  The ideas related to the arrow of time are discussed briefly. I then focus on
the prevalent physical mechanism in the evolution of the universe and
developments in particle physics, spontaneous symmetry breaking, and show that
it explicitly breaks time-reversal symmetry. For simplicity, I do this in a
point mechanics gauge theory with symmetry group O(2). The proof of breakdown
of time-reversal symmetry relies on the use of a time step function to express
the Lagrangian valid for any time.
