Of Particular Significance

Why The Electron Can’t Have a Mass Without the Higgs Field

POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON 11/27/2012

After a hiatus for a hurricane and a trip to a conference in Asia, I am adding one more article to my series on How the Higgs Field Works, following my series of articles on Fields and Particles. (These sets of articles require a little math and physics background, the sort you’d get in your first few months of a beginning university or pre-university physics class.  I’m still thinking about how to structure a similar set of articles that require no math or physics; that’s much harder, of course!)

The first article in the series explained the basic Idea behind how the Higgs field works. Then came an article about why and how the Higgs field becomes non-zero, and a third concerning how the Higgs particle arises as the quantum of waves that oscillate around the non-zero value of the Higgs field.  The new article tries to clarify why there’s no alternative to introducing a Higgs field, explaining that it’s otherwise impossible to reconcile two apparently contradictory features of our world: a mass for the electron (and many other types of known particles) and the properties of the weak nuclear force.

This article contains the most elaborate equations and concepts that I’ve had to introduce to my readers, so it won’t be suitable for everyone (though it still only requires some first-year physics/math.)  But on the other hand, it seems necessary for me to write it, since it’s the only place that I’ve explained not only why the Higgs field can give mass to the known particles, but why it (or something very much like it) must do so.

(Note that in these articles I’m mainly concentrating on the simplest type of Higgs, the Standard Model Higgs field and particle.  However, most of the basic concepts in these articles apply even for more complicated cases.)

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9 Responses

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  3. Hi Mr. Strassler. Forgive me if it is out of topic, but I couldn’t find your email address anywhere. I wanted to ask you some advice about which college would be, in your opinion, the best choice for me. I’m 17 years old, and I live in northern Italy. I’m in Massachusetts now, because I’m staying here this year as an exchange student. I really like physics, and I’m attending an AP Physics class in my american high-school. I’m supposed to come back to italy next year and go to university there. But I was wondering if there’s a better choice. I was thinking about looking for scholarships here or in England, and try to see if I’ll find a good university. I know there are good colleges here in Usa, but I have to take in account that I can’t afford it.
    At school I’m pretty good (here I got an A in the physics class), so maybe there would be a chance to get some good scholarship. Or maybe I should look for a college in England, since I can pay the fee after finishing it.
    What do you think will be the best idea? Take in account that italian universities are good, the problem in italy is working. Maybe I should go to university in italy and then look for a job abroad. What would you suggest me? Do you know any good college that could offer me a significant scholarship?

  4. Professor, it is enlightening- thank you, thank you.

    /The Higgs field has the same spin as empty space — zero. So when the Higgs field’s value (vev) is non-zero, nothing about the basic structure of space and time changes./- well said !- “from empty space to mass, from nothing to being”.

    My innocence was… creation of new space(cooling of universe or spacetime expansion) will be prominent at the micro level of very short distance, electroweak interaction- which could not be observed at the presence of spacetime curve(gravitation).
    Moreover, matter dispersion would have burnt out the Sun- which get conservation of energy(mass) somewhere- which effects the slow process.
    Interaction between neutrino flavor oscillation and Dark Energy may be one of those causes.

    Anyway it is out of topic here.Thank you again.

  5. Professor Strassler,
    dχ/dt – dχ/dx = -μ ψ
    makes no sense; the change in time of a field χ that is affected by the weak nuclear force cannot be proportional to a field ψ that is not affected by the weak nuclear force.

    There are actually four Higgs fields, not one — three of them disappear in the end.

    All of them have zero in some region of space and time, but only the “average” is non-zero – which is evident from the “jitter”. But we Did’t know at which spacetime it become non-zero- we call this jitter as Higgs boson, which is scalar and heavy. It could not escape its brotherly affection of other three simple Higgs fields, but have no place to live with them, seperated by spontaneous symmetry breaking and thus the jitter? – simultaneously acts as χ and ψ ?

    But Higgs field(s) is transcendent so could not be scalar?- but simple Higgs could be?

      1. Sorry Professor,
        electrons have chirality due to 1/2 integer spin, thus χ and ψ particles are exhibiting quantum mixing by Higgs-induced mass term.

        Higgs boson have no chirality due to “0” spin. The jitter or “vev” creates simultaneously “0” (Higgs) and “2” (gravitational or spacetime curve) spins? – which is due to different region of space and time and could not be observed in the presence of gravitational field?.

        1. The Higgs field has the same spin as empty space — zero. So when the Higgs field’s value (vev) is non-zero, nothing about the basic structure of space and time changes. What had spin 1/2 before still has spin 1/2; the only difference is that there is now mixing (flip-flopping) between the χ and ψ fields, which previously were indepedent. There’s no effect on gravity; I am not sure why you are bringing gravity up here.

          Do not confuse the jitter (quantum fluctuations) and the vev (a large average value that remains even when you average over the jitter.) The jitter is a quantum effect. A non-zero value is a (more or less) classical (i.e. non-quantum) effect. You should read the ball-on-spring articles again; the Higgs vev is to the Higgs jitter as the equilibrium value of the ball’s position is to the quantum jitter around that position.

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