gravitons can beget particles(electrons and positrons) which then ultimately meet and decay electromagnetically to photons.
    Does it now make sense?

  78. Gee, declaring virtual particles unreal by virtue of the concept of time, which is itself “virtual”.
    that is clearly non sequitur. “Selective science jiggerying”, eh?

    yours truly,

  79. So could a virtual particle pair | disturbance in the electron field have transient and very highly localised effects on spacetime? If so, that would – when taken cumulatively – result in quite a large effect on the universal scale. Say, enough to account for the effects of dark energy?

    • my thoughts exactly, I done a search to find anyone else with my thoughts on this and you are the only one.

      For some time now I have postulated the idea that these ‘virtual’ disturbances, brief as they may be, are enough of a force to leave a residual gravitational effect. As you say cummulatively enough (maybe, as I do not have enough information to calculate) to account for dark matter – we have to have gone dramatically wrong somewhere to be looking for invisible matter – doesn’t feel right, where as this, well maybe!!

  80. Dear Prof Strassler,

    Thank you for your excellent article explaining virtual particles. Your article was eminently readable and immensely informative. I learned a lot.

    If you are still entertaining to questions on this topic, I do have a few.

    First, is there now a consensus among professional physicists as to the ontic nature of quantum fields? Many undergraduate chemistry textbooks still seem to suggest that the quantum field for the electron is just a mathematical construction. They say the wave equation for the electron has no physical interpretation and it is only the square of the wave equation that has meaning, that being the probability of finding an electron in a certain location. I was surprised and pleased to read in your article that quantum fields are to be understood as real entities, in and of themselves – not only real, but fundamental. I had already come to the same conclusion myself, but I had never seen it so plainly stated as in your article. My reasoning was the same as yours – a field can exist without a particle, but a particle cannot exist without the field. So how accepted is this interpretation among physicists and has anyone told the chemists?

    Along these same lines, I wonder if could you say something about the distinction among the following fields which are easily confused:
    1. Electric Field, as between two charged particles or between plates of a capacitor.
    2. Magnetic Field, as between two poles of a permanent magnet.
    3. Electromagnetic field.
    4. Electron field
    5. Photon field
    6. Ether.

    With my new insights gleaned from your article, I would like to take a stab at answering this one. Please correct me where I am wrong. As I understand it, fields 3, 4, and 6 are really the same thing, that is, the medium for the propagation of light waves, but that it is taboo to use the term “ether” for historical reasons. I like that you call it the photon field. That seems to me to be the most unambiguous way to put it. I had not seen it called that before. It is the quantum field for the photon.

    Field 4, of course, is simply the quantum field for the electron which you clearly explained in your article. The important point here is that the electron field is not the same thing as the electric field nor the electromagnetic field.

    Fields 1 and 2, strictly speaking, are not quantum fields but rather a mapping of a physical property to points in space as one might also have a temperature field or a pressure field or in solution chemistry one might have a concentration field. As such, these fields do not transport energy by wave action, but may represent a kind of conduction or flow of some sort down a gradient. What is it that is flowing in the case of the electric field and the magnetic field? Textbooks call these, electric flux and magnetic flux, but again suggest that these are just mathematical constructs and that nothing is actually flowing. Would you say there is a flow of virtual particles or disturbances in the underlying electromagnetic field? Also, is the magnetic field completely reduceable to an electric field, perhaps a circulating electric field? Does a magnetic field boil down to a particular constellation of circulating virtual particles?

    I hope you can further educate me on these topics. I tutor undergraduate students in introductory physics and chemistry. While they are not required to know these details, a deeper understanding on my part helps me teach them what they do need to know.


    • Oops, I see some typos in my post. Most importantly, the phrase “fields 3, 4, and 6 are really the same thing” should read “fields 3, 5, and 6 are really the same thing”. Less importantly, in paragraph 2, the phrase “If you are still entertaining to questions” should read “If you are still entertaining questions”. Sorry about that. -Steve

  81. First of all, thanks for keeping this blog! I only discovered it a couple weeks ago. I first came across your article about the structure of the proton and it has changed my view of the world. The picture of 3 quarks and 3 gluons just never sat right with me. Thinking of the proton as a “bound state”, essentially a cloud of a very large number of particles buzzing around, but with a particular net balance of them makes so much more sense to me and was a groundbreaking revelation!

