Black Holes
Black is not a colour. So why have a page about black holes? It depends what you mean by black. Suppose you painted a picture using pigments that had all been mixed with a lot of black paint. Suppose you hung it in a room with black walls. Suppose you the pointed an extremely bright spot-light at it. The moon is almost black, yet it looks very bright against the night sky. If it reflected as much light as Carrara marble, or even Cotswold limestone, it would be a dazzling object, perhaps five or ten times as bright
Here is how to make a black hole. Take six square metal sheets, paint them black on one side, and weld them into a light-tight box with the black surfaces inside.. Drill a tiny hole in one side. That is the black hole. Almost none of the light that goes in, comes out. The smaller the hole, compared with the box, the blacker the hole. That's a pretty boring black hole compared with the gravitational kind which will be discussed later in this page, yet towards the end of the 19th century the finest minds in physics could not understand this box.
What is more, the lack of understanding was apparently catastrophic. Calculations showed that the magic of the black hole was that it didn't matter what the box was made of. The spectrum of the radiation that came out of the hole was always the same, and it depended only on the temperature. It didn't depend on the material of the box, nor on the type of radiation going in. That made it very important, because it was universal. Often in physics, knowledge is gained through some idealised object that can never be built. Another one is the perfectly reversible heat engine.
The radiation from the hole is usually referred to as back body radiation or cavity radiation. This spectrum gives the familiar transition from dull red, through red, orange, yellow and white, which we see when an object is heated, though that is only an approximation to the ideal spectrum . The light and heat coming out of the inspection hole of a pottery kiln gives a fairly good idea of the black body radiation. But it is not perfect black body radiation, because you can make out the shapes of the pots in the kiln.
By careful design and construction a fairly accurate black body generator can be made. A famous example is the universe itself, which appears to be filled with radiation corresponding to a temperature of about 2.7 Kelvins. This is believed to exist because the radiation in the in the universe became decoupled from the matter at a certain time after the big bang, and it has been cooling down ever since, as the universe has continued to expand.
The problem with the 19th century black body calculations was that they always predicted an infinite amount of radiation, the difficulty being at the short wavelength, high frequency end of the spectrum, beyond violet. THis was called the ultra-violet catastrophe. The theories of physics were in good order, and able to describe almost all known phenomena, rather like today's "standard model" of particle physics. True, there were still unknown quantities - what determined the properties of the chemical elements and their compounds? But most areas of science looked good, apart from a few little areas like the black body radiation.
Disagreements between experiment and theory can be very fruitful, because they may stimulate both experimenters and theoreticians try for greater accuracy and understanding. This one started a new age in physics.
Somehow it had to be made more difficult for the cavity to emit high frequency waves. The physicist Max Planck published a paper in 1900 which gave a formula which agreed with reality. He achieved his result by assuming that electromagnetic radiation could not be emitted in arbitrary amounts, as classical physics allowed, but only in discrete quanta, or photons. The energy of these photons is hf, where h is a constant value, and f is the frequency of the radiation cycles per second, or Hertz, Hz. The constant h is now called Planck's constant. It is about 6.626196 10-34 joule second. This is so very small that its direct effects are hard to notice in everyday life, but indirectly it affects almost everything we do.
The effect of Planck's idea was that high frequency radiation is emitted in larger quanta than low frequency radiation. By assuming a suitable statistical law, Planck was able to fit the theory to the data. Planck was unhappy about this, because he was not a revolutionary by nature. He spent a lot of time trying to fit the data with the old ideas. Classical physics assumes that every quantity can change smoothly and continuously. The new idea was an alien intruder into a well ordered system.
Planck's constant is one of the most important constants in physics, because it helps to determine the size of everything. Not only does Planck's constant determine the energy of light quanta, it helps to determine the size of atoms. The orbital angular momentum of an electron in an atom has to be a multiple of Planck's constant. Given the electric charge and mass of the electron and the nucleus, the average radius of the "orbit" can be worked out. In 1900, it was still possible for some people to argue that atoms were only a convenient mathematical idea. That idea did not last much longer.
But what about real black holes? The ones that can swallow whole stars. Everyone knows that nothing comes out of a black hole. Anything that falls into a black hole, stays in. The black hole even conceals most pf the properties of the objects that fall in. Once in, you are completely anonymous - you leave no trace. The only properties that survive are electric charge, which has a long range field, angular momentum, which is a conserved quanity, and mass, which shows up in the long range force of gravity.
But in fact black holes do emit radiation. The page on interference refers to. Evanescent waves. These need not be electromagnetic - the page refers to alpha particles escaping from atomic nuclei. Empty space can even produce evanescence. Were it not for the need to conserve energy and momentum, pairs of positive and negative electrons could be produced from nothing. As it is, empty space behaves as though these virtual pairs are flickering in and out of existence. This changes the properties of space in calculable and measurable ways. The probability of these events is related to a number called the fine structure constant, which is about 1/137.036. The physicist Arthur Eddington thought that the denominator was an integer, and that he could calculate the value from theory. He could have calculated it from "Arthur Stanley Eddington", which adds up to 2 X 137, taking A=1, B=2, etc. In fact nobody knows why it has that value.
Near a black hole, the gravitational field is not only strong, it is strongly varying with position, creating strong tidal forces, tending to stretch or break objects. Close enough to a black hole, gravity can grasp one particle of a pair, and drag it down. This particle can lose so much energy that it pays for the creation of both electrons. To create a particle of mass m, the energy needed is E = mc2, and so to create two electrons of mass me we need a total energy of at least E = 2mec2. The electron which is not captured does not sit still - it is in a hostile environment and will be affected by the gravitational field. It can emit Synchrotron radiation, and Hawking showed that the intensity and shape of the spectrum of energy from a black hole is the same as from the 19th century black hole. Not only that, but the entropy is the same as well. Entropy is a mathematical way of calculating disorder. It is very important because it places strict limits on the conversion of heat (random motion) into ordered energy, which is the basis for many types of engine. You cannot make an engine which converts all the heat from a fuel into useful energy. Some is always wasted. The meaning of this law is that you cannot produce order from chaos without some loss of energy.
So the tin box with the hole in it is not so very different from a collapsed star. It's just a lot smaller, and it has a negligible gravitational field. Apart from its treatment of radiation, the tin box differs also in that it is based on probability, whereas the gravitational black hole is absolute. A speck of dust which drifts into the tin box has a slight but real chance of getting out. Not with the real black hole. If you open a very old radio set you will find the dust that got trapped in it over the years.
How is a black hole formed? Some may have been created in the early moments of the universe, but others may have been made since, by the collapse of burned out stars. A massive star is pulled into itself by its own gravity. It is being pushed apart by the pressure of its own radiation. If it has more than about 1.4 times the mass of the sun, when the radiation starts to fail as the fuel becomes exhausted, it will collapse into a neutron star, visible as a pulsar. If it is bigger than a another critical size, it will go on collapsing until it reaches black hole status.
Everyone knows that people who vanish into a black hole will never come back. It isn't even worth waving and smiling as you fall in. Because your time would appear to go slower and slower as you fall into stronger ans stronger gravity, your wave and your smile will be frozen like the Cheshire cat's grin, and your image will get dimmer and dimmer as the light struggles harder and harder to get away. No grand exit, just a slow fading away into oblivion.