Three Monkeys Online

A Curious, Alternative Magazine

Every wave is made of tiny drops. Reflections on Stephen Hawking and the paradox of information loss.

Even a huge wave appearing suddenly in the sea is made up of tiny drops of water and it is the beautiful result of many factors. Similarly, any progress in science is built on a large number of small results obtained by a myriad of researchers, and influenced by other sociological factors. However, it seems to be in the nature of human beings to devote all their attention on one of these contributions. Science does not escape from this process of concentration. In particular, Professor Stephen Hawking has attracted all the media’s recognition for the progress made in the last decades in the field of theoretical physics.

Hawking, in a famous paper published in 1975, showed that black holes – objects formed from the gravitational collapse of massive stars – emit thermal radiation. According to Einstein’s general theory of relativity black holes are so massive that the gravitational field they create forbids anything, including light, from leaving. Stephen Hawking’s result was therefore surprising and remarkable… but not unique. It must be placed within a sea of closely related results that surfaced in the period around the publication of his paper.

It was already known for some time before Hawking’s paper that it is possible to extract energy from particular types of black holes: rotating ones. The gravitational field of these black holes creates a region around them, called the ergosphere, where the energy of a particle may be negative as seen by a distant observer. This property may be counter-intuitive, but is explained by general relativity since the energy of a particle is relative to the observer and therefore different observers may measure a different energy for the same particle. Thus, a distant observer will measures negative energy for the particle lying inside the ergosphere while an observer beside the particle will measure positive energy, as expected. Roger Penrose, in 1969, thought up the following experiment. A distant observer would propel a particle with an explosive device timed to explode once the particle was inside the ergosphere, splitting the particle into two fragments. One fragment would be attracted and absorbed by the black hole, whereas the other fragment would return back to the distant observer. The fragment going into the black hole may follow a path such that its energy is negative as measured by the distant observer. By the law of conservation of energy, the fragment that returns to the observer must have an energy larger than that of the particle that was initially launched by our observer. According to general relativity, it is therefore possible to extract energy from a black hole.

An analogous result applying to waves rather than particles was shortly after discovered and presented in various papers by Churilov, Starobinsky and Zel’dovich. This result applies to various types of waves – electromagnetic and gravitational waves in particular. An electromagnetic wave, such as light, propagates an electric and magnetic field. A gravitational wave (described by Kip Thorne as a ripple in the fabric of space-time) propagates a gravitational field. The researchers showed that, as in the process discovered by Penrose, a distant observer could send a wave into a rotating black hole and recover a wave with greater energy than that of the original, incident wave. Part of the wave carries negative energy into the black hole and part of the wave is reflected by the gravitational field created by the black hole. This reflected wave is returned to the distant observer with increased energy, a phenomenon known as superradiance.

The results explained so far were derived using the general theory of relativity. Similar results were found when quantum theory was used. According to quantum theory, the vacuum state of most fields (e.g. electromagnetic or gravitational) is not absolutely empty, but may be thought of as a sea of virtual particle-antiparticle pairs. These virtual pairs are not generally detectable, since they annihilate each other immediately after they are created. However, near a black hole, the gravitational field is so strong that when the field is in a vacuum state, one of the particles may be pulled into the black hole before the pair self-annihilates. The remaining particle may then escape out of the range of the gravitational field of the black hole and be received by a distant observer. This observer would then see an approaching flux of particles. It would look as though they were emitted by the black hole but in reality they are not escaping from inside the black hole, but are instead being created just outside of it. Unruh found in 1974 that a rotating black hole could emit radiation in this way.

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