Black Hole Information Loss Paradox

By Devesh Sharma

March 10, 2021
Illustration of a Black Hole. Credit: NASA’s Goddard Space Flight Center/Jeremy Schnittman (link)

Paradoxes are the intensive limits of our knowledge and understanding of reality. A paradox arises when our ideas contradict reality.

One such paradox and an active problem in physics is the Black Hole Information Loss Paradox.

In physics, the existence of a paradox means that there is something about the universe that we don’t have any idea about.

Every object in this universe has a unique set of quantum information that describes the composition, position, and microstates of the particles it is made up of.

According to quantum mechanics, Information can neither be created nor destroyed. Physicists call it the Law of conservation of Information.

This is not an abstract idea in physics, rather most quantum mechanics are laid out based on this principle, but the application of this law is debatable around a Black Hole.

When a Black Hole engulfs an object, it gets completely squeezed and lost to us.

Now the problem is, what happened to the quantum information of that object?

To us, it might be lost forever, this paradox arises due to the inconsistencies between Quantum Mechanics and the General Theory of Relativity.


Before going further into this discussion, let’s first understand why Quantum Information is required to be conserved.

Law of Conservation of Information

In classical mechanics, information about an object can be altered and destroyed completely. For example:

You have your school report card which you messed up terribly and you want to hide from your parents. One of the easiest ways would be destroying the report card completely.

You may tear it and throw it somewhere or bury it inside the earth, but there’s always a way that someone manages to get them together and one can know how terrible you are at Mathematics.

The best thing you can do is burn the report card, it’ll get completely ripped off and no one can ever get the mess together, voila! you are safe now.

But let me tell you, it was destroyed only in the eyes of classical mechanics, and here’s a piece of bad news – in quantum mechanics, it is possible to retrieve every piece of information of the particles which built up your report card, at least theoretically you’re still not safe.

This is because quantum mechanics follows the no-hiding principle.

No-hiding Principle

According to the no-hiding principle, the quantum information of a particle remains intact in a system even though the system undergoes any changes.

The no-hiding theorem was proved by Samuel L. Braunstein and Arun K. Pati in 2007 and tested experimentally in 2011, and the results came out positive (really sorry dude, you ain’t safe).

Since Quantum mechanics is a time-reversal invariant meaning, quantum physics doesn’t care about the direction of time.

The system’s information must remain conserved throughout space-time so that when time is reversed, we can reach the initial point of the system without any inconsistency.

So, now you better study hard so that you don’t have to worry about destroying your report card.

Is Quantum Information Lost Inside Black Holes?

We all know that Black Hole has such immense gravity that even light can’t escape it. Once you crossed the Event Horizon, there is no way out.

A concept called the no-hair theorem states that the properties of a Black Hole are independent of the properties of the particles it eats.


That means the quantum information about that object cannot be retrieved ever.

So, what about executing your report card into a Black Hole?

Does it mean that the information about the object is lost forever?

This question is intimidating the scientific community for a pretty long time. Scientists came up with two possibilities – 

  • All of the information about the object vanished (you’ll be safe, execute your card).
  • The surface area of the event horizon increases to compensate for the increased amount of information to be stored (No, you ain’t safe yet).

The first idea violates the second law of thermodynamics (a net decrease in the total entropy of the universe).

The second idea is relatively promising as it considers an increase in the entropy of the Black Hole.

This way, information wasn’t destroyed but got stored on the 2D surface of the Event horizon. This gave rise to the Holographic Principle.

Physicists started believing that information isn’t lost but is just irretrievable.

Everything was going just fine until Stephen Hawking created introduced new havoc among them.

He came up with his idea of Hawking Radiation, which basically states that – with time, a Black Hole radiates and loses its mass.

If the black hole evaporates, the information stored in it will eventually get deleted forever (hopes ain’t dead, you may be safe). 


The Hawking Radiation

According to Quantum mechanics, ’empty space’ is not empty at all.

The vacuum is filled with quantum fields, and disturbances in these fields cause a particle to exist.

In the Quantum Field Theory, a Quantum vacuum is the lowest possible energy in space.

Generally, a quantum vacuum doesn’t possess particles.

Due to Heisenberg’s Uncertainty principle, the energy of empty space is never zero, yet this uncertain energy is not enough to create a real particle.

