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Fast radio bursts (FRBs) are millisecond radio signals from cosmologicaldistances. As they propagate, FRBs can interact with ambient photons andinitiate a quantum cascade that can limit the electric field strength. Thispaper examines whether some observed bright and brief FRBs may challenge thislimit if the source is not relativistic. The size of a static FRB source isestimated as $R\sim ct$, where $t$ is the time scale of the FRB and $c$ denotesthe 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 plotthe luminosity-duration distribution. Most FRBs fall below the limit for astatic source, but two events have higher luminosity and shorter duration. Thissuggests these bursts may originate from relativistic sources, although moredata is needed to confirm this.

Constraint on the relativistic motion of fast radio bursts based on the maximal electric field