  Fast radio bursts (FRBs) are millisecond radio signals from cosmological
distances. As they propagate, FRBs can interact with ambient photons and
initiate a quantum cascade that can limit the electric field strength. This
paper examines whether some observed bright and brief FRBs may challenge this
limit if the source is not relativistic. The size of a static FRB source is
estimated as $R\sim ct$, where $t$ is the time scale of the FRB and $c$ denotes
the speed of light. But for a relativistic source moving at the Lorentz factor
$\Gamma$, the size is $R \sim 2 \Gamma^2 c t $. Using an FRB catalog, we plot
the luminosity-duration distribution. Most FRBs fall below the limit for a
static source, but two events have higher luminosity and shorter duration. This
suggests these bursts may originate from relativistic sources, although more
data is needed to confirm this.
