  We show that plane-fronted gravitational waves induce the breaking of
parallelograms in space-time, in the context of the teleparallel equivalent of
general relativity (TEGR). The breaking of parallelograms can be shown by
considering a thought experiment that consists of a simple physical
configuration, similar to the experimental setup that is expected to lead to
the measurement of gravitational waves with the use of laser interferometers.
An incident beam of light splits into two beams running along perpendicular
arms, endowed with fixed mirrors at the extremes. The reflected light beams are
detected at the same point of the splitting. Along each arm, the two light
beams define two null vectors: the forward vector and the reflected vector. We
show that the sum of these four vectors, the forward and reflected null vectors
along the two arms, do form a parallelogram in flat space-time, but not in the
presence of plane-fronted gravitational waves. The non-closure of the
parallelogram is a manifestation of the torsion of the space-time, and in this
context indicates the existence of gravitational waves.
