system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5:what is information (referring Black Hole Information Paradox)

i understand the logic behind the conservation of matter and energy, but i just can't grasp my head around why the information about the state of a system needs to also be preserved.

if i take an apple and I dismantle it until it is nothing but protons and electrons, how in the world is the information about its previous state conserved?

i am trying to understand why it is so controversial that matter falls into a black hole and then it irradiates away as hawking radiation (without conserving the information about what that matter was)
gpt
Disclaimer: Some simplifications that are not technically true but make it easier to understand the principles.

On a deep level physics doesn't care if time moves forward or backward. Speaking in your apple analogy, it is physically possible to "un-dismantle" an apple and reconstruct it the way it was. Due to entropy it is unrealistically unlikely for something like that to happen, but it's physically possible.

To take this to the next level, if you have the dismantled apple in your hand it is possible to reconstruct how you dismantled it and in which state it used to be before just from looking at where the apple, you and everything involved are *right now*. The movement can sort of be "rewinded", and the rewinding is a process that follows all fundamental laws of physics (it reduces entropy, but again, that's not impossible, only so unlikely that it never happens).

Black holes seem to violate this principle. In standard black holes an electron drops in and photons come out at a later time, but it is not clear what their connection is. On a mathematical level, the process is not reversible: If we take all photons and their times when they exit the black hole we still don't know when and where an electron or something else dropped in.

To put it into an analogy: Let's say some sort of God randomly steals particles from our universe and randomly inserts them at other places. In such a universe we can never say when and where a particle will appear or disappear, and if we look at the universe as it is right now we cannot say what it was like in the past because the God may have stolen particles earlier and from looking at today's universe no trace of them remains. Black holes seem to do a similar thing - they take particles away without going into a state that allows us to trace back that a particle entered at a certain moment.