Using quantum cosmology hawking cleared that the black holes do radiate some sort of radiations and everyone in the physics community surprisingly accepted the idea. The problem rises when he explained the idea in a more elaborate manner. He claimed that the information which falls into a black hole eventually gets lost when it evaporates. That was considered as one of Hawking’s blunder in proposing an idea. They faced a genuine sense of opposition and criticism at that time. This is all because the condition actually violates a very fundamental idea in physics, the laws of conservation of information. This conservation principle is not as popular as the law of conservation of mass, and energy is, but the fact that it is equally more important is undeniable. When we study statistical mechanics, we study the idea of entropy and we treat it in the form of information. We deal with information transfer, just like mass and energy it is always there, in the system. It converts in one form to another but it never dies. Now we cannot simply say that Hawking wasn’t aware of such thing, or he just forgot about it. There is no forgetting of fundamentals! What happens here is actually an outcome of the puzzling nature of quantum mechanics. Hawking never really questions the fundamentals of quantum mechanics. He often quoted, “When I hear of Schrodinger’s cat I reach for my gun”, he never gave a damn about the fundamental ideas in QM. He knew the ideas and he solves the problem, this one time the idea sucks. Leonard Susskind, Quantum Physicist and the co-founder of string theory made an argument about the idea. He even wrote a book about this paradox, namely The Black hole war: My Battle with Stephen Hawking to save the world for Quantum mechanics. To be honest, when I first heard about this book I wasn’t aware of Susskind, it was the time when I used to read a lot of Hawking’s work (not hardcore physics papers but his popular science books). So I was like, Who is this guy to yell hawking’s name in this challenging manner. This was the time when I discovered the second face of the coin, the information paradox. It was quite challenging for physicists back then to clear this paradoxical situation. I should say clearly that there is no true reasoning regarding this situation. But thanks to Physicists like Susskind who came up with some good hypothesis the idea of Holography, actually he advanced the idea. He didn’t actually discover the idea, but it is more like someone introduced the idea, and then someone elevates the idea to a whole new level, so now it’s more of his thing rather than the one who introduced it. When we think about the word ‘Hologram’, we think of something like star-wars-sci-fi-obi-wan-Kenobi-you-are-my-only-hope stuff. But what a hologram really is? According to the Oxford dictionary definition:
“A three-dimensional image formed by the interference of light beams from a laser or other coherent light source”
The definition suggests the idea that you can store the information about the 3-d world in a 2-d world. It resembles the hallmark stickers on books that are in 2d but seems 3d. This suggests that you can really do transfer the information from a higher dimension to lower. Susskind didn’t introduce this idea, he is a string theorist he applied this idea to our modern world. He took this idea to a whole new level. He introduced a new theory that describes nature in a different format. He came up with the ‘holographic principle’ which is now a principle of string theory. But you should know that If you study string theory at a beginner level, you wouldn’t really get an idea of holography since it is related to string theory, but it is not string theory what string theory is. The idea is that much weirder that it holds a spot in the string theory realm jumping from good old quantum mechanics.
The entropy of a black hole is related to the area of a black hole, as a matter of fact, it is directly proportional to its surface area. As I said earlier entropy suggests the state of information of the system. So what’s really happening is that the information is getting transferred into a lower dimension. It applies to everything, every 3d object falling into a black hole posses information that is going to be accumulated on the surface, not inside the black hole! Susskind suggests that it is not a coincidence where a black hole forms a lower-dimensional model of the objects infalling. It’s got to be a holographic effect. In 1997 Juan Maldacena proposed an AdS/CFT correspondence which played a prominent role in the battle. The AdS is an abbreviation for Anti-de-sitter space, it is a negatively curved surface and can be depicted as hyperbolic in nature. We have three types of surfaces, First is good old euclidean flat space, second and third are positively and negatively curved Riemannian spaces. Anti-de-Sitter space is negatively curved space. CFT however is a conformal field theory that is related to quantum field theory. Maldacena linked these two physical theories to elevate the level in the game of information. This was more of a game-changer because this actually expanded Hawking’s vision to write another paper improving his mistake. In 2004, he wrote a paper namely Information loss in Black Holes. He described the fact using Maldacena's paper that the information is not actually lost. The thing we should keep in mind is that this idea supports Susskind’s Holography hypothesis. Hawking’s explanation finally cleared this fact. He described that there exists a stack of Anti-de-Sitter space where the boundaries are conformal. Every point in the inside the space is at infinite distance from the boundaries. As shown in the figure, the hyperbolic disks are aligned in a perfect stack forming a cylinder. The boundary is conformal, the Y-axis is depicting time.
Here is a conclusion made by Hawking regarding the wrapping of the battle:
How does information get out of a black hole? My work with Hartle showed the radiation could be thought of as tunneling out from inside the black hole. It was therefore not unreasonable to suppose that it could carry information out of the black hole. This explains how a black hole can form and then give out the information about what is inside it while remaining topologically trivial.
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