The title of this video - which might change since I'm writing this up just a day after it was posted to YouTube - is a bit misleading. The actual question in the title - why don't railroads need expansion joints - is only answered in the last half minute or so of the video and is answered more thoroughly in a Practical Engineering video that I'll post after a jump.
The bulk of the video is spent explaining how railroad welds using thermite work. The video explains the nuances far better than other thermite videos I've posted before, explaining why the rails must be aligned and peaked, why the rails must be preheated (including a nice demonstration of heat treating), how the crystal structure changes as a result of the weld, and eventually why the rails don't need expansion joints.
This is the second of at least three thermite videos from Dr Derek. I thought I'd posted the first video to both blogs, but I can't seem to find it, so it'll likely show up next week.