Why do galaxies have arms? A couple of years ago I started playing a game called Kerbal Space Program (KSP) and my understanding about how orbits actually work increased dramatically. Because of KSP I was looking at a picture of a galaxy with its spiral arms and something struck me as very odd. The stars closer in should orbit the galaxy center faster than the stars farther out and that would smear out these lanes of stars until they were no longer recognizable. Something weird is going on here!

So why do galaxies have arms? What's bunching these stars together like that?

I noticed that the center of galaxies are all smeared out and bulbous like I think that the rest should look like. So what if all that mass rotating around a common center is warping space around it, like the water draining down your sink, and this warping is what catching matter/stars into the lanes.
The usual explanation of spiral arms involves density waves.
Nonuniform motion leads to matter alternately bunching up (boosting star formation) and spreading out.
Like cars on a congested road, stars move through regions of greater or lesser density over time.
The rotational smearing you anticipate is known as the "winding problem."
This Scientific American article
offers three explanations by professional astronomers.