system
Given the following post, respond as if you're commenting on Reddit:
human
What exactly is information?

In regards to the holographic principle, when physicists state that information is conserved in a black hole, what do they mean by "information?" How is information different than energy?
gpt
The existing answers address what information is in the context of information theory, but do not address what is meant by physicists when discussing whether or not information is conserved in black hole dynamics.  This is actually something a little different.

In quantum mechanics, an initial quantum state evolves over time into a new quantum state, but it is one of the essential features of quantum mechanics that no two initial states can evolve into the same final state.  This comes from a property called *unitarity*.  Thus, the final quantum state tells you what the initial quantum state was; it is in this sense that the information is preserved.

The problem to be addressed with black holes is this.  In general relativity, a black hole is completely specified by its mass, charge, and angular momentum.  Consequently, two different systems -- but which happened to have the same mass, charge, and angular momentum -- can collapse into identical black holes.  This contradicts the principles of quantum mechanics.

This problem was exacerbated by the results of Hawking's first calculation showing black holes radiate ("Hawking radiation"), because the radiation emitted was a perfect blackbody spectrum, and thus when the black hole evaporates and returns to just a bunch of particles, that final quantum state again will preserve no record of what the initial quantum state was that led to the creation of the black hole in the first place.

Thus, we had two ideas in conflict with each other: that two states cannot evolve into the same state (an essential principle of quantum mechanics), and the result that black holes keep no record of what produced them.

While there have been various ideas on how to approach this problem, the general thinking is that there are degrees of freedom in classical general relativity that have been ignored, and that when you keep track of these, the black hole will keep a record of the state that created it and that the final radiation will not be a pure blackbody spectrum, but will in fact have a signature that depends on the original state that led to the black hole.  However, this is not a certainty, and this problem has not yet been resolved once and for all.

Edit: minor fix: "does"-->"do"