Photo by Guillermo Ferla on Unsplash

Black Hole Information Paradox

What is a black hole ?

Black hole is a place where the pull of gravity is so intense that even light cannot get out. This is as a result of matter been squeezed into an infinitesimal space due to death of a star or due to direct collapse of massive dust clouds (causing supermassive like TON 618). They have bright accretion disk of superheated particles which encompasses the event horizon & the singularity of the blackhole

Event horizon is the nearest point in space around the blackhole where the universal constant, speed of light in vacuum has a chance to escape the clutches of black holes gravity. The center of the black hole, which is responsible for all this phenomenon is called a singularity where the entire mass of the star is collapsed into a point size of infinite density & infinite gravitational field and unsurprisingly also the point where the laws of physics as we know break down

How are they formed ?

Stars have two majors forces that balance out their existence. The internal fusion engine that puts pressure outwards towards the surface of the star and gravity that pushes all matter around the surface towards the core of the star. As long as fusion keeps happening, the star burns bright & hot as a by product of fusion & exists happily. But does the fusion engine stop? well eventually, as the elements keep fusing, they keep creating heavier & heavier elements till it encounters iron atom. The presence of iron at the core is equivalent to ever famous apocalyptic phrase “the end is near”

The atomic structure of iron is highly stable and the energy & force required to fuse two iron atoms into nickel is insane which means that at this stage the star cannot sustain its fusion engine & starts giving away to gravity

The number 1.4 times the mass of sun is quite important in astrophysics because it is key to understanding the evolution of stars in the universe. This limit is called Chandrashekhar limit & beyond this limit, stars at the end of their lives either explode into a supernova or explode & collapse into a neutron star or a black hole

What is gravity according to Einstein’s general theory of relativity ?

Enter spacetime:

Spacetime is a kind of mathematical model that fuses the 3 dimensions of space we traditionally know and the one-dimension of time into a single four-dimensional fabric. This mathematical model has been one of the most successful (if not the most successful one) in explaining the relativistic impacts of traveling at or near the speed of light

Einstein’s general theory of relativity explains gravity as a distortion of spacetime caused by the presence of matter or energy. A massive object generates a gravitational field by warping the geometry of the surrounding spacetime

The most recent proof of this comes from the observance of gravitational waves in 2015 by LIGO detecting them in a violent event that happened 1.3 billion years ago when two massive black holes crashed into each other. Its worth to note that the theory is geometric in nature

What is gravity according to Quantum Physics ?

Quantum physics deals with mathematical description of the motion & interaction of subatomic particles. Gravity as a force is so weak compared to other forces in the quantum world, that it is impossible to see impact of gravity in particle physics experiment even with current sophisticated equipment like the LHC. Even then, it must still apply to the micro-world & we do have quantum theory for all forces except gravity

The field of theoretical physics that tries to describe gravity according to the principles of quantum mechanics is called quantum gravity and it speculates the presence of an elemental particle called graviton which is massless, has a quantum mechanical spin of 2, and electrically neutral to mention few of its predicted properties.

Over the years, there have been few theoretical progresses made in the field of quantum gravity. Theories like loop quantum gravity & superstring theory are slightly better known ones. But these theories are out there to be proven and it will take us some time to provide evidence that confirms these ideas

But the importance of combining gravity & quantum mechanics is crucial for building a more generalised theory & also to explain the singularity and even potentially explain the state of the universe just before the big bang when our universe was infinitesimally small.

What is an information ?

Typically, the information we talk about in our day-to-day life is something visible to us. If you see a stick lying on the ground, you can inspect, measure & understand the features of the stick. Its brown, 2 meters long, 0.2 meters thick & still has a dry leaf embedded on it are all the informations of the stick observed visually or measured somehow

What is a Quantum Information ?

Physicists usually use the term quantum information because it dwells and talks more on more absolute terms like quantum particles. They refer to the quantum properties of all the particles that make up the stick itself such as their position, spin & velocity.

Every object in the entirety of the universe is composed of unique quantum properties. So, if we were to consider the whole universe as a closed system, the amount of quantum information must be conserved. Which means quantum information can neither be created, nor be destroyed (hey i’ve seen this one before !)

