Of Particular Significance

Fermions and Bosons

In a world where Einstein’s relativity is true, space has three dimensions, and there is quantum mechanics, all particles must be either fermions (named after Italian physicist Enrico Fermi) or bosons (named after Indian physicist Satyendra Nath Bose). This statement is a mathematical theorem, not an observation from data. But data over the past 100 years seems to bear it out; every known particle in the Standard Model is either a fermion or a boson.

An example of a boson is a photon.  Two or more bosons (if they are of the same particle type) are allowed to do the same exact thing. For example, a laser is a machine for making large numbers of photons do exactly the same thing, giving a very bright light with a very precise color heading in a very definite direction. All the photons in that beam are in lockstep.

You can’t make a laser out of fermions.  An example of a fermion is an electron. Two fermions (of the same particle type) are forbidden from doing the same exact thing. Because an electron is a fermion, two electrons cannot orbit an atom in exactly the same way. This is the underlying reason for the Pauli exclusion principle that we learn in chemistry class, and has enormous consequences for the periodic table of the elements and for chemistry. The electrons in an atom occupy different orbits, in different shells around the atomic nucleus, because they cannot all drop down into the same orbit — they are forbidden from doing so because they are fermions.  [More precisely, two electrons can occupy the same orbit as long as they spin around their own axes in opposite directions.  What is this spin thing?  another article.]  If electrons were bosons, chemistry would be unrecognizable!

The known elementary particles of our world include many fermions — the charged leptons, neutrinos and quarks are all fermions — and  many bosons — all of the force carriers, and the Higgs particle(s).

Another thing boson fields can do is be substantially non-zero on average. Fermion fields cannot do this. The Higgs field, which is non-zero in our universe and gives mass thereby to the known elementary particles, is a boson field (and its particle is therefore a boson, hence the name Higgs boson that you will hear people use.)

Something else you can do with boson particles is form a Bose-Einstein condensate, a phenomenon predicted by Einstein back in the 1920’s but only produced in a definitive way in the 1990’s, in Nobel-Prize winning experiments described in the link above. What these experiments do in making this condensate is cause large numbers of identical boson atoms to all sit as still as a quantum mechanical object possibly can.

[This is all quantum mechanics, by the way.  Einstein didn’t like the implications of quantum mechanics, but you should not have the impression, despite some popular accounts, that he didn’t understand it. In fact his work was crucial in the development of several aspects of  quantum theory.]

In principle you could make something similar to a laser out of any boson.  This has been done for atoms too.  And even more recently, a Bose-Einstein condensate has been made out of photons.


72 Responses

  1. Matt, in his famous E=mc² paper (https://www.fourmilab.ch/etexts/einstein/E_mc2/www/), Einstein said “the mass of a body depends upon its energy-content”. If you scroll down and look just above the last expression you can see how Einstein referred to the electron. So E=mc² is surely saying the mass of an electron depends upon its energy-content. If you haven’t already, it would be good to see you reconcile the Higgs mechanism with E=mc², especially since in your Higgs FAQ 2.0 article, you said the Higgs mechanism did not give the Higgs boson its mass. PS: I was just looking at your book. It made me think of William Kingdon Clifford’s 1870 space theory of matter.

      1. I know Bob Laughlin very well, as I was a Stanford graduate student. While I appreciate Laughlin’s intelligence and his point of view on this matter, I only half agree with it; I think he makes cavalier statements about how easy it is to make aethers with the properties that he cites. When he says, “studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness…” he is both right and wrong. Indeed, this is a point that I emphasize in my book. Space is not merely transparent; there’s more to it than that. (Which is why no particle physicist or string theorist I know agrees with Laughlin.)

