Electrons: On the Outskirts of Atoms

Matt Strassler [January 21, 2013]

Electrons, the tiny objects that inhabit the outskirts of atoms, play the leading role in chemistry, carry electric current across our electrical grid and inside strokes of lightning, and make up the “cathode rays” that were used to create the pictures on 20th century televisions and computer screens.  They are the quintessential example of (apparently)-elementary particles.

By “elementary” I mean that electrons are indivisible, and are not made from still smaller particles.  By “apparently” I remind you that they are only elementary as far as we currently know — what we know about electrons comes from experiments, and our experiments are not infinitely powerful.  If electrons are not elementary, but are so small that our current experiments cannot break them apart, then they will appear elementary to all experiments we’ve done in the past and present, but not to all future experiments.  So someday — just as 80 years ago people thought protons might be elementary but had incomplete knowledge, and 150 years ago people thought that atoms might be elementary but had incomplete knowledge — someday we may discover electrons are not elementary after all.  But for now, since all experiments we can perform show them as elementary, we will assume, provisionally, that this is the case — remembering that this is partly an experimental fact and partly an assumption!

The electron was the first sub-atomic particle to be identified (i.e., the first object whose size is smaller than an atom).  At the time of its discovery in the 1890s (the usual date is given as 1897, but the discovery was, in some senses, gradual) the scientific debate as to whether matter was made from atoms, or whether atoms were simply convenient fictions useful for describing how matter behaves, was nearing an end.  But even those who believed atoms existed were not necessarily sure whether or not atoms were indivisible (as their name, derived from Greek for “not cuttable”, would imply).  A generation later, by the mid-1930s, physicists had confirmed the existence of atoms, understood their basic structure, and learned how to calculate their properties with high precision.  They did these calculations using the equations of a 1920s theory of how matter behaves, called “quantum mechanics”, which was needed because Newton’s famous equations were not able to describe how atoms work.   Many of the key tests of the accuracy of quantum mechanics involved measuring carefully were how electrons behave, within and outside of atoms.

All electrons are identical and indistinguishable; if I switched two of them you wouldn’t be able to tell.  [How do we know this? I'll explain later.] So I can write about the property of “an electron”, and you can be sure that those properties are true of all electrons.  What are these intrinsic properties?

Mass!

An electron has a mass — its mass is small compared to the mass of any atom, so you can usually forget about it in a beginning chemistry class, but not so small that you can forget about it in particle physics, or even in understanding what atoms are.  (Although the electrons in an atom don’t contribute much to the atom’s mass, the electron mass is essential in determining the size of an atom, something which you can read about here.  In fact, this is part of why the Higgs field and particle are important.)  How big the mass is can be written in several ways, each of which gives a different perspective:

  • It is about 9 × 10-31 kilograms = 0.000,000,000,000,000,000,000,000,000,000,9 kilograms (i.e. 0.000,000,000,000,000,000,000,000,000,002 pounds), or about a one (two) millionth(s) of a millionth of a millionth of a millionth of a millionth of a kilogram (pound).
  • It is about 0.05% (more precisely, about 1/1838) of the mass of a hydrogen atom, which is the lightest atom in nature; most of an atom’s mass sits in its nucleus.
  • The energy stored in an electron’s mass, E = mc², is 0.000,511 GeV, (learn about GeV here).  This is about 200,000 times larger than the energy carried by a single photon of green light [a photon is the particle out of which light and other electromagnetic waves are made.]  Often in particle physics we write the mass of a particle using the inverse energy-mass relation: for a particle that is stationary, m = E/c².  In this language, the electron’s mass is 0.000511 GeV/c² .

Electric Charge!

An electron has an electric charge — which means that it is affected by electric (and magnetic) fields.  An electrically charged particle, in the presence of an electric field, will be pushed on by an electric force.  Indeed such forces keep electrons bound inside their atoms.

How big is the electron’s electric charge?  Well, think about static electricity — you walk across a rug in your shoes, and then, when you touch your finger to a doorknob, another person, or (!!!) your computer, you feel a spark.  That spark carries charge from one place to another — typically 10 million million times more charge than carried by an electron.  Physicists measure charge using an arbitrary unit called a Coulomb (just as they measure time using seconds and length using meters).  A typical static electricity charge is about 1 millionth of a “Coulomb”, give or take quite a bit.  The size of the charge on an electron is traditionally called e, where e is about 1.6 × 10-19 Coulombs (that is, 0.16 millionths of a millionth of a millionth of a Coulomb.)

