On Black Holes – II

In the previous article, I talked about the formation of Black Holes. In this one, I will talk about the Black Hole Information Loss Paradox. This is the problem that I had been working on. I will explain what most likely causes this paradox and about the most famous attempt to resolve it. I may go off on relevant tangents in the middle. You can expect a lesser number of rubber sheet analogies here.

The Black Hole Information Loss Paradox arises out of the fact that Black Holes shrink and die. Stephen W. Hawking, in a paper in the 1970’s, proved that Quantum Effects at the Event Horizon of a Black Holes cause a Black Hole to shrink. While the physical interpretation of this remains ambiguous, the mathematics he used was beautiful and the entire scientific community took it as law.

A possible physical interpretation is as follows. There exists an energy-time uncertainty relation in Quantum Mechanics. From this, it is possible to derive a result that is fundamental to Quantum Field Theory. The result we derive is that particle-antiparticle pairs can randomly pop into existence, and annihilate each other. This is really surprising, but, not a single law of physics is violated. For every amount of positive stuff created, there is an equivalent amount of negative stuff created. So, the effective amount of stuff in the universe still remains the same. This is called Quantum Field Fluctuation.

In fact, we have actually observed this effect. We have observed what we call the Casimir Effect, which is caused due to Quantum Field Fluctuations. If we place two metallic plates very close to each other, like a separation of the order of microns or so, effects of Quantum Field Fluctuations will cause plates to come together. We can explain this as follows. Keeping the plates so close together, we are effectively restricting the wavelengths of particles that can form. The smaller the wavelength of particle that forms, the greater, the energy of the created particle-antiparticle pairs. The greater the energy of the pairs, the smaller duration of time they can exist for. Outside the plate, however, there is no restriction on the possible wavelengths. So, all kinds of particle-antiparticle pairs can form and they can exist for larger time periods. So, effectively, outside the plates, there is more stuff than what can in between the plates. We can say that there is a pressure difference developed with ‘low’ pressure between the plates and ‘high’ pressure outside the plates. This pressure difference causes the plates to collide. Though the plates seem to attract each other, they are actually pushed together.

Now, the Quantum Field Fluctuations can happen anywhere and everywhere. The fluctuations happening outside and inside the Black Hole are of no consequence to us, the pairs form and subsequently annihilate each other. It all gets really interesting when it happens at the boundary of a Black Hole, at the Event Horizon. Say an arbitrary pair forms at the Event Horizon. Normally, they would just collide and annihilate themselves. However, the one the form inside the Black Hole (behind the Event Horizon), will fall into the Black Hole, and the other that forms outside the Black Hole (outside the Event Horizon), is free to escape. An observer outside the Black Hole will see only one particle that appears to have been created by the Black Hole itself (actually, the observer would see an entire stream of particles being “emitted” from the Black Hole, this is Hawking Radiation). The observer will feel that an extra amount of energy is added to the universe because the external observer has no way of knowing about the twin particle that fell into the Black Hole. The external observer feels that there is an addition of energy into the universe. However, energy just cannot be formed. So, this is accompanied by a loss in energy of the Black Hole itself. The loss in energy of the Black Hole causes it to shrink. The Black Hole continues to shrink until it disappears completely.

But, the shrinking of Black Holes presents us with a major problem. Nothing can escape a Black Hole once it has fallen inside it. Every particle inside the Black Hole is trapped. As a Black Hole shrinks due to Hawking Radiation, the particles remain trapped inside it. Once a Black Hole has evaporated completely, none of that information is available to us anymore, all that has been lost. Information appears to have been lost due to this. Information Loss violates the principle of conservation of information. This is the Black Hole Information Loss Paradox.

Information just cannot be lost. Physicists will declare you an outcast if you dare suggest that as even a remote possibility. Information must be conserved. Many attempts have been made at resolving this paradox. The most famous of which is Gerard T’Hooft’s Holographic Theory, for which the String Theoretic interpretation was provided by Leonard Susskind.

The Holographic Theory suggests that the Universe is really a 2-dimensional reality of which we are the 3-dimensional projection. For resolving the Paradox, Susskind suggests that there a Holographic Plate surrounding Black Holes. The plate is a 2-dimensional sheet, of which there exists so called ‘pixels’. Each ‘pixel’ has an area equal to the Plack Area. Each ‘pixel’ can contain only one unit (bit) of information. A ‘pixel’ is said to be saturated if light from a particle or the particle itself passes through the pixel. So, when a particle falls into the Black Hole, it has to pass through this sheet. Once it does, a copy of that information remains in that sheet but the particle itself is lost. It is like having a photocopy and losing the original document.

The other postulated resolution to the paradox is that the information is stored in a Planck-sized remnant, another suggests that the information is stored in a relatively large remnant, one suggests that information leaks out during the life of a Black Hole or just bursts out of a Black Hole in its final stages. There are many other postulates, these are just the ones that make the most sense to me. I mentioned the Holographic Theory just because it is really cool, however, I do have some reservations about it. Personally, I feel that of the possible solutions suggested, the information leak proposal and the information burst proposal make the most sense to me. They seem more intuitive than the Holographic Proposal.


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