This is what it looks like when you are correcting the back of the blade.
When you hammer on the edge to draw out more width in the blade, it curves the back because you’re pressing the material on the edge apart. So, you flip it over and hammer it down straight to the anvil. What happens, then?
The sword gets longer. Not much, just a bit. But it also gets thinner from one side to the other, as it’s getting longer and wider (edge to back) If you want a great exercise in understanding conservation of mass, this is it. You neither create nor destroy steel, you just move it around. If you put some sort of modeling clay in a plastic shell, you could hammer it around and get an approximate feeling for what this is like.
I’ve mentioned before that the whole process is a lot of endless refinement. That refinement means removing metal, once the forging is done. Or moving it around (but not adding it) – so the forging process is all about relocation and the grinding/shaping is removal. Your sword gets smaller and thinner. Or, lighter. And it’s a one-way street.