It was decided historically to define the charge on an electron  to be negative (and the charge on an atomic nucleus is therefore defined to be positive) so the electron’s charge is actually -e.

Size?

An electron does not have a known size; it might be a point object with no size at all, or it might have a extremely tiny size, smaller (in radius) than about 10-18 meters — a millionth of a millionth of a millionth of a meter (and a meter is about 3 feet).  It’s at least 100,000,000 times smaller in radius than an atom.  If this weren’t the case, we’d have seen signs of the electron’s size in experiments.

Hmmm…  Actually this is a tricky point (which you can skip if it’s too confusing), because what does an electron look like?  As I discussed in my article on atoms, defining what you mean by the size of an elementary particle is complicated by the fact that an electron, despite the name “particle”, isn’t really like a dust-particle or a grain of sand or salt.  It also has wave-like properties.  In an atom, electrons in some sense spread out around the atom, like a sound wave spreads out on a drum.  In that limited sense, within an atom they are roughly as big as the atom itself. 

But this size is contextual, and not intrinsic to the electron — in fact, I’ll call this the electron’s “contextual size”.  Change the context — take the electron out of its atom and put it inside a tiny metal box, for instance — and the degree to which the electron spreads out (in this limited sense) may grow or shrink.  In contrast, a proton has an intrinsic size, about 100,000 times smaller than an atom; you cannot, in any sense, make the proton smaller than its intrinsic size without breaking the proton apart.  In short, the contextual size cannot be smaller than the intrinsic size. By shrinking the contextual size of electrons as much as we can, mainly through scattering high-energy electrons off of other particles, we’ve looked for signs of an intrinsic size.  So far, none have ever been found.

So we may say, more accurately, that experiments show that the intrinsic size of an electron is smaller than about a millionth of a millionth of a millionth of a meter.  How far the electron spreads out, wave-like, depends on context.

Spin@

You may or may not want to know about this one!  It will bend your brain (at least, it bends mine!)

Among the strange features of our quantum mechanical world is the very weird fact (initially discovered in the 1920s by Goudsmit and Uhlenbeck, who were trying to make sense of data from measurements of electrons inside atoms) that elementary particles can spin — even if they have no size!   This is impossible to visualize; or at least, I certainly can’t do it.  Let us say this as a practical matter: electrons and many other particles of nature act as though they are little rotating tops, in that if they are absorbed by another object, they will cause that object to rotate a little.   [Imagine dropping a spinning chunk of soft clay onto a table that can rotate; the chunk will stick to the table, and the table will then rotate a little bit, proving the chunk was rotating to start with.]

And even more weirdly, each type of particle always spins at exactly the same rate!  We say electrons have spin 1/2; this is the smallest non-zero rate of spin that a particle can have.   We also know other types of elementary particles with spin 1/2, 1 and (we think) 0, and non-elementary particles with spin 0, 1/2, 1, 3/2, 2, 5/2, and on up to very large values.

Magnetism

A rotating ball of electric charge would behave like a magnet, and you might guess that because electrons have electric charge and spin, they behave like tiny magnets. You’d be right! The fact that electrons act like little magnets helps confirm that they really do spin.  Ordinary daily-life magnets, made from (say) iron, get their magnetism from their electrons; lots and lots of electrons, with their spinning all nicely aligned, can make a big magnet out of lots and lots of tiny ones!

Are You Sure Electrons Really Exist?!

Isn’t it time in this article to show a picture of an electron?

Unlike molecules and atoms, which are large enough that we can make pictures of them using special microscopes, there is no way to make any image of an electron.  It’s simply too small and too elusive.  We can make images of tracks of electrons as they pass through matter, as in the figure at right (which actually shows an anti-electron [``positron''], but an electron would look almost the same), but we don’t image the electrons directly.

anti-electron discovery

An electrically charged particle passing through a specially prepared “bubble chamber” will leave a trail of bubbles in its wake.The bubbles quickly grow to a visible size, and the trail can then be photographed. A magnetic field makes the particle’s track bend; the bending direction tells you whether the particle’s charge was negative or positive. This famous 1933 photo shows a thin curved track of bubbles, marked by the red arrows, behaving just like a track of an electron… except that an electron’s track would have bent to the right. The wrong-way bend proves the particle that made the track had positive charge, and thus the track was made by a “positron”, the electron’s anti-particle. (The horizontal bar and diagonal lines are artifacts of the photo and the experimental device.)

But our confidence that electrons exist is very high, and our knowledge of their properties is very precise. Where does that confidence come from?

This is an important issue, because one of the most common questions that particle physicists get asked is whether we really know all these particles exist, or whether we’re just fooling ourselves (and/or everyone else!) and wasting lots of money on stuff that is just hot air coming out of our heads (or worse.)

