The Black Hole Information Paradox

After showing the world that the Universe began as a point of singularity, and the event responsible for the creation of the Universe was the ‘Big Bang’, Stephen Hawking turned his attention towards the mysterious cosmological objects called Black Holes. A black hole is formed when a very massive star runs out of fuel and explodes as a Supernova. The explosion throws away the outer gaseous layers and leaves behind a very massive core packed into a region of very little radius. The black hole has a gravitational pull so strong, even light cannot escape from its surface. The region that demarcates the ‘point of no return’ for light, or as a matter of fact, any other object is known as the event horizon of the black hole.

So the first thought that naturally creeps into our minds is that since the gravitational pull of a black hole is so strong, there should not be any particles or radiation emitted from it. This is precisely what the theory of General Relativity predicts. However, Stephen Hawking showed the world that black holes do in fact emit, if one were to take into account quantum perturbations in and around the event horizon of a black hole. This, quite fittingly, is called ‘Hawking Radiation’.

It is important here to remember one very extravagant statement made by the great physicist John Wheeler, “black holes have no hair!” This most certainly does not imply that black holes are bald. What it truly means is that the properties of a black hole which can be observed from outside its event horizon are dependent on only three classical parameters, its mass, electric charge and angular momentum. All other information (or hair) about particles falling into a black hole is inaccessible to observers outside the event horizon.

A very simple idea about the origin of Hawking radiation can be formulated if we were to consider quantum vacuum fluctuations in the gravitational field of a black hole. A quantum fluctuation is a temporary appearance of energetic particles, as allowed by Heisenberg's uncertainty principle in quantum mechanics. These fluctuations lead to particle-antiparticle production out of pure energy, albeit for a very short period of time. If either of the two particles fell into the black hole and the other escaped the black hole's gravitational pull by a phenomenon known as ‘quantum tunnelling’, the particle which escaped will give rise to Hawking radiation. In order to conserve the total energy in this sequence of events, the particle that fell into the black hole must contain negative energy. This means that the black hole is slowly losing energy and hence, mass. It would eventually evaporate!

Therefore, the information about every particle that ever fell into the black hole, and that of the black hole itself will one day completely disappear. This proposition hits right at the heart of quantum mechanics, which postulates that the behaviour of a particle at any point in the future can be predicted if one were to possess ample information about its current state, which is nicely packed into its 'wave function'. The wave function informs us about a particle's position, velocity, momentum, energy, etc. at any given time. This abrupt loss of information was called the black hole information paradox.

Since millions of black holes have been discovered in the universe, the occurrence of this paradox cannot be quarantined to just one particular situation. If the information paradox exists in the case of a black hole, then it must exist everywhere else in the universe too.

Stephen Hawking remained convinced that information was indeed getting destroyed in a black hole, and that quantum mechanics will have to be suitably modified to take into account these occurrences. This annoyed quite a number of physicists around the world. One of the most offended was John Preskill, who bet Stephen Hawking and was sure that information was not destroyed in a black hole. The winner of this bet would receive an encyclopedia of the winner’s choice, in which information never gets destroyed for sure.

Another notable physicist who was troubled by Hawking’s claim was Leonard Susskind, who wanted to ‘save’ quantum mechanics and publicly declared war against Hawking! He, however, maintained that the two are good friends and their war is only that of ideas. The debate was eventually settled when Susskind showed that information of particles entering a black hole was not lost, but it was smeared or ‘painted’ on its event horizon and got completely scrambled. This is knows as the 'Holographic Principle'. Susskind gave a precise string-theory interpretation, which involved a much higher number of dimensions than the three dimensions of space and one of time. It also took into account the non-zero entropy of slightly longer strings that make up the event horizon of a black hole.

Now that the argument was settled, Stephen Hawking had to gift a copy of ‘Total Baseball: The Ultimate Baseball Encyclopedia’ to John Preskill. Comparing the scrambled and useless information that was emitted by a black hole to ‘burning an encyclopedia’, Hawking remarked that he might as well have gifted Preskill the ‘ashes’.

Kip Thorne, John Preskill and Stephen Hawking. Preskill bet that the information can be recovered, with Hawking and Thorne betting that it is destroyed

Image source: theory.caltech.edu