If two protons are floating in space, they'll feel an electrical field between each other and repel, but if you see them zip by you in space at relativistic speeds, they'll behave differently from your point of view by repelling slower than they should, and you'll see a new force.
But it doesn't matter  the math was invented to describe the behavior, so ultimately it's all mathematical abstraction and you use whatever level of complexity is necessary to solve your problem.
