  We review the interpretation of gauge invariance as a mathematical redundancy
required in a relativistic description of forces mediated by massless spin-1
and spin-2 particles. In this context we also review the Weinberg-Witten
theorem and its implications.
  This leads us to consider a class of models in which long-range interactions
are mediated by Goldstone bosons of spontaneous Lorentz violation. Since the
Lorentz symmetry is realized non-linearly in the Goldstones, these models could
evade the Weinberg-Witten theorem and the need for gauge invariance. In the
case of gravity, the broken symmetry would protect the theory from having
non-zero cosmological constant, while the compositeness of the graviton could
provide a solution to the perturbative non-renormalizability of gravity.
  We also consider the phenomenology of spontaneous Lorentz violation by a
vector VEV and the experimental limits thereon. We find the general low-energy
effective action of the Goldstones of this kind of symmetry breaking minimally
coupled to gravity. We compare this to the ghost condensate that has been
proposed as a model for gravity in a Higgs phase.
  We then summarize the cosmological constant problems and show that models in
which a scalar field causes super-acceleration of the universe generally
exhibit instabilities. We discuss how the equation of state evolves in a
universe where the dark energy is caused by the ghost condensate. We comment on
the anthropic argument for a small cosmological constant and how it is weakened
if the inflaton self-coupling varies over the landscape of possible universes.
  Finally, we discuss the reverse sprinkler, a problem in elementary fluid
mechanics that had eluded a definitive treatment for decades.
