The Black Hole Information Paradox

Written By Sneha Senthilkumar (Grade 12)

The black hole information paradox is one of the most notable paradoxes in the history of physics. All of it started, when a young physicist named Stephen Hawking, published a quirky paper on the evaporation of a black hole. Little did he know, it would transpire into one of the most hair-scratching paradoxes of all time, fuelling countless breakthroughs in a variety of fields in physics.  What is this paradox, and why did it stir such excitement and perplexity in the physics community? 

Let’s start with the basics. Black holes, as we know, are unfathomably destructive objects that exist in space, due to the very strong gravitational force they exert. Black holes form when a star that is heavy enough collapses in on itself. This causes large amounts of mass to get compressed down to a tiny point of infinite density, also known as a gravitational singularity. To give you some perspective, for a regular stellar-mass black hole to be created, one must concentrate 10 suns into a mere point of no measurable size. That would be one really dense point.

So, how does a black hole possess such a strong gravitational force? Einstein’s theory of general relativity states that gravity is caused by warps and curves in the fabric of space-time. If the warp is deeper, the gravity around the body causing the warp will be more. Hence, the singularity of a black hole, due to its infinite density, creates an insurmountable dent in space-time, resulting in unparalleled forces of gravity near it. So anything that passes the event horizon of a black hole, including light, has no chance of return.  

Now let’s go to the basics of quantum theory. As you know, every body in the universe is made of subatomic particles. You can describe the nature of these particles by measuring their spin, charge, etc. This is known as the quantum properties (i.e. information) of the particle. Since every body is made of those particles, we can extrapolate this idea to say that every body is described by its unique quantum information.

Now that you understand what information we are dealing with here, let’s move to the most fundamental theory in quantum mechanics – the conservation of quantum information. If you’ve studied the conservation of energy in high school physics, then this should be a piece of cake for you. 

The conservation of quantum information simples tells us that quantum information can neither be created nor be destroyed. This theorem is also known as the no-hiding theorem.

Now that you’ve got a vague idea of general relativity and quantum mechanics, let’s get closer to the actual paradox. 

Imagine a black hole. We know that any object passing the event horizon of the black hole will practically get sucked into it. The object will be fully destroyed by it, but the quantum information of the body won’t be destroyed. The information will be out of sight and hidden, but it still exists, just in a place we can’t see it. Therefore, the no-hiding theorem is not violated. The black hole will store that information inside it, and it will perpetually grow in size as it consumes more objects.

This was the initial idea. Everything was perfect. No quantum information was destroyed, and no rules were violated. Nothing to worry about at all…

Until of course, in 1974, Stephen Hawking combined general relativity and quantum mechanics in his paper (a very risky move indeed). Allow me to break down what he proposed. 

In the vacuum of space (all around us too), there are pairs of virtual particles that pop into and out of existence very quickly. Vacuums are actually seething with action, with all these virtual particles popping into existence in pairs by taking energy from the vacuum. They quickly annihilate each other and return the energy they took back to the vacuum. This is known as quantum vacuum fluctuations.

Similarly, if this very phenomenon occurs near the event horizon of a black hole, one particle will go into the black hole while the other will escape away from it. But we already know for these particles to pop into existence, they need to take energy from something. In this case, they take the energy from the black hole. Since the particle pair part ways in opposite directions instead of annihilating each other, no energy taken is returned to the black hole. From Einstein’s famous equation e=mc² (c is the speed of light in a vacuum), if energy (e) reduces, then mass (m) also reduces. As a result, the black hole will slowly evaporate and disappear altogether.

Let’s stop right there. If the black hole disappears, then the quantum information of all those objects stored inside the black hole will disappear as well. But that is a direct violation of the most fundamental quantum theory we discussed earlier – no-hidden theory. Quantum information cannot be destroyed! But it just happened. This is the black hole information paradox.

Physicists were baffled and stunned by this paradox but were determined to research more to understand what was going on. Nobody knew whether the information was actually lost forever or was somehow leaked out of the black hole before it disappeared. Hawking even had a bet with two other renowned physicists, Kip Thorne and John Preskill. Hawking and Thorne stated that the quantum information had to be destroyed, which meant that the rules of quantum mechanics had to be changed to fit this observation. On the other hand, Preskill said quantum mechanics showed that information must escape, and so the rules of general relativity should be rewritten. Sounds like a paradox on it’s own 😉 !

However, in 2004, Hawking conceded his bet and agreed that black holes do leak information, so no information is destroyed (no rules violated). Preskill won the bet, and as promised, the winning side of the bet was to receive any encyclopedia to “retrieve information at will” (great joke). And yes, Hawking did indeed gift Preskill a baseball encyclopedia.

Overall, it was found that Hawking’s radiation is not entirely thermal, but also contains encoded information about the interior of the black hole. Other postulates, such as the information moving into another universe altogether as the black hole disappears, information escaping just before the black hole disappears, etc. , were suggested. However, they all have their own contradictions and flaws. Last year, two papers were published suggesting that after half the mass of the black hole evaporates, a wormhole is created, connecting the inside of the black hole with the wider universe. I won’t be getting into too many details unless you want to spend a rather long time reading them.

However, the black hole information paradox will always remain slightly unsolved until we have a proper theory of quantum gravity, which describes gravity in terms of quantum mechanics. It will also contribute to the ultimate goal for a theory of everything.

We are only at the beginning of understanding the mechanics of these calamitous objects we refer to as black holes. Throw quantum mechanics into the mix, and we know that we still have a long way to understand how exactly information escapes out of this abyss of no return.

Featured Image Courtesy – Science Alert