It could turn out that all transitions involving the neutral electron are forbidden - so there would be no inconsistency of Heim theory with reality, at least for this (significant) issue. I believe there are several groups working on this problem - for example, a group at the Perimeter Institute (Waterloo, Canada) led by Lee Smolin; though, more of their efforts are geared towards developing quantum loop gravity (especially work on spin foam).
Oh. It is of course possible that there is a "neutral electron" that has just eluded us. I don't want to give the impression that people have given up pouring over the data in the 40 GeV range (for neutral leptons). But working out the cross sections would be more conclusive.
Is "dimension" a proper scientific term in this sense? I tend to think of a dimension as being a line of measurement (time, mass, distance, etc.), not a place or a region, or generally something you can physically go to. What exactly are they talking about when they say "dimension" in this context?