  Consider critical Bernoulli percolation in the plane. We give a new proof of
the sharp noise sensitivity theorem shown by Garban, Pete and Schramm. Contrary
to the previous approaches, we do not use any spectral tool. We rather study
differential inequalities satisfied by a dynamical four-arm event, in the
spirit of Kesten's proof of scaling relations. We also obtain new results in
dynamical percolation. In particular, we prove that the Hausdorff dimension of
the set of times with both primal and dual percolation equals $2/3$ a.s.
