Supernova searches have been been suggested as a method for determining pre
cisely the current value and time variation of the equation of state, w, of
the dark energy component responsible for the accelerated expansion of the
Universe. We show that the method is fundamentally limited by the fact tha
t luminosity distance depends on w through a multiple integral relation tha
t smears out information about w and its time variation. The effect degrade
s the resolution of w that can be obtained from current data.