Mathematically one way to see it is that the (combined) **step functions** become **Dirac pulses** i.e $\theta(t) \to \delta(t)$, which diverge. When $t \to t'$, the fields have *nearly identical* values, thus the time-ordered product involving *step functions* degenerates into *dirac pulse* (a dirac pulse is the *derivative* of the step function)

Physically another way to see this is: **S-matrix** describes interactions between states and particles, as such a matrix element for $t \to t'$, requires an interaction to take place *instanteneously*, thus it would require *infinite energy* at that point (also related to time-energy unceratinty).

This post imported from StackExchange Physics at 2014-06-27 11:27 (UCT), posted by SE-user Nikos M.