 Arageorgis (1995), Ruetsche (2003, 2011), Lupher &amp; Kronz (2005), and most recently, Lupher (2018) attack algebraic imperialists for using Fell’s theorem in order to denigrate UIRs. Ruetsche’s most important point is that UIRs do real explanatory work in physics, e.g. in quantum statistical mechanics (see Bratteli &amp; Robinson 1997 and Ruetsche 2003) and in particular when it comes to spontaneous symmetry breaking. The coexistence of UIRs can be readily understood by looking at ferromagnetism for infinite spin chains (see Ruetsche 2006). At high temperatures the atomic dipoles in ferromagnetic substances fluctuate randomly. Below a certain temperature the atomic dipoles tend to align to each other in some direction. Since the basic laws governing this phenomenon are rotationally symmetrical, no direction is preferred. Thus once the dipoles have “chosen” one particular direction, the symmetry is broken. Since there is a different ground state for each direction of magnetization, one needs different Hilbert space representations—each containing a unique ground state—in order to describe symmetry breaking systems. Correspondingly, one has to employ inequivalent representations.