Yesterday I talked about black hole thermodynamics, specifically how you can write the laws of thermodynamics as laws about black holes. Central to the idea of thermodynamics is the property of entropy, which can be related to the amount of physical information a system has.

For classical black holes, this is a problem, because if you toss an object into such a black hole, the object (and all its physical information) is lost forever. It is as if the information of the object was erased, which would violate the basic principle that information cannot be destroyed. Now you might argue that being trapped is not the same thing as being destroyed, but for information it is. If you cannot recover the information, then it has been destroyed.

So it would seem that black holes “eat” information, even though the laws of thermodynamics say that shouldn’t be possible. This is known as the black hole information paradox.

Of course black holes aren’t classical. When a bit of quantum theory is introduced, you find that black holes can give off energy through Hawking radiation. It would seem then that Hawking radiation would provide a solution to the information paradox. The idea is that a black hole can trap an object and its information, but since black holes radiate via Hawking radiation (and gradually evaporate away because of it), the information is contained in the Hawking radiation and could (in principle) be recovered.

This would be a bit like ripping a book to shreds. The book falls into the shredder, but all the little book-bits fall out of the shredder. If you could gather them all up and reassemble the book, the information of the book isn’t really lost. But this leads to another problem, known as the firewall paradox.

The original idea of Hawking radiation stems from the uncertainty principle in quantum theory. In quantum theory there are limits to what can be known about an object. For example, you cannot know an object’s exact energy. Because of this uncertainty, the energy of a system can fluctuate spontaneously, so long as its average remains constant. What Hawking demonstrated is that near the event horizon of a black hole pairs of particles can appear, where one particle becomes trapped within the event horizon (reducing the black holes mass slightly) while the other can escape as radiation (carrying away a bit of the black hole’s energy).

Because these quantum particles appear in pairs, they are “entangled” (connected in a quantum way). This doesn’t matter much, unless you want Hawking radiation to radiate the information contained within the black hole. In Hawking’s original formulation, the particles appeared randomly, so the radiation emanating from the black hole was purely random. Thus Hawking radiation would not allow you to recover any trapped information.

To allow Hawking radiation to carry information out of the black hole, the entangled connection between particle pairs must be broken at the event horizon, so that the escaping particle can instead be entangled with the information-carrying matter within the black hole. This breaking of the original entanglement would make the escaping particles appear as an intense “firewall” at the surface of the event horizon. This would mean that anything falling toward the black hole wouldn’t make it into the black hole. Instead it would be vaporized by Hawking radiation when it reached the event horizon.

It would seem then that either the physical information of an object is lost when it falls into a black hole (information paradox) or objects are vaporized before entering a black hole (firewall paradox). Basically these ideas strike at the heart of the contradiction between general relativity and quantum theory.

Just how this all might be resolved isn’t yet clear. This is cutting edge theoretical physics, so we don’t have a solution yet. But because the problem is central to our understanding of quantum gravity the controversy it’s worth studying.

Of course it should be stressed that these are theoretical paradoxes. While we’re pretty sure Hawking radiation is real, it hasn’t been observed. We have no way of observing any firewall either. We do know that black holes exist, and we have a pretty good handle on the dynamics of material near a black hole. We just don’t yet understand exactly what happens when matter crosses a black hole’s event horizon.

Which is why some black hole theorists are having a hole-y war.

## Comments

A ‘firewall’ at the event horizon makes sense to me. An outside observer at rest can’t see it, because it is red-shifted to almost infinity. If an infalling observer reaches the event horizon, he becomes vaporized. So there is no way to cross the event horizon for any particle in any reference frame and no information can disappear.

But doesn’t this mean the following?

If nothing can cross the event horizon then no particle has ever crossed an event horizon either – meaning that straight from the birth of a black hole that never really anything failed into the black hole. Therefore no event horizon should really exist, just layers of dense particles ‘approaching’ the black hole waiting to be potentially vaporized. That sounds to me like that a real black hole can’t really grow from the stage that the tiniest imaginable black hole was created. We know that those tiny black holes are instable and dissolve pretty much straight away. This would mean no firewall either.

I have no real idea and as Brian said, this stretches our knowledge about quantum physics and general relativity and nobody really knows whats going on but my struggle with the firewall is that it’s existence would mean that it can’t be created in the first place.

I don’t know if I make sense here and I struggle a bit putting my thoughts into words.

I have an interest in this, but I won’t evangelise here. Instead, I offer a few approaches that might yield something (but I’m not prepared to offer proof, so put your sceptic hat on).

A quantum approach would get to the bottom of what actually happens, but it should break away from purely probabilistic representation (which has already lost information before you begin to use it!), to a deterministic chaotic representation that has detail smaller than individual fermions, so that you can create and annihilate them without losing fundamental instances (and no, such ideas need not conflict with ‘no hair theorem’ nor hidden variable theory, nor get into trouble with the firewall paradox).

Ideally it would be a mechanism for physicality that incorporates the gravitational interaction with the others. When you look into deterministic models, you can get gravitation for free, but you cannot unify it as a field on equal basis with the fields we know in quantum field theory. Instead, you’d have to pick out observable effects as emergent from the deterministic interaction, and summarise their statistics as fields.

p.s. the above is intended to open doors to explore, rather than offer the reader a complete understanding.

It was written “if you toss an object into such a black hole, the object (and all its physical information) is lost forever. It is as if the information of the object was erased, which would violate the basic principle that information cannot be destroyed.”

Which “basic principle” is this? I cannot find anything in any of my textbooks, which is wird, if it is a “basic” principle…

It was also written: “it would seem that black holes ‘eat’ information, even though the laws of thermodynamics say that shouldn’t be possible. This is known as the black hole information paradox.”

Two questions here: (1) How (or where?) do the laws of thermodynamics say “black holes cannot destroy information”? (2) What is the “Black Hole Information Paradox,” and where can I read more about it?

This whole bit about “hole-y-war” reeks of a total confusion of “information” with “entropy,” which is preposterous: Thermodynamic entropy has nothing whatsoever to do with “information entropy” (a.k.a. Shannon entropy). Leonard Susskind amply demonstrates this total confusion in his book “The Black Hole Wars”: read it! It is a very entertaining work of fiction!

Brian explained the basic principle of thermodynamics earlier and here is the link about entropy:

https://briankoberlein.com/2014/03/31/dying-light/

Question 2.1 & 2.2: The law of thermodynamics basically say that nothing in our universe can destroy information. Not you, not me, not the NSA neither a Black Hole. But our current understanding of a black hole seems to lead to a conclusion that objects falling into a black hole take all their information unrecoverable with it. That is why it is called a paradox because we have a physical law and a current understanding of black holes contradicting each other.

The basic principle that information cannot be destroyed is that physical systems are subjects to equations of motions such as “F = m*a”. This makes sure that the information of a system that you have for some specific time is sufficient to predict its future (determinism) and to reconstruct its past (reversibility), it has the same amount of information at all times. But if thermodynamics and black holes turn up, this concept becomes very subtle.

As for the “Black Hole Information Paradox”, you may also have a look here:

http://www.nature.com/news/astrophysics-fire-in-the-hole-1.12726

If you imagine that the singularity inside an event horizon can be in a particle-like state, then the singularity can also exist in a wave-like state in a superposition outside the event horizon, absorbing and preserving the wave-like nature of an infalling object whose particle-like nature is destroyed by the firewall.

Or, a firewall might instead have a wave-like state, meaning that the wave-like nature of an object falling into a black hole is preserved while its particle state is destroyed.

Just playing around with ideas.