The Higgs Story-Part 9: What makes the Higgs field so special


I have said before that the emerging modern consensus is that there are no particles or waves in the classical sense of those terms, although those concepts are still useful to us in visualizing physical processes. (For previous posts in this series, click on the Higgs folder just below the blog post title.)

Relativistic quantum fields, each corresponding to what we refer to as an elementary particle, are all there is and everything is made up from these fields. All these fields have tiny vibrations even in the vacuum where there are no particles. Elementary particles can be considered to consist of larger (i.e., higher energy) vibrations of the fields corresponding to them, beyond the level of vibrations in the vacuum. If these higher energy vibrations become localized in a region of space, that will give the appearance of a particle being present in that region of space.

These fields are present even in the vacuum and vibrate by tiny amounts. This is one necessary consequence of the uncertainty principle. It is the fact that the vacuum always has these tiny vibrations that results in scientists seeing the vacuum as a dynamic entity that can give rise to some interesting effects, rather than being uninteresting and inert as is popularly thought. This is what physicists mean when they speak of the vacuum or ‘nothing’.

One consequence of these ever-present vibrations of fields is that we can have the creation of what are called ‘virtual’ particle-antiparticle pairs out of this quantum vacuum. These virtual particles can exist for a short time before recombining and disappearing, leaving us with nothing again. For example, one can have the sudden appearance of an electron and an anti-electron (called a ‘positron’) pair out of the vacuum that exists for a short time. So the quantum vacuum can be thought of as a kind of foamy sea where pairs of particles are popping in and out of existence all the time.

If matter can suddenly appear out of nothing, doesn’t this violate the law of conservation of energy? Yes it does. But one form of the uncertainty principle says that such violations are possible for a short time, provided that the amount by which energy conservation is violated, multiplied by the duration of the violation, is less than a very small (but non-zero) amount of the size of Planck’s constant, which is a universal constant of nature that was introduced to explain blackbody radiation that heralded the dawn of the era of quantum mechanics back in 1900.

In other words, the larger the violation of energy conservation, the shorter the time the uncertainty principle allows it to last. For an electron-positron virtual pair, the allowed duration of violation is about 10-21seconds, a really tiny time. And this is about as small an energy violation as you are likely to see, since the electron is one of the lightest particles there is. More massive pairs will last even shorter times. This is why we do not see energy conservation violation in everyday life.

The significance of the Higgs particle is that it is a prediction of the Higgs field which, as we will see later is what, via the Higgs mechanism, gives mass to the elementary particles. Finding the Higgs particle confirms the existence of this field and is thus an important prediction of the Standard Model.

So how does the Higgs field give rise to the masses of other particles? It arises from one key difference between the Higgs field and all other fields.

For all fields other than the Higgs, even though they have vibrations even in the vacuum, the average value of those fields in the vacuum (called the ‘vacuum expectation value’) is zero. But the Higgs field has a non-zero average value even in the vacuum. In other words, all of space throughout the universe is permeated by this non-zero Higgs field. This is what makes the Higgs field so special because it is the presence of this non-zero field that gives rise to the mass of particles.

To use a popular analogy, think of this field as a kind of non-physical syrup that permeates all space. In its absence, all particles would travel unhindered at the speed of light, which is equivalent to them having zero mass. But when the syrup is present, the particles are slowed down by it, which is equivalent to them ‘gaining mass’. The amount by which they get slowed down, and hence their mass, depends on the strength of interaction between the particles and the Higgs field.

Moreover, the average value V of the Higgs field in the vacuum is predicted by theory to be given by V=[GF√2]-1/2, where GF is called the Fermi coupling constant that is related to the strength of weak nuclear force, one of the 19 parameters of the Standard Model that were listed in this earlier post and have to be obtained by experiment. Since GF is a known measured quantity (given by GF=1.166×10-5 GeV-2), we can calculate the value of V and it has the value of 246 GeV. Note that this is the average value of the Higgs field in the vacuum. It is NOT the mass of the Higgs particle. It is large local vibrations in this non-zero Higgs field that correspond to the presence of a Higgs particle in a region, just like it is large local vibrations of the electromagnetic field in some region that correspond to the presence of a photon there.

The Higgs particle has zero electric charge and spin and that is one of the reasons why the Higgs particle is so hard to detect. Its properties are such that it just doesn’t stand out clearly from the vacuum background. As someone once said, searching for the Higgs particle is worse than looking for a needle in a haystack, it is more like looking for a particular piece of hay in a haystack.

But it does have a mass. Unfortunately while the average value of the Higgs field is predicted by theory, the mass of the Higgs particle is not and so it could have had any value. Since the mass of a particle is one of the main features we use to design experiments to detect its presence, this ignorance of where to look was one of the reasons that made the search for it so hard.

There is, however, a element of the theory called unitarity that, if it holds (as we think it does), puts an upper limit to the Higgs particle mass of about 1 TeV or about 1000 times the mass of a proton. As we will see, this fact strongly influenced the design of the Large Hadron Collider.

But that still leaves us with a huge range of masses that have to be searched through to find it.

Next: The non-zero Higgs field in the vacuum

Comments

  1. curcuminoid says

    But if the Higgs field has positive energy, then won’t total energy of the system increase simply by increasing the volume of the system (and decrease by decreasing volume)? Or is total energy of the Higgs Field constant, and its energy at a given point changes in proportion to the change in volume? If the former, wouldn’t that imply the force that the force resisting increases in volume and favoring decreases in volume (ie. gravity) and the Higgs field are related?