    So if I understand this virtual-particle article somewhat correctly:

    — Virtual particles are not particles because they are non-resonant, i.e. the properties of the virtual-particles like energy, wave amplitude and frequency are not at the limited number of specific values (quanta) as that of the resonant particles. In other words virtual particles are not particles because they are not quantized. That’s all the term particle means in quantum mechanics, is that the phenomenon is quantized. Does this make some sense? So virtual particles are not quantized? In other words, they can have any arbitrarily small (or large?) energy, amplitude and frequency, etc.?

    — Maybe I am misunderstanding, but there seems to be a link between the uncertainty principle and virtual particles. For example, in the “universe from nothing” question, the “nothing” is actually a null quantum field that is buzzing with the life of virtual particles. It’s nothing in that there is nothing to observe until a “real/actual” particle comes into existence. The virtual particles cannot be measured because they fall within the limits of uncertainty. So in order for a real particle to emerge from virtual particles, it seems like many little virtual-particle-ripples have to coalesce until their quantifiable properties go above the limits of uncertainty, then a quantized amount of that energy might fly off as a result and “bang” we have a “real” particle… i.e. a quantized field fluctuation which is somewhat long-lived.

    I am envisioning virtual particles like the random and chaotic ripples on the sea, and real particles like the waves that emerge and propagate to the shore. All real particles decay into “nothingness” just like the waves break and crash, but there are always a seemingly unlimited number of virtual particles of all shapes and sizes (i.e. of randomly varying magnitudes and frequencies of ripples on the surface of the sea, etc.). Is this a decent analogy?

    If I am sort of on the right track, then this brings up the question: If two distinct quantum fields have a virtual particle that has the same quantifiable properties, are they different? If the electron field has random fluctuation X and Higgs field has random fluctuation X (all “virtually-measurable” quantities are identical and encapsulated in X), then what makes those virtual particles different? Or are they? In other words, is it a necessity that there are different fields? Why can’t there just be a single field that gives rise to all the particles, and the particles simply vary by their quantifiable properties like amplitude, energy, etc.? Of course, this begs the question on the existence of the fields and whether or not they are simply mathematical abstractions (not real) used to explain the existence of observable (real) phenomena.

  82. A really quick question. The disturbance in the field that pushes two electrons apart, is that a classical electro-magnetic field? So you have one quantum electro-magnetic field; and, where there are disturbances in that field, you have classical electro-magnetic fields – of the sort created by say a charged object or a magnet.

    • A classical electromagnetic field between two electric charges is a very special “disturbance”. However, most disturbances are not classical electromagnetic fields.

      • Dear Dr Strassler,

        I realize you havent commented in over three years but I just wanted one clarification after ive read through your comments.

        The concept of these “disturbances” i.e. virtual particles being separate from the concept used in Feynman diagrams was something you agreed with .

        Why shouldn’t Feynman diagrams interact via these physically real “disturbances”. You even have a Feynman diagram in figure 6. Are you meaning to tell us the interpretation you’ve presented in this article is not the virtual particles in Feynman diagrams? then what is the purpose of this post?

        I realize youve got a lot of questions in the comments but i can assure you my gratitude and insistence exceeds that of the other commentators

  83. Thank you for writing this blog.

    I think sometimes virtual particles are taken too serously, as if they “really exist”. The idea of virtual particles is advocated strongly and many people (especially laymen) think they are therefore “real” or at least have “real observable effects”. But the fact is they appear only when we do calculations using perturbation theory. In this sense I would say that they are due to the perturbative approach and are nothing more than a mathematical tool, which brings intuition and helps to visualize (through Feynman diagrams) which contributions are important.

    The quantum fields are the fundamental objects and if we could perform all calculations without perturbation theory, there would be no virtual particles. The properties we calculate using perturbation theory and virtual particles are not due to virtual particles; we simply use this approximate method to calculate these effects of the fields.

    There are also cases where perturbative approaches do not work (thus virtual particles stop existing?). Further, as is pointed out, for example, in this paper*, virtual particles can also be utilized in classical physics. Yet, not many physicists say that classical phenomena occur due to virtual particles.


    • Of course I agree with you on all the technical points.

      Pedagogically, there’s an issue. “Virtual particles” have entered the public lexicon; if you’re going to explain things, you have to use existing language.

