# Beckenstein's law

1. Oct 16, 2005

### straycat

Hey all,

I am reading Smolin's Three Roads to Quantum Gravity, and have just re-encountered an old idea, Beckenstein's Law, which states: "With every [event] horizon that forms a boundary separating an observer from a region which is hidden from them, there is associated an entropy which measures the amount of information which is hidden behind it. This entropy is always proportional to the area of the horizon." (pages 86-7). Smolin goes on later in the book to relate this idea to the holographic principle, which states that the horizon can be thought of as a computer that represents the state of the object enclosed by the horizon.

Here's my question. Does this principle work in both directions, ie from either side of the event horizon? IOW, can you imagine an observer on the *inside* of the event horizon (or imagine that the black hole *is* the observer), and associate the entropy of the horizon with the entropy of the *outside* universe? If so, does that mean that the entropy inside a black hole is equal to the entropy of the remaining universe (which seems difficult to accept)? Alternatively, does the area of the event horizon look different depending on which side of it you are on?

David

Last edited: Oct 16, 2005
2. Nov 10, 2005

### Careful

I am afraid not It is moreover meaningless to speak about the entropy´´ IN a black hole, this concept cannot be well defined. Entropy is one of the most difficult notions in physics to deal with :what are the fundamental degrees of freedom (of the gravitational field) and how to count them? There does not exist yet a satisfactory definition in my view, although discrete approaches to quantum gravity try to make plausible ansatze (such as in causal sets or spin foam business). The correspondence between entropy (as used in the heuristic science of thermodynamics) and horizon area is nevertheless very striking.

Cheers,

Careful