The charges of the forces

Question

I am trying to establish a simplified understanding of the fundamental forces to explain them to a young audience.

If we say that gravity has one charge (attractive), electromagnetism has two charges (positive and negative), and the strong force has three (red, green and blue), what does the weak force have? I understand it would be something to do with isospin. Is it two, like electromagnetism?

Extended question: The reason I am doing this is because there is a problem explaining gravity as weak. Kids respond by saying, "if it's weak, then how can it swing big things like planets around?" I realise that explaining that it is only additive is very important.

So I am thinking about a simplified system to explain the force's attractive power (as opposed to another 'rating', which would be quantum power - where the strong force is 10/10, Gravity is 1/10, etc....)

Gravity would be 10/10, as its only additive - Electromagnetism would be 5/10, as it only half attracts and half repels.

In this scenario, what would the strong force be? 3.3/10, or 6.6/10? I imagine it is the latter, as red attracts green and blue, not one or the other.

Of course, this is problematic when it comes to the weak force, as (as far as I know) it does not play a role in binding things together. So maybe the best rating for this one is n/a (not applicable)

Answer 1

To say that the strong force has "three charges: red, green, blue" is not the correct analogy to the mass of gravity or the charge of electromagnetism.

Formally, both the mass and the charge classify certain irreducible representations of the Poincaré group and the circle group, respectively. But "red, green, blue" are arbitrary labels for certain directions in the fundamental representation of the strong gauge group $\mathrm{SU}(3)$ - they do not classify different representations, a "red" quark transforms in the same representation as a "blue" quark, and in fact, a gauge transformation turns one into the other. Color is not a quantum mechanical observable, while charge and mass are, as they are (gauge) invariants.

The correct analogy to "charge" is the representation something transforms in - a quark transforms in the "color" (fundamental) representation, an anti-quark in the "anti-color" (anti-fundamental) representation, a gluon in the "color-anticolor" (adjoint) representation.

You cannot talk of simple "attraction" or "repulsion" laws for the strong force (or the weak force, for that matter) because the classical limits of these forces do not give the correct picture of what they actually do. For instance, the linear force law between a quark and an anti-quark, responsible for confinement, does not arise from some classical consideration of the non-Abelian Yang-Mills theory, it arises from an inhererently quantum mechanical computation of the expectation value of a Polyakov loop in the gauge theory, representing a "flux line" between two static quarks.

Also, the classical force law corresponding to the weak force (in the effective model where it is mediated by pions, for instance), would be exponentially suppressed because the mediators are quite massive - this force just vanishes on classical scales.

So, both the strong and the weak "force" are inherently quantum field theoretic concepts. It does not make sense to try and assign "attractive power" or "repulsive power" to them because those concepts are inherently classical.