Once Before Time - Martin Bojowald [94]
When its nuclear fuel is nearly depleted, a star can no longer shine as intensely as during helium fusion. It will initially swell and become a so-called red giant, glowing for some more time. The sun will share this fate in about five billion years, unfortunately swallowing Earth. But when all the fuel is gone, the old dilemma is faced again: Gravity insatiably compresses the star, much more intensely than before the state of the red giant. What counterforce can now become its equal to make a stable object possible?
A light star will, after using up all nuclear fuel, simply cool down and shrink somewhat, until the material pressure suffices for stabilization as in a planet. But this is not possible for heavy stars; there is simply too much mass pushing on the interior of the faded star. Such high pressures cannot easily be produced in the laboratory, and so the behavior of matter in such a state is not completely understood. For a certain range, however, more familiar physics suffices to understand the further collapse of a star.
At first, quantum mechanics rushes to help, as it already did to stabilize a hydrogen atom. It leads to a new but unfortunately extremely counterintuitive force able to hold its own against gravity. As we have seen, electric repulsion has long failed at such high densities. But there is another reason for two particles of the same kind, such as two protons or two electrons or even two electrically uncharged neutrons, to stay away from each other. This was first realized by Wolfgang Pauli and formulated as a principle: Pauli’s exclusion principle, which in 1945 gained him the Nobel Prize in Physics. The use of the term “principle” indicates that this, like so much else in quantum mechanics, has a rather abstract origin. But it is a very real phenomenon, as shown not only by the existence of white dwarfs in the universe but also by a multitude of experiments on Earth.
What we perceive as pressure in ordinary matter, as well as in common stars, is caused by the impact of atoms or molecules on one another. Higher pressure arises from more vigorous pushing of atoms or molecules on surrounding matter, which could result from a raised temperature. But without nuclear fuel in old stars, the ability to increase pressure by heating up is precluded, and the star is doomed to compress under the influence of gravity. The nuclei of atoms, now belonging to heavy and no longer fusable elements, come very close to each other, and their electron wave functions overlap. Once the nuclei are sufficiently close, electrons can easily switch places from the orbit of one atom to a neighboring one; they can no longer be attributed to a unique atom, and instead move much farther away. In this case, one speaks of the formation of an electron gas pervading the dense matter. Electron gas arises at high pressures, pushing atoms close to each other, but it is also realized under natural conditions in metals, where it is responsible for electric conductivity.
In an electron gas, there are no impacts between electrons in the usual sense. Instead, the electron gas resists too strong a compression by behaving according to Pauli’s exclusion principle; the particles are held apart solely by quantum mechanics. For particles such as electrons, protons, and neutrons, it turns out that two wave functions of the same type—for example, two electron wave functions—cannot occupy the same position. Imagining particles in the classical picture as pointlike creates no problem, because a point does not require space. However, the wave function in quantum mechanics must be spatially spread out, and so the exclusion principle, which dictates that two wave functions cannot be at the same spot, means that quantum mechanical electrons must repel each other. This happens when the wave functions come too close, usually at very small distances realized only by high compression.
Such a force requires a rather advanced collapse of matter until it can act. And so the resulting object stabilized by this strange quantum mechanical power