The Higgs Story-Part 7: How fields behave


Perhaps it would be good at this point to take a breath and summarize up the state of play so far. (For previous posts in this series, click on the Higgs folder just below the blog post title.)

In quantum mechanics we have the unifying idea that everything in the universe is made up of relativistic quantum fields that correspond to elementary particles and which I will refer to in the future as simply fields. These fields are wavy-like vibrations and differ from classical waves in that they are not vibrations of a medium (like water for ocean waves or air for sound waves) but vibrations of space itself, if you can imagine it. The word quantum in its name comes from the fact that the energy of vibrations of these fields can only change by small discrete amounts (or ‘quanta’) and not continuously, the way that classical vibrating fields can.

According to the emerging modern consensus, there are no particles in the classical sense, just these fields. These fields are always spread out over all space but not uniformly, and when they are sufficiently bunched up in some region of space, they can look and behave like what we call particles. When I refer to particles in the future, this is what I will mean by that word. The more particles there are, the more energy there is in the corresponding vibrating fields and the greater the vibrations.

The value of these fields at any given point in space is not just a number (as it is for the temperature or pressure fields) but is a more complicated mathematical quantity. These fields interact with each other according to specific laws and can re-arrange themselves to produce the material objects we see in everyday life. Of course, any ordinary object consists of an enormous number of elementary particles and we have no hope of explaining its properties in terms of those fundamental fields, so we reserve use of the field theory framework for situations consisting of just a few elementary particles.

The fundamental fields are those associated with the 19 elementary particles that we described in Part 3 in this series, consisting of six quarks (up, down, strange, charm, bottom, top), six leptons (electron, muon, tau, electron neutrino, muon neutrino, tau neutrino), six force particles (photon, graviton, gluon, W+, W-, Z) and the Higgs particle.

These particles do not form a random collection because there are some interesting patterns among them.

The six quarks all have mass and electric charge and other properties in common and interact with all other particles via the strong, electromagnetic, weak, and gravitational forces. The leptons all have mass and consist of three charged leptons (electron, muon, tau) and three neutral ones (the neutrinos) and are chiefly distinguished from the quarks by the fact that they do not interact with anything via the strong force.

Furthermore, the six quarks can be grouped into three pairs (up, down), (strange, charm), (bottom, top) such that each pair seems to mirror in properties the one before, except at a higher mass. The same thing is true for the six leptons which can be grouped into three analogous pairs (electron, electron neutrino), (muon, muon neutrino), (tau, tau neutrino), again in order of increasing mass.

In addition, each of those sets of pairs of quarks and leptons can be grouped into three larger groups (called ‘generations’) of four (two quarks and two leptons) in order of increasing mass. There are theoretical suggestions that there can be no more than the three generations we already have, ruling out the possibility of discovering yet other elementary particles of higher masses. In other words, we have reason to think that with these 19 particles we may have reached the end of the search for elementary particles, unless it turns out that these particles are themselves composites made up of yet smaller entities, in which case we are off to the races in a new search.

Furthermore, the six force particles (photon, graviton, gluon, W+, W-, Z) emerge naturally out of something called ‘gauge theories’ (which is why they are called ‘gauge bosons’) that were invented to explain the above patterns amongst the quarks and leptons.

It is the existence of such patterns and connections that give physicists hope that we are on the right track and can find a unifying theory that integrates them all. If all the elementary particles had seemingly random properties with no patterns, that would make the search for a unifying theory much harder and cause one to suspect that it may not even exist.

In amongst all these nice patterns, there are three jarring anomalies. One is that when it comes to the strong, electromagnetic, and gravitational forces, there is just one particle associated with each, the gluon, photon, and graviton respectively. But for the weak interactions, we have three particles W+, W-, and Z. The second anomaly is that when it comes to the masses of these particles, not only do we not know where those masses come from and why they have the values they do, there seems to be no discernible pattern among them. The third anomaly is the Higgs particle. The Higgs is an odd duck among the other 18 particles because it does not belong in any of the sub-grouping patterns that I listed. While it shares many of the properties of the other force particles and is often lumped in with them the way I have done, it is not itself a particle associated with any fundamental force or, to put it technically, it is not a gauge boson because it does not emerge out of a gauge theory of quarks and leptons.

It turns out that all these three anomalies are related to the presence of the Higgs field, which I hope gives you some idea of why the search for the Higgs particle was considered so important. But before I get to it, it is advisable to take a look at something I have ignored so far, and that is gravity.

Next: Gravity and the graviton

Comments

  1. troll says

    Is each particle of a given type a discrete field, or are individual particles just different points within a single field of the particle type?

  2. Rob Grigjanis says

    For each type of particle, there is one field permeating space, and all the particles of that type are local excitations in that field. So, one electron field, and all electrons are excitations in that field. Same for each of the other elementary particles.

    Using ‘field’ can be confusing, because it has such different usages.

  3. curcuminoid says

    Do we expect the properties of the fields to change as the magnitude of space does, since the former is a vibration of the latter?

  4. Mano Singham says

    That is a really interesting question to which I have no answer off the top of my head. The expansion of space takes us into the field of general relativity and we do not as yet have a theory of quantum gravity, so the answer may well be that we do not know. But maybe someone who does know more about this will chime in.

  5. Rob Grigjanis says

    My limited understanding is that the changes in fields/field properties that have occurred since the Big Bang have been due to cooling rather than spatial properties. In other words, what we see now is as a result of phase transitions that have occurred as the background temperature has dropped, breaking symmetries that were there ‘at the beginning’ (whatever that means!).

    There’s no doubt that the particles one observes depends on frame of reference.

    …a state which looks like a vacuum to one observer can look like a heat bath to another accelerating with respect to the former observer.

    But this does not reflect a change in the properties of the fields.

  6. Mano Singham says

    I will be talking about those phase transitions later when we get to the Higgs mechanism. Sorry it is taking so long to get there!

  7. Marshall says

    Mano, are you planning on explaining entanglement in the context of fields? How is it that local excitation of a field can somehow share properties with an excitation somewhere else? Does the field sort of wrap-around back on itself, so an excitation at one point also excites another?

    I’m imagining taking a sheet and bringing two distance locations together so they’re touching. If you jiggle one, it jiggles the other as well. But this is just me making up explanations again….what’s the real deal?

  8. Mano Singham says

    Quantum entanglement (i.e, the EPR paradox) is a problem that is somewhat independent of the the issue of particles being considered to be fields. I may address entanglement at a later time as an independent topic.

  9. embertine says

    This is fascinating! thank you so much for doing this; cannot wait for the next installment.
    *chinhands*

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