David Asks: Does Beckenstein's Law Work Both Ways?

[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

 

[Careful]

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

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

 

[denian]

,

This is a great question and one that has been debated among scientists for many years. The short answer is that Beckenstein's Law does work both ways, but the interpretation of this law is still a subject of ongoing research and debate.

To understand this better, let's first define what we mean by "working both ways". Beckenstein's Law, as you stated, relates the entropy of a black hole's horizon to the amount of information hidden behind it. This can be thought of as a one-way relationship, where the entropy of the horizon determines the amount of information that can be observed by an outside observer. However, as you suggest, we can also consider the perspective of an observer inside the black hole, where the horizon is now the boundary between the inside and outside of the black hole.

In this case, the entropy of the horizon would be related to the information that is hidden from the inside observer. This means that the entropy of the horizon can be seen as a measure of the information that is inaccessible to both inside and outside observers. So, in a sense, it does work both ways, but the interpretation of what that means can be different depending on the observer's perspective.

As for your question about the entropy inside a black hole being equal to the entropy of the remaining universe, this is still a subject of debate and ongoing research. Some theories, such as the holographic principle, suggest that the entropy inside a black hole is indeed equal to the entropy of the remaining universe. However, other theories suggest that the black hole's entropy may be related to the information that is lost when matter falls into the black hole.

In summary, Beckenstein's Law does work both ways, but the interpretation of this law and its implications for the entropy of black holes and the universe as a whole are still being studied and debated by scientists. I hope this helps to clarify your question. Keep exploring and asking questions, as that is what science is all about!