They create virtual particles that come out into existence in matter-antimatter pairs and annihilate each other in a moment.

When this happens near a Black Hole’s Event horizon, one particle of the pair escapes away, and the other drifts towards the center of a Black Hole.

The quantum modes of the vacuum scatter in the presence of a high gravitational field, and this scattering creates certain De Broglie waves, and we know that waves in the quantum field represent a particle.

Later on, studying the waves, it was found that it follows a similar pattern as thermal radiation.

So basically, the Black Hole is losing its mass into heat energy.

Also, these waves have a wavelength the size of the Black Hole. The larger the Black Hole, the larger would be the wavelength of the De Broglie wave.

Hence, the lower will be the radiant energy (remember that the smaller the wavelength, the higher its energy would be).


So, bigger Black Holes are cooler than smaller ones. It makes the whole process very slow.

A Black Hole of the size of the Sun will take trillions of years to evaporate completely.

When Black Holes are reduced to the size of a molecule or atom, they evaporate explosively as the energy of the radiation is very high due to its small wavelengths. 

This phenomenon was so intimidating for Physicists that it was refused by the scientific community initially, but later on, it was accepted and appreciated.

Still, its existence was a threat to the Law Conservation of Quantum Information, on which most quantum mechanics works.

Black hole's evaporation diagram Penrose, illustrates the black hole information paradox
A Penrose diagram of a black hole that forms, and then completely evaporates away due to Hawking radiation. This illustrates the black hole information paradox. By Raidr – Own work, Public Domain.

If a Black Hole evaporates completely, information stored inside it would be deleted forever.

Hence, the information won’t be conserved anymore – the information loss paradox.

To solve this problem, some scientists assumed that the information stored inside the Black Hole will escape through Hawking radiation.

Professor Stephen Hawking denied this idea as the No-hair theorem suggests that a Black Hole has only three independent fundamental properties, i.e., mass, charge, and angular momentum.

Hence, the properties of radiation coming out should be independent of information stored inside a Black Hole.


With that being said, information inside the Blackhole will find no way outside and will be lost with Black Hole (report card execution hopes still alive?).

This triggered war among Physicists which is famously known as Thorne–Hawking–Preskill bet (Although they were good friends).

But later Hawking conceded the bet and admitted that radiation must leak out the information inside the Black Hole somehow (shattering hopes blames on Hawking).

In July 2004, Stephen Hawking published a paper in which he described that quantum permutation may allow information to leak out of a Black Hole through Quantum tunneling, but this explanation was too abstract to be tested.

At this point, Stephen Hawking accepted that Information must escape from a Black Hole, and hence, he lost his bet.

Losing the bet Stephen Hawking owed Preskill a baseball encyclopedia from which information can be retrieved on will. Stephen joked that he must have given the ashes rather. 

Solutions for the Black Hole Information Paradox

This problem is now more than 40 years old and in the meantime, many physicists came up with many solutions but still, there is no solution on which everyone would agree.

Let’s have a look at these available solutions: 

Blackhole Remnant

Hawking assumed the nature of large black holes while elaborating on his theory of Hawking’s Radiation.

As larger black holes will provide a smooth space-time curvature, due to their really peaceful gravitation waves and then the effects of the black hole’s gravity at the quantum level won’t be significant.

But some Physicists believe that when a Black Hole shrinks to a small enough size then its influence on the quantum level would get turbulent and Hawking’s radiation will not work.

It leaves us with the remnant of the Black Hole inside which all of the information is still preserved and will remain intact forever.

But this phenomenon can’t be proved without the theory of quantum gravity and hence is just a hypothesis.


Quasi-stable Black Hole Remnant

It’s also not necessary for the Remnant to stay as it is forever. It might leak information at its later stages.

Though we don’t have any idea how will it happen, it is believed that it will take a very long time. Hence, it is called a Quasi-stable remnant of a Black Hole.

Information Escapes Black Hole

Physicists have been figuring out how Information does leak out of the Black Hole during its evaporation. Professor Stephen Hawking believed that Hawking radiation is random.

Due to the no-hair theorem, thermal radiation properties should be independent of the information inside the Black Hole. Still, Don Page argued that Hawking was wrong.

