Momentum is not exclusive to moving mass. The usual equation L = m*v is a special case for massive objects.
Waves carry momentum without actual net-movement of mass. This applies both to mechanical waves (where there is moving mass, but its average velocity is zero) and electromagnetic waves (which have no mass). The wave-part is simply negligibly small in most applications.
Cant explain the details of how exactly light obtains momentum, thats beyond me.
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