Author: Leonard Susskind
Publisher: Little Brown and Company 2008
But, do people really understand what a black hole is?
Ian Frazier who wrote the book “Travels in Siberia” states that a “black hole” entering Tunguska in 1908 was not possible because if that is the case, then there should have been an exit explosion on the other side of the Earth, in the north Atlantic. I have no clue what he was talking about.
David Reich who wrote the book “Who We are and How We Got Here—Ancient DNA and The New Science of the Human Past” says the following.
“At each place in the genome, if we trace back our lineages far enough into the past, we reach a point where everyone descends from the same ancestor, beyond which it becomes impossible to obtain any information about deeper time from comparisons of people living today. From this perspective, the common ancestor at each point in the genome is like a black hole in astrophysics, from which no information about deeper time can escape.”
Even David Reich, a Harvard geneticist, who changed his field of study from elementary particle physics to genetics, does not know what a black hole is.
Black Hole War started when Stephan Hawing stated that “information that falls into a black hole is lost information”. Now this is a physicist who famously proved that black holes have entropy and black holes radiate away energy. This radiation is known as the “Hawking radiation”. All physicists believed Hawking except possibly two; Gerard ’T Hooft, and the author of this book, Leonard Susskind. They argued that if that is the case, then that violates one of the major conservation laws of physics, the conservation of information.
But, ’T Hooft and Susskind had no counter argument at the time, even though they knew that something was amiss. The decades long quest for a proof that information is not lost in a black hole and finally convincing everyone including Hawking that information conservation is preserved in a black hole is the story of this book. Apparently, Wheeler was wrong. “Black holes have hair; plenty of it.”
The following is the gist of the Black Hole War story.
Information Conservation
If you know the present with perfect precision, then you can predict the future for all time and you can be absolutely sure of the past. This mathematical reversibility of quantum mechanics (known as unitarity) is critical to its consistency. Without it, quantum logic would not hold together.
The laws of quantum mechanics allow randomness to coexist with both energy conservation and information conservation.
The Plank Length, Plunk Time, and Plank Mass
The Plank length is about \(10^{-35}\) meters. The plank time is about \(10^{-42}\) seconds. The Plank mass is about \(10^{-8}\) kilograms. Compared to other two units, Plank Mass is huge, roughly the mass of ten million bacteria.
The Plank time is the time it takes light to travel a Plank length. Together the three units have an extraordinary meaning. They are the size, half-life, and mass of the smallest possible black hole.
A bit of information is a single irreducible unit of information. A bit of information can be stored in a Plank length size cube.
Entropy
The entropy is a measure of how much information is hidden in the details—details that for one reason or another are too hard to observe.
Heat is the energy of random chaotic motion. If a tub of water is cooled to absolute zero, then the location of each atom of the ice crystals are known. There is no hidden information. That means, the entropy is zero. Now add a little bit of heat by warming the ice. Molecules are beginning to juggle a bit. We lost track of few molecules. That means the entropy increases.
The temperature is the increase in the energy of a system when you add a one bit of entropy.
Energy and entropy are not the same thing, Energy takes many forms, but one of those forms is heat and heat is joined at the hip with entropy.
Black Holes have Temperature
Hawking found that if \(M\) is the mass of the black hole, then the temperature \(T\) of the black hole is given by
\(T=\frac{1}{16\pi^2}\frac{c^3h}{GMk}\),
where \(h\) is the Plank constant, \(G\) is the gravitational constant, \(c\) is the speed of light, and \(k\) is the Boltzmann constant.
That is, large black holes are colder. Consider a stelar black hole with mass about \(10^{31}\) kg (about 5 times the mass of our star). The temperature of this black hole is \(10^{-8}\) Kelvin. That is, about 10 billionths of a degree above the absolute zero. Nothing in natural world is that cold. (The temperature of the inter-stelar space is about 3 degrees Kelvin.)
However, since a black hole has temperature, it has entropy.
Adding one bit of information to a black hole increases the area of the horizon by one square Plank unit. (A one square Plank unit is about \(10^{-70}\) square meters.) Now imagine building up a black hole bit by bit. By the time the black hole is completed, the area of the horizon will be equal to the total number of bits hidden in the black hole. That means, the entropy of a black hole is proportional to the area of the horizon. (This fact was first realized by Jacob Bekenstein.) Hawking proved that the entropy of a black hole is exactly one quarter of the area of the horizon measured in Plank units.
Alice and Bob
Suppose Alice decided to fall into a black hole and Bob observes her from a safe distance. According to the Equivalence Principle of general relativity free falling Alice will not feel the effects of the black hole’s gravity. She will feel nothing as she sails through the horizon. Information is lost. (She will feel the tidal forces when she gets near the horizon, but Bob cannot see anything beyond the horizon.) On the other hand, Bob concludes that Alice getting heated and scrambled and stretched throughout the horizon according to the principles of quantum mechanics. Every bit of information is accounted for. But Alice is scrambled far beyond recognition.
The reason for the Bob’s observation is due to the temperature of the black hole. Even though it is very small a photon which is always moving at a speed of light has to loose a lot of kinetic energy to escape. By the time a high energy gamma ray that rises near the horizon, its energy is so depleted that the escaped ray is a very low-frequency radio wave. Conversely, a radio wave observed by Bob must be a high-energy gamma ray when it left the horizon. That is the same thing as saying it is very hot near the horizon.
So it appears that there is a contradiction. General relativity and the Equivalence Principle says that information sails uninterrupted down through the horizon, quantum mechanics brings up the opposite conclusion: the in-falling bits, though badly scrambled, are eventually returned in the form of Hawking radiation.
This tension—the apparent inconsistency between the horizon as a surface packed densely with material bits and the horizon as a mere point of no return was the casus belli of the Black Hole War.
String Theory
The incompatibility of gravity and quantum mechanics was the stumbling block. What was needed is a theory that has gravity and quantum mechanics coexisting harmoniously. String theory was such a theory. The plan of attack can be summarized as follows.
Take string theory to be the model of “some world” and then calculate whether or not information is lost in that world. If the information is not lost in that world, then Hawking is wrong because he claimed that black holes must destroy information in any consistent world.
That is exactly what expired 20 or so years after the Hawking statement. In the process, Black Hole Complementarity, The Holographic Principle, The Brain Worlds, Stretched horizon of a Black Hole were discovered.
This is a fascinating story of achieving a set goal and advancing and finding new ideas during the process. The story is very well written and the physical explanations are exquisite.
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