Free A Brief History of Time by Stephen Hawking Page B

the troughs reflected from the other side. The colors corresponding to these wavelengths are absent from the reflected light, which therefore appears to be colored.
    Interference can also occur for particles, because of the duality introduced by quantum mechanics. A famous example is the so-called two-slit experiment ( Fig. 4.2 ). Consider a partition with two narrow parallel slits in it. On one side of the partition one places a source of light of a particular color (that is, of a particular wavelength). Most of the light will hit the partition, but a small amount will go through the slits. Now suppose one places a screen on the far side of the partition from the light. Any point on the screen will receive waves from the two slits. However, in general, the distance the light has to travel from the source to the screen via the two slits will be different. This will mean that the waves from the slits will not be in phase with each other when they arrive at the screen: in some places the waves will cancel each other out, and in others they will reinforce each other. The result is a characteristic pattern of light and dark fringes.

    FIGURE 4.1

    FIGURE 4.2
    The remarkable thing is that one gets exactly the same kind of fringes if one replaces the source of light by a source of particles such as electrons with a definite speed (this means that the corresponding waves have a definite length). It seems the more peculiar because if oneonly has one slit, one does not get any fringes, just a uniform distribution of electrons across the screen. One might therefore think that opening another slit would just increase the number of electrons hitting each point of the screen, but, because of interference, it actually decreases it in some places. If electrons are sent through the slits one at a time, one would expect each to pass through one slit or the other, and so behave just as if the slit it passed through were the only one there—giving a uniform distribution on the screen. In reality, however, even when the electrons are sent one at a time, the fringes still appear. Each electron, therefore, must be passing through
both
slits at the same time!
    The phenomenon of interference between particles has been crucial to our understanding of the structure of atoms, the basic units of chemistry and biology and the building blocks out of which we, and everything around us, are made. At the beginning of this century it was thought that atoms were rather like the planets orbiting the sun, with electrons (particles of negative electricity) orbiting around a central nucleus, which carried positive electricity. The attraction between the positive and negative electricity was supposed to keep the electrons in their orbits in the same way that the gravitational attraction between the sun and the planets keeps the planets in their orbits. The trouble with this was that the laws of mechanics and electricity, before quantum mechanics, predicted that the electrons would lose energy and so spiral inward until they collided with the nucleus. This would mean that the atom, and indeed all matter, should rapidly collapse to a state of very high density. A partial solution to this problem was found by the Danish scientist Niels Bohr in 1913. He suggested that maybe the electrons were not able to orbit at just any distance from the central nucleus but only at certain specified distances. If one also supposed that only one or two electrons could orbit at any one of these distances, this would solve the problem of the collapse of the atom, because the electrons could not spiral in any farther than to fill up the orbits with the least distances and energies.
    This model explained quite well the structure of the simplest atom,hydrogen, which has only one electron orbiting around the nucleus. But it was not clear how one ought to extend it to more complicated atoms. Moreover, the idea of a limited set of allowed orbits seemed very arbitrary. The new theory of