Does the weak force get transmitted at speeds less than $c$? The force carrier of EM is the photon (or off-shell photons at least). These are massless field disturbances. However the force carriers in Weak interactions are the $W$ and $Z$ bosons. Having mass, do they transmit information at subluminal speeds then?
 A: The weak interaction is mediated by a field, not by particles, despite the poetic/lazy language that physicists sometimes use. The W and Z particles are special manifestations of the W and Z fields that mediate the weak interaction, but the fields are not made of particles. Analogy: a tornado is a special manifestation of the dynamics of the atmosphere, but the dynamics of the atmosphere is not made of tornadoes.
With that clarification in mind, we can address the question using a simplified model in which the mediating field is a single scalar field $\phi$ whose equation of motion is
$$
 \partial^2\phi+m^2\phi\propto J,
$$
where:

*

*$m$ is the mass of the corresponding particle ($m\sim 90\,\times$ the mass of a proton),


*$J$ is the appropriate "charge density" of the quarks/leptons (using the word "charge" in a generalized sense, not referring to electrostatics at all),


*the units are such that $\hbar=c=1$.
This equation of motion has two properties relevant to the question:

*

*For simplicity, temporarily think of $\phi$ as a classical field (instead of as a quantum field). Unlike waves in the electromagnetic field (which would have $m=0$ in this analogy), waves in the field $\phi$ are dispersive: an initially localized wavepacket spreads out along the direction of motion as it propagates, so the leading edge travels faster than the trailing edge. The group velocity (speed of the wavepacket's centroid) is less than the speed of light, but the leading edge still moves as the speed of light.


*For simplicity, temporarily think of the "charge density" $J$ as a static classical quantity. The "force field" of such a source depends on the distance $r$ from the source like $\phi\sim (e^{-mr})/r$. Since $m\sim 90\,\times$ the mass of a proton, this "force" is completely negligible on scales larger than the size of a proton.
In reality, $\phi$ is a quantum field, and the quarks/leptons that define $J$ are quantum entities, so the idea of the "speed of transmission of the weak force" is even fuzzier than point 1 already emphasized, especially since its extremely short range (point 2) keeps it firmly on the quantum side of the spectrum of behaviors. We can still say that the influence cannot be transmitted any faster than the speed of light, but to say much beyond that would require reframing the question in terms that make more sense for a quantum field that behaves in a very non-classical way — not like classical particles or classical fields.
A: Yes it does. Massive particles cannot move at lightspeed, although arbitrarily close to it if they have enough energy.