Well, yes, we know what we’re doing. And we have for over a hundred years. Part of our confidence comes from pictures such as shown in the photograph at right. But there are many other sources of confidence, which I’ll write about in a later article.

[How we know electrons exist: Coming Soon]

[How we know electrons are indistinguishable and all have the same properties: Coming Soon]

73 responses to “Electrons: On the Outskirts of Atoms

  1. Pingback: Electrons and Their Properties | Of Particular Significance

  2. Does the fact that quarks have rather weird fractions of the electron’s charge (-1/3 and +2/3) help to argue for the case against the electron being a fundamental particle?

    • Good question. It certainly raises the issue, but in fact the answer is no, it neither helps nor hurts. It turns out that there are very nice mathematical structures (more than one, interestingly) in which particles that are affected by the strong nuclear force all come with charges of 1/3 times an integer, while particles that are not affected by the strong nuclear force all come with integer charges. Those structures are perfectly consistent with both quarks and electrons being elementary (or “fundamental”, as you called it — I tend to avoid the term for various reasons.) These mathematical structures are also consistent with all of them being composite. So it could go either way.

      • Would it be valid to take the electron’s charge as -3, making all electric charges multiples of the down quark’s charge? (That is, are the quark’s ‘odd’ charges just an artifact of them being discovered later, or is there a way in which the electron’s charge is,f undamentally-1?)

  3. That’s a remarkable statistic, to make an electron, a mere whiff of a particle compared to some in the subatomic zoo I would need a fifth of a million green photons. I think light has become substantially less substantial to me.

    On intrinsic size, what exactly IS it? Does a proton have a solid surface separating inside and outside or is it merely probabilistic? Does the notion of size make sense or is it merely a nice approximation?

    Spin: can we say that the electron itself spins in some sense, or only that it acts as if it were spinning? I take it they have angular momentum, but is it possible to possess this without actually spinning? Also, spin being limited to multiples of 1/2, do you have a link to a simple explanation or layout of this? I am not nearly as conversant with this subject as I’d like and even the notion of spin 1/2 makes my head ache.

    Also,I was under the impression that as you shrink a rotating ball of certain electric charge the magnetic field it produced decreased, is this not the case? Does it stay constant at a constant distance from the sphere, like gravitational fields from compressed masses?

    • Photons of visible light are pretty wimpy; that’s why they are safe. Photons from medical x-rays are 5000 or so times more energetic; that’s why they can pass through the body and why they can do damage to your DNA. And when an electron and positron annihilate (as they do, for instance, in positron emission tomography [PET scans]) the photons are more powerful than x-rays by another factor of 50. Another way to say this is that it takes heating something to thousands of degrees to get it to glow white hot, emitting lots of visible photons, whereas to make it so hot that it readily emits pairs of electrons and positrons you have to heat it to billions of degrees.

      If something has an intrinsic size, you can get it to vibrate internally by hitting it hard enough. You can tell an atom has structure because it has “excited states” — with enough energy, you can get the electron(s) to move further away from the nucleus than they usually are. This would be impossible if the atom were an indivisible, pointlike particle. There’s no solid surface to an atom, but it is clear it has a size. Exactly how you define size is somewhat up to you…

      Spin: “can we say that the electron itself spins in some sense, or only that it acts as if it were spinning?” I think it is probably better to say that it acts as though it were spinning. Earlier today I was thinking about whether I wanted to revise that section to be a little clearer about this. The main point is, as you say, that they have angular momentum. But it seemed to require too much discussion to explain in this article what angular momentum is, and that it is quantized in units of Planck’s constant h divided by 4 pi, and that the electron’s spin=1/2 means that the angular momentum of the electron is (1/2) (h / 2 pi) . To prove spin is quantized in this way, in a world with three spatial dimensions and special relativity, involves some math.

      Shrinking a rotating ball: are you holding the rotation frequency fixed, or the angular momentum fixed, as you shrink the ball?

  4. I like to imagine particles as tiny little knots on space. I know it’s probably far from reality but it helps to visualize some of their strange properties.
    Imagine we have a long flat ribbon. That’s our space. Now turn one end of the ribbon 180 degrees around its longitudal axis. On both ends the ribbon is still flat but somewhere in between we suddenly have a particle. Now, where exactly it is and what is its size? An antiparticle can be introduced by rotating the end 180 degrees in the opposite direction. Our particle and antiparticle can pass through each other, or annihilate, decreasing the pull on the ribbon slightly (i.e. releasing energy). Etc etc. Of course, not many knots can be done on a ribbon, especially such ones that can be untied by meeting appropriate “antiknot” but that doesn’t really apply on knots on 3D space.
    My imagination doesn’t go much further but it’s enough to keep me happy and not getting worried about things like particle size, spin, or uncertainity principle.