  2. We know electron by what it does, not by what it is. / by Israel Socratus /
    a) Planck and Einstein found the energy of electron as: E=h*f
    b) Sommerfeld found the formula of an electron as : e^2=ah*c
    c) Dirac found two (2) more formulas of electron’s energy:
    +E=Mc^2 and -E=Mc^2
    d) According to QED in interaction with vacuum electron’s
    energy is infinite: E= ∞
    e) Electron tied with atom by the energy: E=-me^4/2h*^2= -13,6eV
    Nobody knows why electron has six ( 6 ) formulas and we don’t know
    what are interactions between these formulas.
    Electron has six (6) formulas it means that the electron can be in
    six different states and electron can come from one state to another.
    To come from one state to another one must be some mechanism
    of changes. What is mechanism of its changes? Nobody gives answer.
    =====. .
    Electron is not stable, solid, firm, steel particle .
    Electron’s size, mass, energy is dependent on its velocity.
    Electron’s size, mass, energy is dependent on its spin / angular momentum.
    The angular momentum can be different: 1/2, 3/2, 5/2, 7/2 . . . . etc.
    When angular moment is stronger, its size is smaller, the frequency is higher and
    the energy is bigger: E=h(bar)f.
    a) The electron follows Fermi- Dirac statistics.
    b) The electron obeys Pauli Exclusion Law.
    c) The Heisenberg Uncertainty Principle / Law
    d) Electron takes important part in Maxwell’s electrodynamics ( Lorentz force –
    – theory of electrons: F = qE + qv × B )
    e) The electron must observe
    ” The Law of conservation and transformation of energy/ mass”.
    Why does ” simple” electron obey fife ( 5 ) Laws ?
    Conclusion from some article:
    ”One of the best kept secrets of science is that
    physicists have lost their grip on reality.”
    ===============. .
    Today electron is an abstract, symbolic construction.
    Mainstream physics doesn’t know what electron is.
    Book ” What is the Electron?”, by Volodimir Simulik Montreal, Canada. 2005. /
    In this book:
    ‘ More than ten different models of the electron are presented here.
    More than twenty models are discussed briefly.
    Thus, the book gives a complete picture of contemporary theoretical
    thinking (traditional and new) about the physics of the electron.’
    And In the internet is possible to find 100 different models of electron.
    All of these models of electron are problematical.
    We know electron by what it does, not by what it is and the orthodox style
    of thinking wouldn’t open the door to understand what electron is.
    =================================. .
    Best wishes.
    Israel Sadovnik Socratus

  3. Wow, I am doing research for an IMAX movie titled: “Secrets of the Universe ”
    I noted to study Super Symetry months ago. The fact that all physical things, and all forces of nature and power, are eieither Fermions or Bosons is a staggering revelation to lay persons like myself ; and worthy of explanation in the movie. Fascinating !

  4. According to all known laws
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    should be able to fly.

    Its wings are too small to get
    its fat little body off the ground.

    The bee, of course, flies anyway

    because bees don’t care
    what humans think is impossible.

    1. How a bee flies is well understood scientifically. Just an old wives tale that bee flight is not understood.

  5. A question unrelated to any of the preceding: it appears that black holes and the speed of light are deeply related. Are photons embedded in event horizons, and are event horizons and waves different expressions of the same thing?

  6. This is intriguing information presented quite plainly- clear, consise, and helpful. Thank you writer of article!

  7. Could the phase between electric and magnetic waves be what distinguishes fermions from bosons? Bosons have no phase shift and fermions have a 90 degree shift. Everything in the universe would just be electromagnetic waves. Bosons travel through the space dimensions at the speed of light and fermions at rest travel at the speed of light through the time dimension.

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  10. Photons (bosons) can form laser, fermions cannot.
    But electrons occupy different orbits means, different energy levels – an evidence of angular momentum
    Bosons like photons, also have polarity as angular momentum. Every color have different energy- why we could not call it different orbits ?

    1. Well we have to be more specific here. Photons that are *exactly* identical, that is, are the same color, can form a laser, electrons that are *exactly* identical cannot. You can form a beam with electrons of different energy but it is NOT a laser where all the particles are ‘in step’ and the beam interferes with itself and is quite messy.

      All photons also have the *same* angular momentum, no matter what their color; their spin is always 1. Their linear momentum depends on their color or energy. (I believe it is equal to h/2pi)

      This can be seen if you take a bunch of bosons or fermion and take away all the energy you can from them. Fermions will form different orbits, you *cannot* take away their different energies, which is why they form orbits. Bosons will all sink into one state; you *can* take away their different energies. This is why we can’t call their different energies ‘orbits’.

      1. I thought fermions could create Bose-Einstein condensate as well, and therefore function at similar energy “outputs” or behaviors as boson in that state of matter?

        So I understand the emphasis on *can* for boson, but *cannot* for fermion I’m having trouble accepting/understanding.

