The Information Paradox and its Connection to Hawking Radiation
Growing up in a heavily accessible information world, it is easy to understand the importance of the collection, dissemination, and retrieval of information. When you delete files on your computer, where does it go? Is it lost in space or stored elsewhere? Similarly, it is famously said that nothing can escape a black hole, not even light. Does that include the information itself? To understand this, we have to understand what black holes are first.
The anatomy of a black hole starts from the outermost edge, the accretion disk, which is the large sum of matter that surrounds the black hole. That matter is comprised of asteroids, star remnants, and anything else floating in space. Slowly, that matter gets pulled in by the tidal forces from the black hole and begins approaching the event horizon; considered to be a place of no return, where even light itself can’t escape. Once the matter has passed this point, gravity violently forces matter into what is known as the singularity, where all the mass accumulates inside the black hole. However, new geometrical shapes have been proposed such as, a ring singularity, but it is not known at this time what the actual shape is.
Black holes are comprised of three characteristics: mass, angular momentum, and charge. Two kinds of black holes are Schwarzschild black holes, or static black holes, and Kerr black holes. Schwarzschild black holes are known to be perfect black holes, meaning they have no spin or electric charge. A Kerr black hole has spin, but also no charge. In reality, a Kerr black hole is the only black hole we will probably ever see. Among these, there are three types of black holes: stellar, supermassive, and intermediate black holes. Stellar black holes come from collapsed stars that occur after a large star has exploded into a supernova. Supermassive black holes are black holes that sit at the center of every galaxy, and intermediate black holes are thought to be black holes found from the merger between stellar black holes and other large objects in space.
So, where is all of the information? If light itself cannot escape, according to Einstein’s theory of general relativity, what happens with all of the information? A few ideas emerge, either the information gets sucked into the black hole, never enters, or as proposed by Stephen Hawking, does it evaporate? In the 1970s, an astrophysicist named Jacob Bekenstein suggested that the second law of thermodynamics and Hawking’s Area theorem were similar, which Stephen Hawking took a step further by saying they’re equivalent.
According to Stephen Hawking’s theory, because the total amount of entropy for an isolated system can never decrease over a period of time, the same could be said for the area of a black hole; it can only increase. This implies that black holes act like any thermodynamic system, and they must radiate energy. If an object is radiating energy, it means that over time the black hole could eventually evaporate. As explained by Alexander Furrier, “The quanta radiation (now known as Hawking radiation) causes black holes to lose energy and mass, ultimately resulting in particle “evaporation”, at which they cease to exist.” The reason Hawking radiation occurs is because of the way particles interact with a black hole’s event horizon.
As told by Antonini, Martyn, and Nambiar on page 3, “Blackhole radiation is similar to pair production,” They are referring to a Hawking pair or antimatter and baryonic matter pair of particles. When these two particles appear in front of the event horizon of a black hole, the pairs can become separated. One of the particles is pulled by the tidal forces of the black hole while the other particle escapes. That escaped particle is what is categorized as Hawking radiation. Stephen Hawking also theorized that after an extremely long period of time, a black hole would evaporate and become nothing. However, this violates a law in quantum mechanics that states that nothing can be lost, including information. This violation created the information paradox.
The way that the information can split off in such a way was theorized by a researcher from the University of Utrecht in the Netherlands and a researcher from Princeton, New Jersey, United States. Together, they used a principle in quantum mechanics called tunneling. At the point of the event horizon, you can imagine a barrier where there is a cut-off for going inside and remaining outside; one particle then tunnels through the barrier while one stays out. Stephen Hawking retracted his theory and insisted the information is actually returned. He explains that over time, as the black hole evaporates, the matter and information begin to leak out until the black hole fully evaporates and returns all of the information and matter to space again. Stephen Hawking stipulates that it is returned in a different state. There is also no explanation on how to return matter and information to its original form.
Dr. Don Page, a colleague and prior student of Stephen Hawking, envisioned a different approach and argued the idea that black holes must preserve or release information. He believed that because you cannot reverse the effects of a black hole, it violated the symmetry of time. Using the example of a 100-kilogram astronaut falling into a black hole, when that astronaut falls in the black hole, it grows 100 kilograms in mass. Once the 100 kilograms of radiated mass emits, it has no structure and could not be distinguished between an astronaut or anything else. This defies laws in quantum mechanics, and so he began to think about quantum entanglement. He proposed that the radiation still maintains a link to its original place, and when you measure the radiation and black hole together, it shows a pattern. He calculated the total amounts of the black hole and the entangled radiation, it begins at zero when the black hole has yet to emit radiation, and by the end, it should also be zero. For that to happen, Dr. Page thought that as entropy increases, at some point, the entropy must then reverse to become zero again. This became known as Page’s curve, where the precise moment it turns is known as Page time.
Unfortunately, Dr. Page made the claim that the point where entropy reverses begins in the middle, this was heavily contested by other physicists. This produces the issue that the black hole should still be large enough that the laws of physics should still apply, and that the entropy of the black hole should still be increasing. The calculations do not show a reason that entropy should decrease considering the fact that it is only halfway through its life cycle. However, Dr. Page’s calculations did provide insight as to what physicists needed to do next, they need to figure out at which point entropy begins to reverse in the black hole. Thankfully, physicists now only need to calculate when entropy begins to reverse to explain why information does escape a black hole.
Another theory from researchers at the University of York, UK, theorized that the entire event horizon itself is quantum mechanical in nature. The event horizon would then have parts of Hilbert’s space for tunneling throughout its barrier. Hilbert space refers to an infinite-dimensional space of vectors that can be closed or finished. According to physicsworld, this model is different from the pair model that is theorized by Stephen Hawking because it allows for no information to be lost and has no need for Einstein’s theory of general relativity.
The most recent theory, according to Quantamagazine, proclaims with confidence that information does, in fact, escape a black hole. With gravity itself and some quantum effects, information can slip out. They explain the work of Stephen Hawking and various colleagues in the seventies as semiclassical. The new theory is compatible with Einstein’s theory, has new configurations on gravity, and begins to take effect once the black hole is old. Quanta describes it as, “The hole transforms from a hermit kingdom to a vigorously open system.” Although there is no current explanation as to why information comes out, the math shows that the information inside the black hole is released. The math also shows that any new information that tries to enter the black hole gets spewed outward almost instantly.
With all of the leading theories about black holes, it never occurred to me that no one had ever seen a black hole until it was broadcasted worldwide. As recently as April 2019, astronomers had captured the first image of a black hole. Using a network of telescopes, each telescope took a picture of the precise location of the black hole, uploaded each image to a data center, and then combined those images into a singular one. It created a slightly blurry yet incredibly awe-inspiring image that had the world talking about space for weeks.
Although we now have that image and have made great leaps in our knowledge about black holes; the many ideas that have surfaced about what a black hole is, whether or not the information is destroyed, preserved, or even enters a black hole, and what is inside a black hole remain baffling. Hawking radiation and the information paradox seem to share a fate similar to that of a famous cat inside of a box, and so the question remains, is it there or not?
References:
Website: Quantamagazine: The Most Famous Paradox In Physics Nears Its End.
URL: https://www.quantamagazine.org/the-black-hole-information-paradox-comes-to-an-end-20201029/
Website: Physicsworld: Information paradox simplified
URL: https://physicsworld.com/a/information-paradox-simplified/
Website: Medium: General Relativity and The Black Hole Information Paradox
Academic Research Paper: Stefano Antonini, John Martyn, Gautam Nambiar, “The Black Hole Information Paradox” December 14, 2018
URL: https://www.cs.umd.edu/class/fall2018/cmsc657/projects/group_2.pdf