    • The idea that particles might be knots, or some other topologically stable object, has a long history. And if that were true, then yes, an anti-particle would be an anti-knot. It’s a good idea, but no one has ever been able to make it work in detail. The mathematics that people have developed just doesn’t generally agree with what we observe.

      You know, it’s fine to speculate — but speculation isn’t physics. Speculation that is turned into equations and calculations and (if possible) concrete experimental predictions for physical phenomena — that’s physics.

      By the way, I’m afraid that even if particles are knots, that will not get you away from the problems of the uncertainty principle or particle size and spin. Electrons, even if they are knots or strings or composite objects, do have spin, period — that’s observed in data. Generally, the consequences of the uncertainty principle, the spin of the electron, and the size of the proton are things which are observed experimentally. You can ignore them only by ignoring large amounts of data… which again is something a physicist cannot lightly do.

      • I never meant that as serious proposal that particles may be knots. I only mean that it works for me way better than imagining particles as little spheres, for instance it’s pretty hard to imagine that a sphere can have only two spins (up or down) while it’s much easier to imagine that a knot may be tied one way or another way and it’s still the same knot and there is no third way of tying it and it’s pretty unclear which spatial direction the tying goes.
        Of course it’s good to not go too deep because otherwise problems will start jumping out and you soon start running out of dimensions etc, but as a visualising tool for individual or simple combinations of properties I think it’s good enough.

  5. The analogy of the spinning electron being like a lump of spinning clay falling on a table that can rotate and imparting a bit of its rotation to the table is the best visualization of spin that I have come across. Thanks!

  6. Nice. Are you will write a book? So I wil buy it

  7. On size: An excellent response from an angle I hadn’t considered. I must now ask, do all objects with an intrinsic size posses an internal structure? That is, if we detected the electron has a certain intrinsic size, would that be proof of it not being elemental? I ask this as it seems naively to me that in order to have an excited state something must be composed of two or more parts.

    On spin: Your points are noted, many thanks.

    On shrinking a ball: Keeping rotational frequency constant while the radius shrinks and charge density increases.

  8. For me it’s easier to visualize particles as a wave than it is to work with anti-knots; my elementary math teacher was a fan of them and they’ve always perplexed me. So it goes.

  9. Why can’t a size for the electron be estimated by the strength of it’s magnetic field, it’s spin, and it’s charge?

    Perhaps my understanding of spinning, charged objects is mistaken. I envision that the charged particles accelerate in order to follow a curved path, and this acceleration generates the magnetic field. The charge has to be a nonzero distance from the center, else it doesn’t accelerate by following a curved path.

    Is this part of the mystery of quantum spin? If so, what size would the naive calculation suggest?

    • If you calculate the size as a function of charge, spin, mass and magnetic field, assuming it has the shape of a ball, you’ll find the answer is ambiguous, and that it’s possible for the ball to be of any size. That’s because the magnetic field depends on the charge, mass and spin (= angular momentum) and not on the size.

      In the simplest equations that you can write for an electron in quantum field theory, the electron is treated as a particle with no intrinsic size. Now of course the simplest equations might not be the right equations (and for a proton they are not.) But those simplest equations for a spin-1/2 particle (where you put the mass and charge as numbers in by hand) do produce the right magnetic field, without there being any size at all. In fact the subtle quantum effects of “virtual particles” [ http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ ] can be computed and agree to high precision with experiment.

  10. Does an electron, considered as a particle, have a shape? I have a vaguely recall hearing a claim that electrons are quite precisely round, but I have not been able to find the reference. I would enjoy hearing about any experiments that find the limits of measurement of the shape of the electron. How do these experiments compare to other experiments that measure the shapes of other particles? I am presuming that the shape of the proton, for example, is well-known because its size is known. Or is what is really known just the area of the cross-section?

    How large would the electron have to be for its size to start appearing in existing measurements? For example, I imagine that it would ultimately limit the beam density that can be produced by an accelerator.

    I am making the assumption that the whole wave versus particle interpretation is neatly handled by some sort of transform, Fourier or otherwise, and that it is acceptable to measure in one domain and then speak confidently about the measurement results in the other domain. Is my assumption correct?

