Spiral density wave theory attempts to describe the spiral pattern in spiral galaxies in terms of a long-lived wave structure with a constant pattern speed in order to avoid the winding dilemma. The pattern is consequently a rigidly rotating, long-lived feature. We run N-body simulations of a giant disc galaxy consisting of a pure stellar disc and a static dark matter halo, and find that the spiral arms are transient features whose pattern speeds decrease with radius in such a way that the pattern speed is almost equal to the rotation curve of the galaxy. We trace particle motion around the spiral arms. We show that particles from behind and in front of the spiral arm are drawn towards and join the arm. Particles move along the arm in the radial direction and we find a clear trend that they migrate towards the outer (inner) radii on the trailing (leading) side of the arm. Our simulations demonstrate that because the spiral arm feature is corotating, the particles continue to be accelerated (decelerated) by the spiral arm for long periods, which leads to strong and efficient migration, at all radii in the disc.