      My choice is to treat “Virtual particles” more generally than simply lines in a Feynman graph — to describe them more generally as “what fields do when they aren’t rippling as real quanta”. [Solitons or instantons would not fit in this category.] I find this covers most situations — in particle physics, what is most commonly encountered pedagogically is Green functions with some kind of boundary condition (this includes the classical phenomena and the lines in Feynman graphs) and integrals over Green functions (loops in Feynman graphs) or resummations of sets of lines and loops (as happens when a quark turns into a jet of quarks, antiquarks and gluons.) This way of talking gets away from the verbiage of treating “Virtual Particles” as though they have a reality beyond the math, and treats them not as “particles” but as “field phenomena”. It doesn’t quite get to the point of saying that they are calculational artifacts… but that’s because the field phenomena which they represent are presumably *not* calculational artifacts… yes? In other words, I feel it is useful to describe “Virtual particles” in terms of the field phenomena that they are used to describe… and so far, it has worked very well on this website, in that it hasn’t caused many pedagogical contradictions.

  84. Hi Professor Strassler,

    I read through the article and the comments. But I’m not very good at science so I’m not entirely sure if I understand the explanation. I was wondering if you would be willing to tell me if I got it right per below:

    Some experiments showed that when two electrons pass by each other in a vacuum, they are repelled as we would expect (negative charge + negative charge = repulsion). But at that moment, when the electromagnetic fields of the two electrons interact, they create a disturbance. This disturbace is short-lived and has a variety of properties such as mass, momentum, energy, etc. The disturbance could be loosely described as a “shadow” of an electron. This is called a “virtual particle”.

    Likewise, in a similar manner, when a positron and an electron pass each other, their positive and negative fields interact and create a disturbance. This disturbance is called a virtual photon. But like the virtual particle, it’s not an actual, “real” particle (like an electron).

    In other words, the virtual particle really is a popularized term that describes all manners of these disturbances between real particles. There are various ways to calculate the disturbances and one popular method is called the Feynman Diagram. The lines in the diagram are called “virtual particles”. In other words, the disturbances exist but technically speaking, virtual particles only exist in a Feynman diagram. We can’t even call the disturbances “virtual particles” because depending on the method of the calculation, the term “virtual particle” might not even be a part of the language used in the particular method. Technically speaking, the term “virtual particle” is a convience, a way of describing one part of a mathematical diagram.

    Mathematically speaking, it can be shown that with enough energy, the disturbance (or “virtual particle”) can actually result in a real particle. So instead of a disturbance/shadow of a real particle, a real particle can actually be formed from the disturbance.

    Also, particles such as electrons are really just long-term, stable disturbances in certain fields. For example, an electron isn’t a little ball found in textbooks – it’s a disturbance in an electron field. The disturbance in the electron field is called an electron.

    If I got it right, I was wondering about a few things related to cosmology:
    1. Does String Theory describe the factors/events that cause these disturbances (the “virtual particles”)?
    2. Is it possible that the Big Bang came from one very energetic disturbance that created real particles in a similar manner to how “virtual particles” are created but on a much larger scale? Would I be way off mark to say that the interaction of the fields in an “other” state (prior to the universe’s existence), disturbed enough to create an event similar to a virtual particle? (The event being the Big Bang.)

    Hoping you can shed some light!

    • You’re pretty close on most things… a few little details are wrong, but your general impressions are in pretty good shape.

      1) The “factors/events” that cause these disturbances are already described by quantum field theory. String theory doesn’t really change the story I’ve told you. There are “virtual strings” too, which are disturbances in string fields.

      2) Yes, perhaps. It’s actually much more subtle than you suggest — but the suggestion that the universe emerges as a disturbance in space-time itself has certainly been made.

      • Thanks for the reply! I was wondering if you could correct/point out where I got it wrong. I probably won’t understand it all if it’s too technical but I’d love to have a starting point to learn.

        I don’t think I see any articles on quantum field theory in your collection. I was wondering if you might be able to write one? Or maybe provide a dumb-down version of it?

        What would you say is the most common thought on how the universe emerged among scientists like yourself?

  85. Thank you for the post and responses to the many good questions of your readers. I have learned a lot from both. Please keep up this effort and get your book published soon so we can all read it.

  86. Great post, as usual.
    There is however an important point that you did not tackle: what is the relation with the uncertainty principle? (every book mention it without actually explaining it much…)
    I think it’d be good if you address this issue in a revised version of this post (if you ever revise it).

  87. Hello,

    Great explanation. It greatly helped by just stating that one should just forget the term “particle” when talking about virtual particles.

    Isn’t it possible to make this explanation possible as a pdf-document (easier printing)?

  88. Hello professor Matt Strassler,

    Just a second pair of questions.

