Day and Night Machine

It's Jess's thirteenth birthday. She's been in bed for nearly a year, the result of a car accident that killed her father. Surprisingly, she finds a birthday present from him, an unusual gift for a girl and one which she, her mother, and her grandfather, puzzle over. In the course of playing with it, Jess discovers that it has some highly-unexpected properties.
But then, purely by accident, she discovers its most amazing feature.