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The light acts as if it follows all paths from point A to point B,
but most of those paths cancel out: the wave arriving by almost
every path interferes destructively with the wave arriving via some
other route. The minimum time path, however, can't cancel out: the
wave arriving that way arrives first, before any other candidate for
interference.
So the light wave traveling along the minimal time
path is the one that actually occurs, the one that is actually
observed.