  One of the most important advances in our understanding of the physical world
arose from the unification of 3-dimensional space with 1-dimensional time into
a 4-dimensional spacetime. Many other physical concepts also arise in similar
3+1 relationships, and attempts have been made to unify some of these also.
Examples in particle physics include the three intermediate vector bosons of
the weak interaction, and the single photon of electromagnetism. The accepted
unification in this case is the Glashow-Weinberg-Salam model of electro-weak
interactions, which forms part of the standard model. Another example is the
three colours of quarks and one of leptons. In this case, the Pati-Salam model
attempts the unification, but is not currently part of the accepted standard
model.
  I investigate these and other instances of 3+1=4 in fundamental physics, to
see if a comparison between the successful and unsuccessful unifications can
throw some light on why some succeed and others fail. In particular, I suggest
that applying the group-theoretical methods of the more successful unifications
to the less successful ones could potentially break the logjam in theoretical
particle physics.
