The point is that for ##N_e=1## only one spot will appear. How does the thermal interpretation explain this?
This exchange does raise a follow-up question that I didn't ask at the time (because I was focused on the case of a high intensity beam): the explanation given is basically spontaneous symmetry breaking. But spontaneous symmetry breaking occurs because a single equation that has a certain symmetry has multiple solutions that, taken individually, do not share that symmetry. For example, the classical bar under vertical pressure obeys an equation that is symmetrical about the bar's axis: but each individual solution of that equation describes a bar that is bent in one particular direction, i.e., not symmetrical. There is no individual solution that describes a bar bent in all directions at once.Conservation of mass, together with the instability of macroscopic superpositions and randomly broken symmetry forces this, just as a classical bar under vertical pressure will bend into only one direction.
However, in the case of the SG experiment for ##N_e = 1##, we don't have that. We have a single solution of the equation describing the system that shares the equation's symmetry: it describes a superposition of a spot in the "up" position and a spot in the "down" position. We don't have two solutions, one of which describes a spot in the "up" position and one of which describes a spot in the "down" position. So how can spontaneous symmetry breaking explain why we only observe one spot?