*Advanced particle physics today:*

Today I’m continuing the reader-requested explanation of the “triplet model,” (a classic and simple variation on the Standard Model of particle physics, in which the W boson mass can be raised slightly relative to Standard Model predictions without affecting other current experiments.) The math required is pre-university level, just algebra this time.

The third webpage, showing how to combine knowledge from the first page and second page of the series into a more complete cartoon of the triplet model, is ready. It illustrates, in rough form, how a small modification of the Higgs mechanism of the Standard Model can shift a “W” particle’s mass upward.

Future pages will seek to explain why the triplet model resembles this cartoon closely, and also to explore the implications for the Higgs boson.

Please send your comments and suggestions!

## 5 Responses

Prof. Strassler:

In classical mechanics the gravitational force on a particle depends on the presence of other masses through a potential field but not the mass of the particle itself. In a quantum field the potential energy density of a field is partly or wholly depends on the rest mass of the field quantum times the square of the amplitude of the field itself. Is this simply a quantum field phenomenon that one just has to wrap one’s head around? Or is there a more “concrete” explanation/description. Or perhaps there is an analogy in classical electrodynamics since I never studied it.

The issues raised in your first two sentences really aren’t related. The first is about how gravity responds to the presence of localized energy (mass being just one form of energy) within particles. The second is about how much energy is associated with spread-out fields, and has nothing to do with gravity and nothing immediately to do with particles either. The logical way to connect them is this:

(1) take the potential energy V of fields F as a given. If I *uniformly* change the value of a field away from its vev everywhere across space, it will increase the energy-per-unit-volume of the universe.

(2) consider a ripple in F, with very small amplitude ; this “quantum” or “wavicle”, as it is often called, has energy both due to the fact that it is rippling in space and time and also due to the fact that, because F is *locally* different from inside the ripple, there is some potential energy from V; together this energy divided by c^2 gives it its gravitational mass, and

(3) because it has gravitational mass, it will both create and respond to gravitational effects, such as those due to other particles.

[Note that gravitational mass = rest mass only if the particle is stationary and its rest mass is non-zero.]

Many thanks for the clarification. I forgot that the amplitude of a quantum field at a space-time point represents the number of particles at that space time point.

Particles placed at a spacetime point instantly spread out (uncertainty principle). You are better off understanding that a wave with definite wavelength is made from “particles” [i.e. “wavicles”, or “quanta”] with the corresponding momentum; that statement, at least, is true indefinitely for a free field, and for a while for a field with only relatively weak interactions with other fields.

Thanks for your detailed and step-by-step physics explanations. You make very complex particle physics a little bit simpler for us. I write this comment here because it concerns formatting. My suggestion is to add MathJax to your WordPress posts (seems that there’s such plugin) what I believe will make reading easier. I think I can volunteer some time to test latex support if there’re technical problems.