Can strong and weak "forces" manifest in Newton Units?

Question

The Newton unit ($\text{N}$) is a unit of force on a macroscopic scale:

$$1\text{N} = 1 \text{kg m/s}^2.$$

1. Gravity has so-called the gravitational forces (such as shown in the Newton theory of gravity ${\displaystyle \mathbf {F} =m \frac{GM}{r^2}\hat{\mathbf {r}} }$) that can be quantified in the Newton unit ($\text{N}$) in a macroscopic way.

2. Electromagnetism (EM) has so-called the EM forces (such as shown in the Lorentz force ${\displaystyle \mathbf {F} =q\,\mathbf {E} +q\,\mathbf {v} \times \mathbf {B} }$) that can be quantified in the Newton unit ($\text{N}$) in a macroscopic way as well.

We also call strong interactions and weak interactions (understood in the framework of quantum field theory with path integral and lagrangian formalism) with strong and weak forces.

Question:

Can either strong and weak interactions manifest them in order 1 in the Newton Units on a macroscopic scale?

If not in order 1 in Newton Units, why are strong and weak interactions counted as forces (macroscopically)?

However, it seems to me that the strong interactions and weak interactions manifest in the subatomic scale.

• The strong interaction confines the quarks in the nucleon and controls $\alpha$ decay.

• The weak interaction controls $\beta$ decay.

Answer 1

I wonder why you appear to think that a force can only be called a force if it manifests itself macroscopically, or of order 1 Newton.

If you neglect quantization, the strong and weak fields manifest themselves in a Lagrangian very similar to the Lagrangian of the electromagnetic force. Since the Lagrangian is an action density, and action is energy multiplied by time, and energy is related to force, they are indeed forces. The only profound difference between electromagnetism and strong and weak fields is that the latter are self-interacting, i.e. nonlinear, in a gauge-invariant way.

When it comes to the interaction between fermions and the strong and weak gauge bosons, there is of course no non-quantized "strong or weak Lorentz force", due to the smaller scales of the strong and weak forces. Rather the fermions are coupled by the Dirac equation to the gauge bosons (just like the quantum mechanical EM interaction is ruled by the Dirac equation), and the Dirac equation is genuinely quantum mechanical.

I guess you could formulate a classical strong or weak Lorentz force, but it would just not be valid on any scale, first of all because quarks are confined to very small volumes.