    Tangential to what you mentioned about the creation of virtual particles, something been bugging me about the Casimir effect for a while. Consider two frictionless plates in the following cycle (ignore the underscores, their there for formatting):
    1. |_____|
    2. ||
    3. |
    __ |
    4. |
    _______|
    5. |_____|

    The energy released by the plate moving in at 2 is greater than the energy required to move the plate out at 4 (because in the latter step the plates don’t overlap and therefore aren’t acted upon by the Casimir effect). The only way I can see that the energy balances is if there would be a force resisting the parallel movement of the plates, equal to the potential of two parallel plates at infinity (overlapping non-overlapping parallel plates, as in step 5, would release energy equal to the potential at infinity less the potential at that distance). But for the life of me I can’t see what part of the Casimir effect would create a force with those properties. Do you have any knowledge or insight on the matter?

    I apologize if I’m bugging you with questions.

  2. Rob Grigjanis says

    “Unfortunately while the mass of the Higgs field is predicted by theory…”

    “vacuum expectation value” rather than “mass”, no?

  3. Mano Singham says

    To answer only the first question because I am in a rush, the value of the Higgs field has the units of energy but that does not mean it is an energy. As a parallel, torque has units of energy but is not an energy.

    As to the Casimir effect question, I am not that familiar with the issue you raise so I will have to look into it a bit more before responding, unless someone else has some ideas.

  4. Rob Grigjanis says

    You’re doing work in sliding the plate (step 3). The energy of the system in (2) is negative, and proportional to the area of the plates. As you slide the plates apart, the effective area decreases, thus increasing the energy of the system.

  5. curcuminoid says

    Unless I’m missing something, what you said explains why work must be done but not the how that happens. Assume the plates are frictionless and very light. Unless there is a force that resists the lateral motion of the plates relative to each other, it takes essentially no work to move the plate but the energy of the system is increased. No energy has gone into the system, but its total energy would change, which seems to me a violation conservation, so the aforementioned resistive force must exist. But how does that force arise?

  6. Rob Grigjanis says

    The force arises because maximal alignment of the plates corresponds to the minimum energy state (if the distance between the plates is constant). Any sliding of the plates (while maintaining the distance) results in a higher energy state, because the effective (face-to-face) area is reduced. The resistive force is just a consequence of the energy gradient.

  7. Rob Grigjanis says

    More precisely, the resistive force is the negative of the energy gradient.

  8. curcuminoid says

    But I don’t see how its sufficient for there just to be an energy gradient. (Its entirely possible that as a biochemist I’m out of my depth here, so maybe I’m just being a bit thick. If so, sorry.)

    Imagine a circular river. If you place a plate attached to a tower through a spring into the river, the system will reach an energy minimum when the torsion of the spring equals the force of the current. If you life the apparatus up out of the river, the potential will no longer be at the minimum and the spring will compress, at which point the apparatus can be lowered back into the river and we’re basically where we started. In this case, there was no resistive force preventing the apparatus from being lifted (ignoring friction and gravity) despite this moving up a negative energy gradient.

    There’s no problem in this hypothetical because getting work out of this cycle comes out of the river and slows down the current (eventually to 0). But with a field in its ground state, there’s no where for the energy to come from since the energy of the field can’t go down by definition.

  9. Rob Grigjanis says

    “Imagine a circular river”

    Where I come from, they’re called moats. Not much flow apart from Coriolis effects. :)

    You may be overthinking this. Forget springs and rivers. Go to first principles. A system is in a certain sate (e.g. two identical plates facing each other a (small) distance apart). Can you calculate the energy of this configuration? Yes, and it is proportional to their common area, and negative. OK, now consider a configuration in which one of the plates has been moved slightly while maintaining the distance between them. The common area has decreased, so the energy of this configuration has increased, because the initial energy was negative. If the energy has increased, there is a force (by definition; F=-dE/dx) pushing the new configuration toward the original one.

    An analogous scenario: Imagine an apple lying on the ground. Now imagine it one foot above the ground. However it got there, it is in a state of higher energy (gravitational energy is proportional to -1/R, where R is distance from centre of Earth), and there is therefore a force directing it back to the ground.

  10. filethirteen says

    For an electron-positron virtual pair, the allowed duration of violation is about 10-21 seconds, a really tiny time.

    Wouldn’t Hawking radiation (if it exists) exceed that?

  11. Mano Singham says

    curcuminoid,

    Sorry for the delay in replying. I did not at first understand the question that well and the little diagram you gave but your dialogue with Rob has clarified it for me and Rob has addressed your question well.

    What I would add is that due to the Casimir effect of virtual photons being created, there is an attractive force between the plates. When the plates are perfectly aligned with each other, the force is perpendicular to the plates and brings them straight towards each other and there is a reduction in energy. There is also no lateral force.

    But when you start moving the plates laterally, as soon as they move out of alignment, the symmetry is broken and there is a component of the force that tries to pull it back and in order to overcome this force. To continue the lateral motion, the external agent has to provide some energy to the system. It is not noticing this that may have puzzled you.

    For an analogy, think of the force between the two plates being due to a spring, except that this is a spring where the force gets smaller as it is extended, to keep in line with the nature of the Casimir effect. As long as the plates are aligned, the spring is perpendicular to the faces of the plates and there is no lateral force. But when you pull one plate laterally, now the spring will try to bring it back into alignment.

    This can be also be seen with electrically charged plates, where the forces are lectromagnetic and not the more exotic Casimir ones.

    Hope that helps.

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