Don Page
Don Page

He said the vacuum inside and outside the Black Hole is entangled. He formulated, what is called a Page Curve which represents the entanglement entropy of the Black Hole from its birth till its complete evaporation.

The curve looks like an inverted ‘V’ indicating that information that entered the Black Hole will eventually escape it.

Information Escapes Into a Baby Universe 

This idea is admired by Sci-Fi lovers that there is a whole universe inside the Black Hole, it is known as Black Hole cosmology.

According to Einstein–Cartan–Sciama–Kibble’s theory of gravity, a Black Hole leads to a whole new Universe.

When Physicists were studying the creation of the Universe from the seemingly impossible, extremely dense, and hot ‘singularity,’ they thought that every Black Hole should trigger the formation of a baby universe inside them as they also have a singularity.

With that being said, it’s also possible that the information inside the Black Hole might end up there and hence, inaccessible to us. Though it is mathematically inconsistent, most physicists don’t believe it.

Information Stays on the Surface of Black Holes

There is another possible theory that talks about Information escaping out of the Black Hole gradually. Leonard Susskind put forward the concept of Black Hole Complementarity or BHC.

He said that for an observer outside the Black Hole, the object never reaches the center of the Black Hole, and hence for the outside observer information about the object stays on the surface of the Black Hole.

But if we try interpreting the perspective of that object, it will reach the center of the Black Hole.

This seems to violate a concept termed the no-cloning theorem.

Still, Leonard argues that an observer will not see both things happening simultaneously, so it should not violate the no-cloning theorem.


A Dutch physicist Gerard ‘t Hooft said that any object falling into the Black Hole does leave a 2D imprint over the Horizon and during Hawking Radiation, particles are disturbed by these imprints carrying away the information of the object with it.

It showed that information about 3D objects inside the Black Hole could be described by the 2D information on the surface of Event Horizon.

There would be nothing wrong in saying that 3D objects inside the Black Hole are the projection of a 2D image over its surface, similar to how a hologram projector works; we call it the Holographic principle.

Astonishingly, if we test this idea on a hypothetical Universe inside something that’s called an AdS (anti-de Sitter space), it turns out that it works on the hypothetical Universe as well.

Though it’s still a matter of debate whether it works for our Universe or not. 

Solving the Information Loss Paradox

This paradox is almost 40 years old but still, we can’t figure out why it exists and how we can get rid of it.

It is for sure that we still lack a fundamental understanding of the universe.

Firstly we need to understand that this problem is not exactly about information, it’s about the time reversibility of quantum mechanics.

In quantum mechanics, every event is time-reversal invariant because each event has a definite path by which a particle in one state will end up in another state.

Two particles in two different states can never end up in the same state. Hence if we have information about the current state of a particle, we can evaluate the initial state using the evolution equation, i.e. Schrödinger equation.

Therefore, information plays an important role in setting up the time-reversal invariance of a system.

Still, in Black Holes, every particle eventually ends up in the same state according to relativity which is inconsistent with quantum mechanics.


And so is why, we need a theory that is more fundamental to both General Relativity and Quantum Mechanics, i.e. Theory of Quantum Gravity.

For now, this paradox remains unsolved for practical reasons. Every solution for this paradox is somehow based upon different assumptions made by Physicists.

Though many of them are consistent with mathematics, still we can’t agree upon a single solution with a lot of assumptions.

The main reason behind this is that we are doing physics, not mathematics, and physics doesn’t work based on assumptions.

It requires real data, and we cannot really test things out on a Black Hole to obtain reliable data.

The temperature of Hawking radiation is even less than one Kelvin which is impossible to measure with the current technology.


This problem may at least possibly take another few decades for Physicists to figure out.


The Black Hole Information Paradox left us with havoc on Physics, still, it led us to create amazing ideas that help us understand our Universe better.

The existence of a paradox is just an indication that there is still a lot to know.

Though we yet couldn’t explain this paradox, it led physicists to have fascinating ideas, taking from the Holographic Principle to the String theory.

Physicists believe that our Universe is not weaved upon the fabric of space-time as Einstein suggested, but space-time itself is an emergent property of something more fundamental.

This will lead to the same revolution in Physics that happened in the early 20th century.

The universe surely has a lot for us in coming.