    • Yes, I know what you are referring to… I really didn’t like the way they phrased those media articles. Just as spin tells you that in some sense an electron rotates — or rather, behaves as if it rotates, even though it might not have a size — there are measurements that you could make that can test whether there are asymmetries in the electron that are in some sense a test of whether it is round — or rather, behaves as if it is round, even though it might not have a size.

      In the case of the proton, which has a known size, talking about “shape” makes more sense. Actually there are still occasional debates about the proton’s shape — there was one less than 10 years ago — but I don’t know where the most recent data and theory on this point stand. The measurements are not so easy and the interpretation isn’t either.

      “How large would the electron have to be for its size to start appearing in existing measurements? For example, I imagine that it would ultimately limit the beam density that can be produced by an accelerator.”

      The beam density in an accelerator isn’t going to be affected by the electron’s size. You should ask how the proton’s size can be detected. You can calculate the rate for electrons to scatter off of protons at a particular angle if protons and electrons are pointlike. You discover in experiments that the data doesn’t agree with the prediction. Further experiments reveal all sorts of interesting things, and in particular that the proton has all sorts of excited states, just like atoms do, in which it vibrates or distends internally. In a similar way, electron-electron or electron-positron scattering (or production of electron-positron pairs in LHC collisions) can be predicted, assuming the electron is a point-like particle. If those predictions ever start to disagree with data (and right now they don’t) then we’ll have to consider why the predictions are failing, and electron size may be one of the possibilities. Current limits on the electron size are something like 1/1000 or so of the proton’s size. In fact it’s probably closer to 1/10000, but I haven’t looked at any numbers recently and so I wouldn’t want to make a strong statement.

      As for wave-versus-particle — in the context of quantum field theory, where “particles” should really be called “quanta” (waves, in a field, of minimum energy and amplitude) the size question is encoded in the complexity of the equations that describe the field of which the particle is a quantum. If the equations take their simplest form, the particle has no intrinsic size. If the equations are more complicated, then the nature and magnitude of the complication is telling you something about that intrinsic size. Experiments that should detect the size will be affected by those complications, and deviate from the predictions of the simple equations, only when the experiments are sufficiently energetic. Uncertainty and relativity tell you that if you do a relativistic scattering experiment of energy E, and data disagrees with prediction because one of the particles has a size, that size S is of order h-bar c / E, where h-bar is Planck’s constant divided by 2 π and c is the speed of light.

  11. Quantum fields are the basic ingredients of the universe, and the particles are just bundles of
    energy and momentum of the fields. “Material particles can be
    understood as the quanta of various fields. If an electron is a material particle, an extended singly-excited field(as field quanta – energy = hν), what is the main difference of it’s behaviour outside and inside of an atom ?, Any difference in mass?

    • There’s no change in the electron’s mass. [I speak here of its "rest mass", which is what particle physicists call mass. Sometimes people still speak about a "relativistic mass", which is the E/c^2 even when a particle is moving... but we particle physicists just call that quantity "energy divided by the square of the speed of light."] The energy, momentum, and the quantum spreading-out of the electron will change.

      A small language point: An electron is a quantum of the electron field, or equivalently, a “single excitation of the field”.

      • /Energy-momentum is transmitted discreetly though, and depends upon the frequency of the wave. As everything is waves, in process, no fundamental process can be precisely localized (uncertainty principles on position-momentum and time-energy). How one goes from the wavy process to the localized energy-momentum, the theory does not say, and is therefore incomplete/- Patrice Ayme.
        /this comment is based on quantum mechanics, and it all gets a fresh coat of paint, of a different color, in quantum field theory./- Prof Strassler.

        Can we say Energy is quantized frequency(energy can change, not frequency) of the field, if momentum is added it become quantum(single excitation) ?

        /Ordinary daily-life magnets, made from (say) iron, get their magnetism from their electrons; lots and lots of electrons, with their spinning all nicely aligned, can make a big magnet out of lots and lots of tiny ones!/

        So bundles of energy roaring around inside electron, nicely aligned to create its rest mass – like two photons inside a closed system create “rest mass” ?

  12. But you never told us what is charge in general , be it color ,electric or magnetic charge ?

    • You can’t speak of charge without speaking of the field to which it is associated. An electric charge tells you the strength of the interaction between a particle (and its field) and the electric field. “Color”, or strong-nuclear-force charge, determines the strength of the interaction between a particle (and its field) and the gluon field.

