A handy video from AsapSCIENCE, below, maps out why this might be. A part of our brain, the anterior cingulate cortex, that recognizes physical pain is also triggered by extreme emotional pain. And verbally, we do resort to pretty visceral descriptions for how heartbreak feels —"he ripped my heart out!", "a slap in the face!", "scarred." The language we use to describe pain reveals how our body processes emotional and physical distress in very similar ways. The video claims that most people would even prefer to be physically hurt than to lose a relationship, which has some scary implications, but that's another topic for another time.
Our body's understanding of pain traces back to evolutionary theory, of course. As humans evolved, romantic and social relationships became intrinsic to our survival. Pain tells us something is wrong or dangerous, so if we lose an important relationship, science suggests it's because we feel our very survival is in jeopardy. In order to self-preserve, we turn to loved ones and friends to remind us life goes on — and so will we.
Basically, all this pop science merely backs up what anyone who is flesh and blood already knows firsthand. Personally, when it comes to matters of a broken heart, no medical jargon expresses real pain quite like pop music can. As Skeeter Davis once mourned, "Don't they know it's the end of the world? It ended when you said goodbye." We do, Skeeter, we do.