A Snag in the Fabric: The Black Hole Information Paradox
Black Holes. Engines of destruction, swallowers of light and an infinite source of wonder and mystery for astronomers.
A black hole is a region in space where the force of gravity is so strong, not even light can escape.
One reason astronomers are attracted to black holes like a moth to a flame is that they form a singularity, an infinitely small and infinitely dense point in space. Another famous singularity would be the Big Bang singularity, where the curvature of space-time is infinite. At these points, our laws of physics, which are based on the assumption that space-time is nearly flat, completely break down.
Delving into the world of black-holes has lead to groundbreaking insights into the general theory of gravity and quantum mechanics. This paradox is no different. Let’s get down to the nitty-gritty and examine the black hole information paradox for ourselves.
Hawking Radiation
Hawking radiation is blackbody radiation released by black holes, due to quantum effects near its edge. A simplified way of looking at Hawking Radiation can be done with virtual particles. (Not to be confused with real particles, virtual particles are just calculational tools)
Virtual particles — fluctuations in the quantum field — pop into existence and the particle and its antiparticle exist for a moment and annihilate each other. (To learn more on virtual particles, read my article here) When this occurs near a black hole’s event horizon, one particle may fall into the black hole where the other goes into space. This escaping particle causes the black hole to evaporate. This process leads to Hawking Radiation.
Due to the intense curvature of space-time, virtual particles get boosted to become real particles. The black hole needs to give up a part of its mass in order to create this energy and, in essence, evaporates into blackbody radiation. But, along with the black hole, the information of the quantum state also disappears, albeit slowly.
Leading us to the question: Is Hawking Radiation more destructive than the black hole itself?
The black hole information paradox is the idea the Hawking Radiation may be deleting quantum information, defying our preconceived understanding of quantum mechanics.
First, let’s take a look at the law of conservation of information, to fully understand the paradox posed by Hawking Radiation.
Law of Conservation of Quantum Information
The laws of physics that govern our world are deterministic, meaning information about the current state of the system allows us to predict the future state of the system.
Some systems are time-reversal symmetric. This allows us to know the past states of a system given the present state.
Looking at the diagram above, we see that the first system is not time-reversal symmetric. If we know the current state of the system as E, we are unsure if the previous state was A or C. But knowing the current state as B allows us to predict the next state to be D. On the other hand, the system on the right is time-reversal symmetric, which means knowing the current state allows us to predict the past.
Quantum Mechanics ensures conservation of information and the time reversal symmetry, because of the conservation of probability.
Quantum Mechanics is largely characterized by the Schrodinger Equation which is dependent on the wave function. The Equation perfectly predicts the past and future evolution of a wave function. It’s deterministic and time reversal symmetric.
This essentially means that quantum information cannot be lost along the way. Given the knowledge of the universe at present, the entire history of the universe should be perfectly knowable.
Information is indestructible.
This law is important to know because it is this law that black holes seem to break!
The Information Paradox
But, where is the information stored in the black hole in the first place?
The law of thermodynamics tells us that the entropy of a system will only increase. This means that a black hole must have entropy, opposed to what was previously thought. Scientists have agreed that this means the information of whatever falls into it is essentially encoded on the surface area of the black hole.
The information digested by the black hole still persists in the black hole, just away from our reach. But before the blink of an eye, Hawking Radiation swoops down and destroys this information, evaporating the black hole into a hodgepodge of radiation.
Stephen Hawking's calculations show that this radiation is pure thermal black-body radiation. It depends only on the mass of the black hole. Two black holes with different information encoded on the surface but with the same mass will have indistinguishable radiation patterns.
For example, imagine Black Hole One. This black hole has managed to suck in a 50-kilogram satellite and a 25-kilogram space telescope that malfunctioned and wandered off.
A rather unfortunate 75-kilogram astronaut in a mission gone terribly wrong finds himself sucked into Black Hole Two.
Now let's assume the mass of both black holes started off the same, and even after gobbling up the satellite, telescope, and astronaut we can see the mass of both black holes are still the same. Then, Hawking Radiation Theory tells us that the radiation will also be the same! This makes the information that different objects entered the black hole, irretrievable. The information once held by the black hole is therefore lost.
Stephen Hawking’s noteworthy theory seems to have found a way to erase quantum information, shattering one of the pillars of quantum theory.
So which theory is correct?
Is information truly destroyed as a black hole evaporates? This would mean we are yet to discover laws for black hole evaporation. Or does the emitted radiation somehow contains this information? Is there more to Hawking radiation that waits to be unraveled?
It could be neither, or it could be both! This paradox only highlights our incomplete knowledge of the general relativity and quantum field theory. Like every paradox, the black hole information paradox has lead to many searches and solutions that continue to broaden our perspective of the universe.
What seems like a small snag in the fabric may lead to the unraveling of the tapestry that is our preconceived perception of the universe.
This problem continues to perplex physicists. It even led to the famous bet between Stephen Hawking, Kip Thorne, and John Preskill, where Hawking conceded and ended up giving Preskill an encyclopedia on Baseball!
Physicists continue to propose solutions to this paradox, some more unbelievable than others. Some scientists believe this could imply our universe is a hologram, a 3-dimensional projection on a truly 2-dimensional surface, where others suggest quantum tunneling carries the information.
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This isn’t the only mystery that shrouds black holes! Find out more on the Black Hole Firewall Paradox if you wish to continue this quest.