      Magnetic charge needs more discussion. The electron does not have net magnetic charge — if it did, its magnetic field would go off in all directions with equal strength, and decrease as 1/(distance)2. Such an object would be called a magnetic monopole (which can exist in principle, but none has ever been observed [more precisely, confirmed as observed.]) Instead it is a magnetic dipole, as if, just like any magnet with a north and south pole, it is made from a positive (north) and negative (south) magnetic monopole separated by a certain distance. Of course, I write “as if” because the electron does not, in fact, have a size, nor does it have little magnetic monopoles inside it.

      One picture (not pretty but effective) showing the difference between the fields generated by monopole (non-zero magnetic charge) and dipole (zero total magnetic charge made from a positive and negative charge slightly displaced) is here: http://sites.sinauer.com/animalcommunication2e/images/07/WT07.03Mono-Dipole.jpg . The radially-symmetric field is shown by the arrows in the left figure; the typical field of an ordinary north-south magnet, which is also that of an electron if you shrink the distance between the two poles to zero while keeping the distant field values unchanged, is shown at right.

  13. I am still missing the point , what i mean is ; if electron IS a ripple in e-field , what IS charge w.r.t e-field or w.r.t. electron ripple itself , it cannot be mere interaction or else why there are + and -ve charges and what this sign actually represent ?

    • An electron is a ripple in the electron field. It has a known energy content and is well behaved. However this ripple also causes effects in other fields, the gravitational field for example and the electromagnetic field. Those ripples do not have a nice definite energy and are not well behaved. This is how an electron’s (electromagnetic) charge works. It is not color charge and we do not consider it a ‘magnetic’ charge even though all electric charge must generate a magnetic field of some kind.

    • It does represent the mere interaction of the electron field with the electric (i.e. photon) field. To see why the sign matters, you actually have to calculate how the photon field’s interaction with a particle of charge q causes it to interact with particles of charge q’. In particular, you need to see how the photon field causes electrons to interact with electrons, and how it causes electrons to interact with positrons or protons. What you discover is that when two electrons scatter, they tend to be pushed apart, and an electron and a positron or proton tend to be pulled toward each other. You actually have to do the (simple) calculation to see this. Simply put, the energy of the two particles that are far apart is proportional to + q_1 q_2 / r , where q_1 and q_2 are the two charges and r is the typical distance between them. This formula tells you that charges of the same sign repel and that charges of opposite sign attract.

      The calculation is so simple that perhaps I’ll put it on the website at some point.

  14. Hi Matt,
    A naive question, if an electron is really an infinitesimal point (or a very close approximation of one), then surely its electric field energy would rise exponentially as one approached closer and closer? In a sense, wouldn’t a small enough electron size result in an energy density large enough to form a (very small) black hole? Are electrons actually a special king of black hole, or would something like the quantisation of the electric field prevent this?

    • a) not exponentially but geometrically (1/r^2, where r is the distance.)

      b) this is where it is very important that we live in a world described by quantum field theory. When you get to sufficiently small distances, you discover that the electric field does not behave as you expect because the vacuum does not behave as you would expect. This is because the vacuum is full of fluctuating fields, including fluctuations of the electron field. (These are often called electron-positron virtual particles, but they are best thought of as non-particle fluctuations of the electron field. http://profmattstrassler.com/articles-and-posts/particle-physics-basics/virtual-particles-what-are-they/ ) Even fluctuations in other charged fields, such as muon fields and W particle fields, become important at sufficiently small r. And fluctuations in gravitational fields (i.e. in space-time itself) become important at extremely small r.

      The effect of this is that the energy density of the electron never becomes large enough for it to form a black hole. For an object to be a black hole, it needs enough mass that its size would be larger than the Planck length, which is where the fluctuations in gravitational fields become important. That distance is about 10^(-33) meters, and tiny as that distance is, an object would need to have mass about 10^21 times larger than the electron’s mass for it to form a black hole.

      [In this answer I've assumed gravity and space are of their naive form. The numbers might change if, for instance, there are relatively large extra dimensions of space. But even so this wouldn't change my main conceptual points.]

  15. The rest mass of the electron arises from the Higgs field being nonzero. If there was no Higgs field electrons would be massless like photons. You may wish to check out several pages on the Higgs field on this site.

  16. I have thought of this also and a brief back of the envelope calculation shows that the size of a black hole of an electron’s mass is so utterly tiny that it doesn’t really present that much of a lower limit. Also I am not sure if physicists have determined the minimum size a black hole can be, but I believe it is heavier than an electron’s worth of mass. (At either rate, Hawking radiation would make such a tiny black hole unbelievably unstable.)

    There’s also a difference it seems between being infinitely small (An intrinsic size of 0?) and not having an intrinsic size.

