I'm just crazy, really.

People who have lost a limb often have phantom sensations that the limb is still there and attached to the body. It happens a lot more than you might expect—50% to 80% of amputees report it—and it is generally said to be painful.

Beyond just pain, though, is the concept of having an actual phantom limb. Some people report that their phantom limb makes gestures as they talk. Particularly compelling is this example, which shows that the phantom feelings are not abstract physiological white noise, but rather specific and concrete:

I placed a coffee cup in front of John and asked him to grab it [with his phantom limb]. Just as he said he was reaching out, I yanked the cup away.
"Ow!" he yelled. "Don't do that!"
"What's the matter?"
"Don't do that", he repeated. "I had just got my fingers around the cup handle when you pulled it. That really hurts!"
Hold on a minute. I wrench a real cup from phantom fingers and the person yells, ouch! The fingers were illusory, but the pain was real - indeed, so intense that I dared not repeat the experiment.

They used to think that the sensation was caused by something in the nerve endings where the limb was supposed to be, so they'd try amputating a little bit more of the stump. This only complicated the problem, though—people afterward would not only continue to have the phantom limb sensation, but would also experience phantom feelings of the stump that was also now gone.

What happens is that the brain reorganizes when it finds that sensory input is cut off from that limb. The somatosensory cortex, which receives the data, will instead start taking data from another area of the body—thus the brain doesn't figure out that the limb is gone, because it starts to again receive sensory data indicating that all is well.

And sometimes when I don't have my phone with me I still feel it vibrating in my pocket.