The answer to this question is somewhat involved, but the bottom line is that by the "motion" of a magnetic field line, we mean that path in time that is traced out by low energy plasma that is initially spread along the field line. This plasma moves because it drifts in the electric field arising because of the time-changing magnetic field. As time progresses, the low energy plasma moves with the "field line" as we have defined it--that is we use its motion to define the concept of field line motion.

Thus the motion we show in our computer visualizations has a physical basis--it is the motion we would observe for tubes of low energy plasma initially spread along the various magnetic field lines as the situation evolves in time.

This is a familiar concept in space plasma physics.

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