        1. Under the right conditions, fermions subject to attractive forces can form stable pairs. A stable pair of fermions is a boson, and these bosons can condense. I think this is what you are referring to. This happens in superconductors and in various other materials.

          But unless the fermions form stable pairs (or some other stable combination of even numbers), this can’t happen. (By stable, I mean the pair stays together for a time scale longer than the existence of the condensate you’re trying to make.)

          Notice that atoms themselves are made predominantly from fermions (electrons, quarks, anti-quarks, plus bosonic gluons) and so the existence of Bose-Einstein condensates of bosonic atoms [with an even number of fermions in them] already raises these issues.

  11. Hi. I have a question regarding spin 1/2 fermions. If a particle like the electron can be seen in a cloud chamber, and a wave can be seen in the double slit experiment, does that indicate that the electron is a particle in one direction and a photon (wave) in the other? In other words, something in the experiment determines the outcome rather than interpreting the electron as a wave and a particle at the same time. I know that waves are viewed as probability waves, but it seems to me that spin could be re-interpreted so that in one direction a particle is evident while a wave would be seen in the other direction.

    1. The first thing I would note is that particles with spins other than 1/2 (And even integer spins) can be seen in a cloud chamber. (Notably the alpha particle with a spin of 0) and that such particles are no more or less ‘wavy’ than electrons. (Interestingly high energy electrons can be fired through a double slit into a cloud chamber. They will leave particle-like tracks but the sum of all the tracks resemble an interference pattern.)

      Simply because something only affects things in a limited location does not mean that it is a particle. A neat example is the ‘vortex cannon’ which produces a self-contained wave of air in the form of a ring: http://www.youtube.com/watch?v=4b2SV3ASUxY These rings move in straight lines and do not spread in the way a plain wave would. They can be made (with difficulty) to bounce off surfaces or interfere with other rings.

      A lot of what we think of at particle behavior can be displayed by waves with little difficulty.

    1. That depends on what the two particles are; an electron can absorb a photon, then re-emit it afterwards, an electron and anti-electron neutrino can become a Z boson (If they collide with enough energy.) And of course at high energy all sorts of particles and antiparticles may form.

  12. /there is quantum mechanics/
    /What these experiments do in making this condensate is cause large numbers of identical boson atoms to all sit as still as a quantum mechanical object possibly can(Bose-Einstein condensate)/
    /Two or more bosons (if they are of the same particle type) are allowed to do the same exact thing./
    /Two fermions (of the same particle type) are forbidden from doing the same exact thing./

    Single photon is massless, more photon(s?) in closed system(turn around) create rest mass.

    Exciting “The science”

  13. How large is a “Bose-Einstein condensate” made of the same atoms? Is it as small as the size of the single atom (or somewhat?/much? larger than that)? Does the condensate stay the same size or get larger and larger in volume as more atoms fall into the same state/place?

    1. A BEC can be considered an unusual gas. For various reasons the more atoms you add to it the larger it will tend to be. Also, like a gas, it is much, MUCH larger than the atoms that make it up, a lot of it is ’empty’ space. What differentiates a BEC from a normal gas is that all (or most) of its particles are in the lowest quantum state.

  14. Could you please elaborate this statement

    ” Two or more bosons (if they are of the same particle type) are allowed to do the same exact thing”

    Does that mean that two (or more) bosons could occupy same place in space?

    1. Yes, in fact many things can.

      Fermions are picky, no two can be exactly the same. Two fermions can be in the same place, if they are different in some other way. That is why electrons in atoms ‘pair up’ they occupy the same place as another electron because their spins are different. However each pair then refuses to share that space with any more electrons, this is what keeps atoms apart and our world solid. If you fill a box with atoms, eventually they refuse to get any closer and the box is full.

      Bosons however can be completely identical and have no problem sharing the same space with as many other bosons as you please. You can stuff as much light into a box as you want, and the box will never get full.

      1. I am no expert on bosons or fermions, but I enjoy looking through the commentary to see what I can understand. All I know is what 8th grade general science has taught and what little I find on the internet. So, please explain why bosons like photons have no mass but carry force while others both have mass and carry force. F=M•A?

