PeterDonis said:
However, because this interaction is so weak, and because it is never present by itself--it is only present in situations like atomic nuclei and radioactive decay where the strong and electromagnetic interactions are also present--it is never observed as an actual "force" that causes attraction or repulsion because its attraction or repulsion is too small compared to the strong and electromagnetic interactions; it is only observed by the particular radioactive decays that it causes. That is what
@Drakkith was describing in post #2.
I'd say the fact that the "weak interaction" (I'd abandon the word "force" from all relativistic physics right from the very beginning ;-)) "is never present by itself", which I guess means that you don't "feel" it in our macroscopic world, is due to the fact that it's of very short range, which is due to the large masses of the corresponding gauge fields, whose particle-like excitations are the ##W## and ##Z## bosons. That's of course due to the Higgs mechanism at work in the description of the weak interaction. Note that there's also the photon within this theory ("quantum flavor dynamics" aka "Glashow-Salam-Weinberg model"), which is "un-Higgsed" and thus massless. The corresponding gauge field is of course the electromagnetic field, which is observable in our macroscopic world, even in its "free states", i.e., electromagnetic waves of a wide range of wave lenghts (note that these "macroscopic fields" are no photon states but rather coherent states or thermal (Planck) radiation, etc.).
To make the discussion complete, there's also the strong interaction, which holds the quarks together to form hadrons (among others protons and neutrons, making up the nuclei forming the macroscopic matter around us). It is described by quantum chromodynamics, QCD, which is also a gauge theory, but it's completely "un-Higgsed". Nevertheless, we also don't "feel" it although it's by far the strongest interaction in Nature. Here the reason is much more complicated: It's called "confinement".
Phenomenologically it means that we never observe free quarks (the fundamental/elementary spin-1/2 particles carrying color charge and thus participate in the strong interaction) nor free gluons (the quanta of the gauge field) or the corresponding free field. The reason is that in a non-Abelian gauge theory the gauge bosons themselves carry charge.
The formal argument, why we don't observe anything carrying color charge is gauge invariance: We can't observe anything which is not gauge invariant and we can't form color-charged gauge-invariant observables. That's why all we can observe are color-neutral objects, the socalled hadrons, which are very complicated bound states of quark and gluon fields. Usually they come as mesons (bound-states of a quark and an antiquark) or baryons (bound-states of three quarks). There are also hints of more "exotic" varieties like tetra quarks (consisting of two quarks and two antiquarks) as well as glue balls (formed purely by the gauge field/gluons). All we can observe of the strong interaction in a sense of "force" (if you want to use this word at all ;-)) is the residual interaction between color-neutral hadrons.
From a theoretical point of view in our macroscopic world, quarks and gluons are not the appropriate degrees of freedom to describe the strong interaction but rather effective theories of hadrons, which use the (residual) symmetries of QCD to constrain the corresponding models. Most important in this context is the approximate chiral symmetry of QCD in the light-quark sector (u- and d-quarks; to lesser extent also s-quarks), from which the pretty complicated interactions, e.g., between nucleons (protons and neutrons) can be understood, which describes then both the scattering between the nucleons as well as the formation of atomic nuclei as bound states of protons and neutrons. These interactions go also beyond simple two-body interactions, and an understanding of nuclear structure from these "first-principle approaches" is a (already quite successful) topic of ongoing research.
The understaning of the formation of the hadrons as bound states of quarks and gluons, however, is much more complicated. The most successful technique is lattice-gauge theory, where QCD is numerically evaluated approximating its action on a discrete space-time lattice using Monte-Carlo techniques. There are two varieties: "vacuum lattice-QCD". Here one of the greatest successes is the calculation of the hadronic mass spectrum, including the prediction of higher-mass states not yet observed. The other variety is "finite-temperature lattice-QCD", which studies the equation of state of strongly interacting matter and the corresponding phase diagram. In Nature this is relevant for (a) neutron stars and neutron-star mergers, which nowadays can be observed with "multi-messenger astronomy", i.e., via electromagnetic waves in a large range of wave lengths and, since 2015, with gravitational waves (as well as with neutrinos, at least in principle), and (b) in collisions of heavy nuclei (relativsitic heavy-ion collisions) as done at the LHC and SPS (CERN), RHIC (BNL), GSI (Darmstadt) and in upcoming new facilities like FAIR (Darmstadt), and NICA (Dubna).