    As I wrote in my previous post: it helped me a lot by getting rid of the idea that a virtual particle is a kind of real particle. Maybe too many textbooks suggest that a virtual particle is a kind of very short lived “real” particle which just can’t be observed because it disappears very very fast. But still is real.

    Right now I am reading “Deep Down Things. The Breathtaking Beauty of Particle Physics” by Bruce A. Schumm (I would recommend this book). It’s maybe trivial, but just realizing that W bosons (mediators of the weak force) are neither called leptons or are made up of quarks shows that W bosons are not real matter. Right?

    I am still confused why a mass can be determined for W bosons. How does this fit in your explanation above? I also wonder how the Heisenberg uncertainty principle fits in your explanation.

    Best wishes,

    The Netherlands

  89. I think we need to re-evaluate what we mean by “real” and “virtual”. Every physical phenomenon is “real” in the sense that it can be observed (whether indirectly or directly). I’m not implying any assumptions on anybody’s understanding (surely, my own is quite lacking), but giving up preconceived notions of what “real matter” is (as opposed to unreal matter?) is indispensable in coming to grips with modern physics — no need to get metaphysical either. Of course, there are some deep metaphysical questions which are highly relevant to human interests into what IS “reality”. Virtual particles are some kind of fluctuation in a field, so are real particles… they are just two different kinds of fluctuations. That’s it, right? The pictures above where the electrons are the particles and “interact” by “exchanging virtual particles” is misleading as well (it’s a model, after all) because the electron is also simply a special type of disturbance in the electron field. The real particles are not even “real”, in the sense that they are not actually “solid globs of stuff”. The field IS the underlying “real stuff” — similar to the collection of water molecules being the real stuff and ice cubes aren’t really “real things” in the sense that they are just collections of water molecules. The water molecules are the actual real things. The ice cubes are just a particular arrangement of water molecules.

  90. Reading your articule has improved my understanding greatly.
    Could you answer a couple of short question that appear not to have been raised yet.
    1) How does a real particule create a disturbance in the field surrounding it? Is the disturbance a superposition of the real particules wave function and the background virtual disturbances caused by the uncertainity principle. As I understand it the disturbance can extend to a quite large distances although at large distances it is also very weak.
    2) How do these disturbances cause an attraction and repulsion of electrons and positrons. Ie through the neutral photon field.

    • It all has to do with the interaction of one field with another (or even with itself, in some cases.)

      To answer these questions actually requires solving the equations that describe the interaction between the electron field and the electromagnetic (i.e. photon) field. It’s similar to solving the equations for the electric field due a charged particle in ordinary first-year physics, but including quantum mechanical effects and the fact that the charged particle is itself a ripple in its own field.

      But anyway, at this point you actually have to solve equations… not so difficult ones, but too advanced for this website.

  91. Dear Matt Strassler:

    Suppose you try to make a distinction between the realm of concepts and the realm of objects, so that with virtual particles it is all in the realm of concepts, and we humans are still in need of locating the objects to which they the virtual particles correspond to in the realm of objective reality.

    Can you explain virtual particles in that manner?

    Or it is all impossible because of the complexity of the issue whatever, and without a complex and complicated mind, it is impossible from your part to explain to them folks with no such complex and complicated mind.

    Marius de Jess

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  94. Dr. Strassler,

    Perhaps you can clarify for me a point (about black hole “evaporation”) that I can’t seem to get straight. I don’t understand the “energy arithmetic” involved. Here’s my puzzlement.
    If a virtual pair is created just outside the event horizon, and one of the pair goes in and the other out, it looks to a distant observer that a particle has been emitted. Fine. But the other one has gone in and *added* its mass (or energy, same thing) to that of the black hole. How does the net mass/energy of the black hole decrease?
    And if one would argue that the entering particle is an antiparticle half the time (fair enough) and would annihilate with an existing particle inside, that only eliminates the mass, not the net energy inside. And even if one says that the virtual particle pair is created slightly inside the event horizon and one of ’em tunnels out, that’s fine, too; but still: how would this decrease the mass or energy of the black hole?
    It is interesting to me that if radiation from a black hole *is* due to virtual particle creation near the event horizon, then the rate of evaporation would seem (to me) to be proportional to the surface area of the event horizon, which is proportional to the square of its radius, which in turn is proportional to its mass. So larger holes oughta evaporate faster (which apparently *isn’t* true) unless the severe bending of spacetime in this neighborhood affects these admittedly Euclidean calculations.

    Help, please! Thanks!

