In Stephanie Meyer's novel New Moon, vampire Edward Cullen leaves the love of his existence, Bella Swan, after Bella inadvertently cuts herself and Jasper, Edward's brother, almost attacks her. Edward never wants Bella to be in that kind of danger again, nor will he agree to change Bella into a vampire. Instead, he declares that Bella would be better off without him, living a normal human life. He says he will go, and it will be as though he never existed.
Bella falls into a deep depression after Edward's departure, so deep that her father wonders if she will ever come out of it. After a few months, though, Bella makes an important discovery. When she puts herself at risk and adrenaline courses through her body, she can hear Edward's voice rebuking her for taking risks and telling her to stop. When she hears Edward's voice in her mind, she feels like she is surfacing “out of some dark pool.” Her mind clears, and for a moment, Edward is with her again.
Of course, Edward is not really with Bella. The voice she hears is just a hallucination produced by her subconscious mind, and she cannot see Edward, other than in her memory—although later in the book there is a moment where she seems to see him when she is about to drown, though this is either just another hallucination or a very vivid imagining.
Bella wants to hear Edward's voice again, the voice that for a few moments eases her pain, so she takes more risks. She begins riding a motorcycle, for instance, because she loves hearing Edward's voice scold her. She even tries cliff-jumping.
Since Edward's voice is a product of Bella's own mind, Edward himself cannot see or hear her. In fact, the only knowledge he has of her comes from the imperfect visions of the future experienced by Alice, his sister. Edward does not know what is going on in Bella's world. He has no idea that she is in danger from the vampire Victoria, or he would have returned to Forks almost instantly.
When Alice sees Bella jump from the cliff, she does not realize what Bella is doing, nor can she see Jacob rescue Bella, so she rushes back to Forks to find out what has happened and to comfort Charlie. Edward knows only what Alice has seen, and since she cannot see Jacob (because he is a werewolf), Edward does not know that Bella is still alive. When Edward calls Bella's house to check, Jacob only tells him that Charlie as “at the funeral.” Edward immediately assumes that he means Bella's funeral, and he sets himself on a course of self-destruction that Alice and Bella stop only just in time.