Hawking and how black holes preserve information

[Umbran]

That's one possibility. But, there would seem to be other possibilities, where there is interaction.

I'm going to guess that's not the case. Reasons below...

One would be like the surface of the ocean, which has interactions, but mostly uninteresting ones. Another could be something more like Conway's game of life, as a simple example having more interesting interactions. What would seem to determine what interactions occur is how the information is embedded physically, and what rules (physics) apply to the embedding. Since the superset of those rules (physics as a whole) allow very complex interactions (weather patterns on Jupiter; life here on Earth), there seems to be a wide range of possible interactions.

The problem is thermodynamics.

The whole point of hypothesizing that information is stored in the surface of the black hole is that, thermodynamically, losing information is a *huge* problem. Losing information in the black hole violates energy conservation (and thereby causality), and the property known as "unitarity" - the requirement that the sum of probabilities of all outcomes of a quantum system be 1. We thus require that the black hole preserve information dropped into it until such time as it is extracted (through Hawking radiation). Basically, any information you drop in there must be preserved pretty much forever.

To see the violation of energy conservation: the entropy of a black hole is proportional to its surface area. So, if the entropy of the black hole grows, it gets bigger! But, its surface area is also related to its mass - so increasing its entropy means increasing its mass! This is fine, if that mass and entropy are falling in from the rest of the universe - the black hole is a big sink for it. But it better not generate new mass *on its own*. That would be bad.

Interactions, in general, are lossy - the second law of thermodynamics tells us that the entropy of a system with interactions will tend to increase, and increase in entropy is equivalent to loss of information.

Another way to think of it is that most of the interactions you likened to - waves and weather, include *friction*, which transforms organized energy and disperses it as undifferentiated heat, losing the original details of the system, and thus increasing entropy.

So, interactions on the surface that lose information are not allowed. You can stack the books up, and rearrange them, but only in such a way as they never lose their original identity.