  95. sir, i am not a physicist so i want to ask you that many books say that the so called virtual particles have more energy than that of its initial condition so they don’t conserve energy will you please clarify that they don’t conserve energy thanks

  96. Hello prof s.
    can you weave your magic to explain gravitons, mass, gravity, and how gravity works at huge distances – ripples in the gravity field?

  97. Great article thanks. Learned a lot.

    Small typo, repetition of “in”

    electrons spend some of their time as a combination of two disturbances, one **in in** the electron field and one in the electromagnetic field.

  98. Hey Professor Strassler,
    Great article. Right at the beginning what caught my eye is your comment about how you were once a “layperson” yourself, at age 16, reading these types of articles. i should say I am in that particular situation; I am 16 as well, trying to gobble up as much scientific information about physics in general as I can. Do you have any recommendations on where to go and what to do during my high school years so I can prepare myself? And is there anything that can be done to get a “feel for” the math involved in this (unfortunately I don’t think I will be taking differential equations until I reach University).
    I think it is great to be interested in the fields of physics (pun intended) and thanks a lot for putting this website up, it is very informative and useful.
    Thank you!

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  100. In my seldom humble opinion, it makes no sense to talk of real particles as real and virtual particles as a mistaken terminology. The reason I say this is because all we can ever have in physics are models that are hopefully predictive. The idea is of a particle itself is a model dependent concept based on our classically wired brains. So in my opinion, virtual particles are as real , or as unreal , as so called “real” particles. I think as models go , virtual particles are a very useful and visual way to model things in QFT.That’s why this terminology has persisted despite the criticisms of more purist thinkers.

  101. Dear Matt,
    excellent article. Maybe it is a rather technical question but I try: what is your idea on what is often called “pomeron” ?
    Is it a very peculiar disturbance of the gluon field?

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  103. I believe the hypothesis that the virtual particles might be responsible for the missing gravitation called dark matter won’t work. My rationale is that one would expect the gravitational force due to virtual particles to be nearly uniformly distributed (homogeneous) whereas the few calculations that have been made of dark matter distribution are not consistent with this.

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  105. Dear Dr.Strassler,
    In the beginning of this article, you use the swing to explain what is “ripple” and what is “disturbance”. The paragraphs around Fig.3 & Fig.4 said that the statement “a particle like an electron is a ripple purely in the electron field” is an APPROXIMATE statement. And the next paragraph you said “The disturbance in the electron field is not an electron particle, and the disturbance in the photon field is not a photon particle.”

    Then my confusion emerged. Before I read the statement “Even to say a particle like an electron is a ripple purely in the electron field is an approximate statement”, I thought as you said that a so-called particle is a ripple in its field and that a so-called virtual particle is a disturbance in its field whatever the field was caused by other particle. So that I confused a statement “The disturbance in the electron field is not an electron particle, and the disturbance in the photon field is not a photon particle”. In that sentence, you said “disturbance” first and then “electron particle”. I knew what you actually mean but confuse the usage of the words. So the correct statement is “The RIPPLE in the electron field is not an electron particle, and the RIPPLE in the photon field is not a photon particle”?

    On the other hand, after I read the black statement under Fig.3 and the so far correct interpretation: “The electron can turn into a virtual photon and a virtual electron, which then turn back into a real electron” beside the Fig.4, does the meaning of ripple remains meaningful? Due to the truth explanation of the electron is the black statement you wrote, we do NOT have to use the word RIPPLE anymore just because it is only the approximation concept? If it would right, then we can get rid of the concept of the ripple? And then said: “the virtual particle is the disturbance of its field, and the real particle is not the ripple of its field but the combination of several, maybe 2, disturbances of their belonging fields”?

    On the other hand, in the article “Particles Are Quanta”, the paragraph under Fig.6 say ” Electrons are quanta in the electron field”. Is that exactly right? Or “Electron is the combination of a virtual quanta(electron) in the electron field and a virtual quanta(photon) in the electromagnetic field”?

    Am I too carp? Or…… 🙁

  106. Doesn’t the distinction between “real” and “virtual” depend on a fixed background (which of course QFT has, so I’m not disputing anything you say in the article)? It seems to me that, if we were to generalize this to some kind of theory of quantum gravity, you’d need to know which intervals were timelike vs. spacelike to tell virtual particles from real particles, which information isn’t prior to the dynamics.

    I’m an amateur, so I assume some part of what I just said is (at best) wrong. Care to comment, Matt?

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