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Originally, astronomers had the idea that the arms of a spiral galaxy were material. However, if this were the case, then the arms would become more and more tightly wound, since the matter nearer to the center of the galaxy rotates faster than the matter at the edge of the galaxy. The arms would become indistinguishable from the rest of the galaxy after only a few orbits. This is called the winding problem.

Lin and Shu proposed in 1964 that the arms were not material in nature, but instead made up of areas of greater density, similar to a traffic jam on a highway.[3] The cars move through the traffic jam: the density of cars increases in the middle of it. The traffic jam itself, however, does not move (or not a great deal, in comparison to the cars). In the galaxy, stars, gas, dust, and other components move through the density waves, are compressed, and then move out of them.

Apparently they're rather static: https://en.wikipedia.org/wiki/Density_wave_theory

Spiral arms are density waves. They move at different velocity than stars that make up the arm.

http://i.imgur.com/dtb8WrD.gifv