        1. The equation F = ma applies only to massive particles. It does NOT say how much ‘force’ a particle carries, instead it relates force on a particle to its acceleration given its mass. For massless particles this means that any force should produce infinite acceleration (a = F/m, tending to infinity as m drops to zero.) which is sort of what we see, all massless particles move at light speed and are NEVER seen to ‘sit still’

          The term ‘force’ here is a bit broad. Let us say instead that massive and massless particles can carry *momentum* instead. In that case the momentum of a particle depends on its energy, whether that energy be in the form of rest mass (Protons say) or not (Massless photons carrying momentum proportional to their energy.)

  15. Right. This I think explains some slightly chemistry-ish physics I had wondered about.

    I take it the lowest electron orbital (1s) can hold four ‘electrons’ (Two antielectrons, two eleectrons, each pair of particles with opposite spins.) and something similar gives us ‘positronium’ (But I think the four particle ‘atom’ is energetically unfavorable.)

    And if electrons were bosons any number of them might cluster around an atomic nucleus, correct? Because the 1s orbital is the lowest energy configuration they can enter into.

    Therefore the same thing should be possible for other bosons; can electrically charged bosons like the W particle get ‘trapped’ around a positive atomic nucleus like leptons can?

  16. Are all fermions “massive (with rest mass)” and bosons “massless”? If so, why? Why is “1/2 spin” associated with a particle with rest mass? (and integer spin with massless particles?)

    1. The answer to your first question is No. There is no connection between spin and mass. Photons are massless spin-1 particles; W and Z particles have spin 1 and are massive. The Higgs boson is spin-0 and is massive. Electrons are spin-1/2 and have mass; but if the Higgs field were removed from the world, electrons would be massless (and still spin-1/2).

      1. hmm, strange.. so you can make a coherent beam with massive bosons:W and Z boson laser and Higgs boson laser?? Laser with mass?? And also you can cram as many these massive bosons as you like into the same point/place/state without limit? hmm, but the reason electrons cannot occupy the same place is not only due to exclusion principle but also due to its charge or not? For example, is it not possible to cram lots more of neutrinos into a tiny volume than electrons even though they are both fermions? Neutrinos do not interact much with matters on earth but they interact with each other very strongly? Neutrinos repel each other via exclusion principle? Does that mean a neutrino beam spreads out(attenuates) quickly and cannot travel together in the same direction that long? (compared to a photon laser?)

        1. In principle, yes. In practice the extremely short lifetime of the W, Z and Higgs particles makes this impossible.

          You can make Bose Einstein condensates from these things too, just as you can with bosonic atoms.

          The fact that you cannot cram infinite numbers of neutrinos (and other fermions) into the same state plays a crucial role in supernovas.

          You are right that there is repulsion among electrons due to their electric charge that complicates the story a bit, but the Pauli exclusion principle that gives us all of atomic structure and the periodic table of the elements has everything to do with the fact that electrons are fermions, and almost nothing to do with electrostatic repulsion.

  17. Today I read “The Elegant Universe” by Brian Greene…. Supersymmetry? That’s when I got confused and stopped dead before I went any further….

  18. I’ve read that, in Quantum Mechanics at least, one can conceive of an in-between class of particles called ‘anyons’. I understand the exchange/phase principle behind these hypothetical particles (which I appreciate you probably don’t want to go into here), but I’m just wondering whether anyons are sensible concepts in Quantum Field Theory (i.e. not just Quantum Mechanics) and whether they are taken as serious possibilities by theoreticians today or just viewed as mathematical curiosities?

    1. Anyons make perfect sense in two spatial dimensions, and are studied in detail in the context of materials that have a slab-like structure. In three spatial dimensions they don’t work. It has to do with the fact that rotations in a two dimensional plane are very simple, since you can rotate only clockwise or counterclockwise, whereas rotations in three-dimensional space are a lot more complicated, since you can rotate around any axis you like, and doing two rotations in one order gets you to a different orientation then if you do the rotations in the opposite order.

      1. I’m very late to the party but if you’re still around I have a question.

        What if you think about the universe as the 2d object? Isn’t there a popular theory that the universe is flat? And that every object exists on top of it? Could it be that the anyons exist on/in the “fabric” of the universe? I have no idea if these questions make sense but it’s fun to think about!

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A decay of a Higgs boson, as reconstructed by the CMS experiment at the LHC