    • /There’s also a difference it seems between being infinitely small (An intrinsic size of 0?) and not having an intrinsic size./- I like this statement.
      “0” is the minimum possible unit, like “on and “off” – having relative potential to become “on”- energy and momentum mixed in proper proportion. But “0” came from nothing. That infinite proceeds from this infinite. Inbetween 0 and nothing is ripple(nature), ripple is ineffable but without ripple is difficult to fathom ?

  17. According to what you said , if there is no such concrete thing called charge which is mere interactions among fields , now we may ask ; are these particular specified interactions necessary or contingent / could be otherwise ?
    What determines their special properties ?

    • “are these particular specified interactions necessary or contingent / could be otherwise ?”

      Both. The assignment of charges (i.e. the arrangement of which fields interact with each other) appears fairly arbitrary and could certainly have been different from the point of view of quantum field theory. That said, the nature of the various interactions with the electromagnetic, strong nuclear and weak nuclear forces is quite constrained by tight consistency conditions. Even stronger conditions apply when one includes gravity.

      So there is some freedom, but not complete freedom, in choosing which interactions are allowed, when you write down a quantum field theory, and less freedom if the fields in the theory interact with gravity. We do not know why, among the many possible quantum field theories interacting with gravity, the one we observe in nature was “selected”.

  18. I was a bit puzzled by your saying that an electron may be composed of other particles. I thought that, given the electron’s small mass, any components the electron is composed of would have showed up as decay particles in particle accelerators, like the LHC? Or are you hedging because you are concerned the theoretical components of an electron could have a mass so small that they would be lost in the error bars of a particle collider’s collision analysis?

    • No, there’s no issue of the sort you raised. The problem is that you are (understandably) using non-relativistic intuition, of the sort that works for atoms but does not work even for protons.

      Remember that a proton has a mass of 1 GeV/c^2, but the quarks and antiquarks that it contains have masses below 0.01 GeV/c^2 and the gluons that hold it all together are massless. http://profmattstrassler.com/articles-and-posts/largehadroncolliderfaq/whats-a-proton-anyway/ So your question really should be: given that the protons are made from particles that are so lightweight, why didn’t we discover those particles before we discovered the proton? or at least, discover them long before we actually did historically?

      The answer has to do with the way the proton’s mass comes about, and how the quarks, antiquarks and gluons are trapped inside the proton. It is quite subtle (and confused physicists for a number of years before they figured it out) and it is not at all obvious. I do not know a way to explain it in very simple terms, or even in a simple calculation. It’s simply a non-obvious and very important fact about how relativistic quantum field theory works. For some surprises about how protons behave, and how different they are from atoms, see http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-apparently-elementary-particles/jets-the-manifestation-of-quarks-and-gluons/

      The electron could similarly be made from massless particles that are permanently trapped inside the electron, just as quarks etc. are trapped in a proton. This could even be true of a massless electron. The possibility of very lightweight, or even massless, composite particles in a world like ours was uncovered in the late 70s or early 80s. Many examples of theories that produce such objects were found in the 1990s. So yes, electrons may be made from objects that are very light but we’ve never seen.

      It is also possible for a low-mass particle to be made from objects that have large masses, as long as the force between the objects with large masses is strong enough to create binding energy that, if large and negative, could cancel off the mass-energy of the heavy particles, so that the total energy of the system (at rest) — which, divided by c^2, would be its mass — might be much less than the mass-energy of the objects that it contains. We know a few examples of this also, from string theory and its relation to quantum field theory.

      So the world could be quite a bit stranger than you imagine. Indeed, if all you know about is atomic physics, the proton looks pretty strange!!

  19. Very, very interesting.

    Does the scale at which these fluctuations become important relate in any way to the strength of the force involved. (As in its relative strength compared to say the electromagnetic force.)?

    Secondly, does this mean there is a ‘resistance’ to a force’s field becoming arbitrarily strong? (That is if I had a small object and I started adding charge to it, would there be a point where I would see fluctuations in the electromagnetic field that mitigated this effect, or do those fluctuations always occur on the same scale no matter how strong the local field?)

    • There are many ways that mass and distance scales arise in quantum field theory, and there are different formulas appropriate to each one. There’s no simple answer to your first question, other than “yes but not entirely and it depends on specific cases.” To go into this in detail is, I think, too technical for this site; maybe I’ll write about it at a later time.