This also means that if you were to pass that stick through a shredder, its quantum information is never deleted & hence you can actually put together the pieces of quantum information to re-create (theoretically) the obliterated poor stick from its most basic composition & properties

This law is called conservation of quantum information and most of modern science as we know is built around this law

What is information paradox ?

Consider the stick entering the black hole’s vicinity. The stick gets spaghettified, torn to sherds, broken down into into most basic composition at & beyond the event horizon. But where does this information go ? Its as if the information about the object has completely left the universe itself. If it is so, the law of conservation of quantum information has been broken

Well, we do know very little about a black hole. So is it possible that it resides inside the event horizon somewhere or perhaps at the event horizon itself encoded as the most basic information of itself. This way, the information is not lost but it is just in a place that we cannot access it. We do know however that as blackhole consumes more & more objects on its way, the event horizon size increases. So does it mean all information about a star the blackhole ate for breakfast is conserved somewhere within the blackhole or at the event horizon? Well, not exactly.

Enter the Hawking radiation

(why do i hear boss music ?)

In 1974, Stephen Hawking came up with a theory that black holes thermally create and emit sub-atomic particles, until they exhaust their energy and evaporate completely. According to this theory, black holes are not completely black, and neither do they last forever (jaw drop!). The radiation emitted by the blackhole is called as the Hawking radiation

He showed how the strong gravitational field around a black hole can affect the production of matching pairs of particles and anti-particles, as is happening all the time in apparently empty space according to quantum theory. If the particles are created just outside the event horizon of a black hole, then it is possible that the positive member of the pair (say, an electron) may escape — observed as thermal radiation emitting from the black hole — while the negative particle (say, a positron, with its negative energy and negative mass) may fall back into the black hole, and in this way the black hole would gradually lose mass and evaporate into nothingness

This theory was greatly acclaimed as it was one of the very few theories to combine the general theory of relativity & quantum mechanics into one. The theory that the darkest phenomenon in the entire universe gives away highly energetic quantum particles was staggering when it initially came out in ‘74

But what does this have to do with the paradox itself ?

Well, this only further strengthens the paradox. Even if we were to assume the quantum properties of the particle are embedded at the event horizon, hawking radiation says there are equal amount of particles falling into the black hole & escaping the event horizon. The information of the particle falling into the black hole is still lost forever. Also, the constant evaporation means information is steadily being erased over time & completely vanish once the black hole vanishes

Possible theories

  • It could very well be a misunderstanding of how the quantum theory & general theory of relativity interact with each other (we know they are quite difficult to combine) i:e the theory of everything should be able to explain this paradox
  • It is possible that the information is encoded in the escaping particles in the way we are yet to uncover
  • Hawking earlier suggested that it is possible that the information is perhaps conserved but not in our observable universe but in a parallel universe or multi-verse as a whole (modified Einstein-Cartan theory) which says that rotating blackholes give birth parallel universes accessible by wormhole and hence the information itself is passed from our universe to another parallel universe. This way, the law of conservation of quantum information still remains valid when we consider the entire multi-verses as a closed system
  • Hawking, later in 2004, came back with a new theorem that quantum tunnelling from within the black hole could interact with the holographic horizon and carry information back out into our universe. Losing a 7 year old bet with Kip Thorne & John Preskill that information is forever lost in a blackhole
  • Susskind proposed that when an object falls into a blackhole, the information that makes it up, is scrambled into 2D around the edge of the black hole. He also believes that a similar process occurs in the observable universe on its entirety which would mean that we live in a holographic 3D universe on top of a 2D space encoded with information. This is known as holographic principle & is even more mind-boggling to think that everything 3D we know of is just a hologram of its information

The paradox has the scientific community searching for answers for decades. Nonetheless, it has helped us uncover the unknown & take a step towards understanding them. We may not have answers to all the questions the universe throws at us but we sure can hope to keep exploring & cracking its deep mysteries

Interesting fact: Current limit of microchips is governed by Heisenbergs uncertainty principle. If the holographic principle becomes the new limit, we might hit a scenario where we try to pack denser and denser information into smaller place and end up creating a black hole :)

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Data Scientist @Royal Dutch Shell | Deep Learning | NLP | TensorFlow 2.0 | Python | Astrophysics ❤

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Sundaresh Chandran

Sundaresh Chandran

Data Scientist @Royal Dutch Shell | Deep Learning | NLP | TensorFlow 2.0 | Python | Astrophysics ❤

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