Temporal anomaly

[Darwinian]

Here's weird thing..

Currently watching Harry Potter and while in Hagrid's home, Hermione was struck by a carved pebble which she then put into her pocket. Later on she went back in time and threw that same pebble at her earlier self who, as we now, picked up the pebble and put it in her pocket only to later go back in time.. etc. etc..

Questions:

- If the pebble existed prior to Hermione putting it in her pocket, where did it come from?
- And if it constantly gets taken back in time to be thrown then has it, from the reference point of the time after they traveled to the past, simply ceased to exist?
- Is it destined to only ever exist within that 2 hour period of time, looping over and over again?
- Did it ever have a beginning and will it ever have an end?
- The fact that the pebble is destined to be thrown at a young girl for the rest of its own lifetime must mean that it will eventually wear away to nothing. How will this affect that part of history as the past must be gradually changing everytime that pebble is thrown?