      As for your second question: yes, there is. If you make an electric field too strong over too large a region, electron-positron pairs will pop right out of the vacuum and partially neutralize the field. The same is true of the strong nuclear force; if you make its “electric-like” [often called "chromoelectric"] field too strong over too large a region, quark-antiquark pairs will appear and partially neutralize it. See http://profmattstrassler.com/articles-and-posts/particle-physics-basics/the-known-apparently-elementary-particles/jets-the-manifestation-of-quarks-and-gluons/

      Fields can however be very strong indeed in a small region around a particle. Whether the effects of the vacuum make the force stronger or weaker than you’d expect from a 1/r^2 force law depends on the force. Fluctuations in gravity are special, however, because once space-time itself can fluctuate, you can’t even talk about the “size” of the region in a clear way.

  20. That makes perfect sense. (I did wonder if the electromagnetic field would behave the same as the strong field.) Many thanks for the concise and informative answers.

    • The difference between the electromagnetic and strong nuclear forces is that the former’s field spreads out as 1/r^2 at distances longer than the electron Compton wavelength (and is slightly stronger than 1/r^2 as you look at shorter and shorter distances) while the latter’s field is slightly weaker than 1/r^2 as you go to at short distances, but goes to a constant and still rather large strength at long distance, forming tubes rather than spreading out uniformly, at r larger than the proton’s radius. That is why the proton is so structurally different, in so many respects, from an atom, and so much more complex than an atom.

      The neutralization of a strong field by particle-antiparticle annihilation is similar in the two cases, but the circumstances in which it occurs and you can observe it are very different. The strong field appears very readily in the case of the strong nuclear force, because it is always sufficiently strong at long distances. The electric field at long distances is typically weak, so you have to work hard to make a field strong enough to make electron-positron pairs.

  21. In The Feynman Lectures, he talks about the shape of the electron (I think it’s the chapter on electromagnetic mass). I remember that he says that if you try to find the EM energy of a point charge, it diverges. But if you then treat the electron as an object with some size (not a point) to avoid the divergence, then you run into problems like what holds the electron together (I think it had something to do with Poincaré stress, I don’t have my copy with me right now to verify). Ultimately he said that no one has managed to really fix the situation.

    However, Feynman wrote that 50 years ago. Has the situation improved?

    • Yes, that’s a reflection of somewhat out-of-date thinking. Not that his calculations are wrong, but the statement “no one has managed to fix the situation” is out of date. Asyptotic freedom (1972-73), grand unification (1974), string theory (1980s version) — none of these were around yet, and all of them give ways of potentially ameliorating the situation. We don’t know if one or more of these ideas is relevant to the real-world electron, but it clearly isn’t an unavoidable problem.

  22. Thanks for these really enlightening articles. If electrons spin, do we know what powers the spin, and if so do we know where that force comes from?

    • No force is necessary; the electron, when created, is already spinning, and will do so forever (or until annihilated.) This is perfectly reasonable. Once something is spinning, like the earth or sun, it will continue to spin forever unless friction stops it. This is because angular momentum is conserved, just like energy is conserved and momentum is conserved. No force is needed to keep the earth spinning (friction on the earth isn’t zero, but it is tiny). Friction is a macroscopic effect that does not affect microscopic elementary particles, so similarly, no force is needed to keep an electron spinning.

  23. Then when you say ( selected ) you are referring to a higher level laws as there must then exist a selector mechanism, do we imagine any thing about such higher level thing ?

  24. If the various interactions are ( tightly constrained by consistency conditions ), then we must assign some constraining mechanism to ” force ” interactions to be consistent , we can imagine a universe where interactions could in principle exist without being consistent , do we have any idea about such mechanism ?
    THEN we need a ( selector ) mechanism , and a ( consistency inforcing ) mechanism .
    Are the a/m can be considered a higher level physics ?

    • We don’t know how the constraints are realized, how charges are selected, etc. This lies beyond our current understanding of particle physics. Experiments at the LHC may yield insights, or the mechanisms involved may not be found for centuries or longer. There’s no way to know how long it will take.

  25. Now as far as we can grasp reality we see that there are no mass , no charge , no thing , only fields interacting , but fields interactions are just flashes of existence , here at the foundations of the cosmos there are nothing concrete , solid , firm , stable …….all are changing , decaying , annihilating , popping , an ocean of activity….. whence stability comes ?
    I can with firm affirmative stand say that stability IS the information directing , guiding and controlling all that activities……
    The cosmos is built not on fields but on active information……..
    WONDER OF WONDERS
    REFLECT

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  27. Based on the discussion of mass and charge, the article seems to address a shielded electron, not a bare electron. Yet the discussion of size raises the possibility that the electron could be a point particle with no size at all. How could a shielded electron be infinitely small? I think a discussion of mass/charge/size for shielded vs. bare electrons would be very useful.

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