  Einstein observers in flat space-time are inertial observers which use light
to synchronize their clocks. For such observers, speed of light is a constant
by construction. However, one can use super-translations to change coordinates
from Einstein to BMS coordinates. From the point of view of BMS observers,
speed of light is not a constant all over the space-time and in all directions.
So in general, clocks which are synchronized for Einstein observers are not
synchronized for BMS observers, and vice versa. Based on this fact, we propose
a local observable for detecting the soft hairs, which is the variations in
speed of light for such observers. We also investigate the relation of this
observable to gravitational memory, which is a permanent change of position of
test particles at infinity, after a gravitational wave passes completely from
them. It is shown that the BMS time coordinate is the physical time after a
gravitational wave, and it is the legitimate time to be used to calculate the
light speed. Based on this argument, the analysis predicts a permanent change
in the speed of light rays which propagate in asymptotics after a gravitational
wave. Moreover, it is explained how this change is related to the gravitational
memory by comparing their significance in observations.
