Stars much heavier than the Sun burn their fuel much more quickly, and then collapse to form a neutron star or a black hole.
Neutron stars have masses about one to three times that of the Sun, circumferences of 75 to 100 kilometers (about the size of Chicago), and densities the same as the nucleus of an atom: a hundred trillion times more dense than rock and the Earth. Indeed, neutron stars are made of almost pure nuclear matter: atomic nuclei packed side by side.
Black holes (Chapter 5), by contrast, are made fully and solely from warped space and warped time (I’ll explain this weird claim in Chapter 4). They contain no matter whatsoever, but they have surfaces, called “event horizons,” or just “horizons,” through which nothing can escape, not even light. That’s why they are black. A black hole’s circumference is proportional to its mass: the heavier it is, the bigger it is.
A black hole with about the same mass as a typical neutron star or white dwarf (say 1.2 times as heavy as the Sun) has a circumference of about 22 kilometers: a fourth that of the neutron star and a thousandth that of the white dwarf. See Figure 2.5.
Since stars are generally no heavier than about 100 Suns, the black holes to which they give birth are also no heavier than 100 Suns. The giant black holes in the cores of galaxies, a million to 20 billion times heavier than the Sun, therefore, cannot have been born in the death of a star. They must have formed in some other way, perhaps by the agglomeration of many smaller black holes; perhaps by the collapse of massive clouds of gas.
Magnetic, Electric, and Gravitational Fields
Because magnetic force lines play a big role in our universe and are important for Interstellar, let’s discuss them, too, before diving into Interstellar’s science.
As a student in science class, you may have met magnetic force lines in a beautiful little experiment. Do you remember taking a sheet of paper, placing a bar magnet under it, and sprinkling iron filings (elongated flakes of iron) on top of the paper? The iron filings make the pattern shown in Figure 2.6. They orient themselves along magnetic force lines that otherwise are invisible. The force lines depart from one of the magnet’s poles, swing around the magnet, and descend into the other pole. The magnetic field is the collection of all the magnetic force lines.
When you try to push two magnets together with their north poles facing each other, their force lines repel each other. You see nothing between the magnets, but you feel the magnetic field’s repulsive force. This can be used for magnetic levitation, suspending a magnetized object—even a railroad train (Figure 2.7)—in midair.
The Earth also has two magnetic poles, north and south. Magnetic force lines depart from the south magnetic pole, swing around the Earth, and descend into the north magnetic pole (Figure 2.8). These force lines grab a compass needle, just as they grab iron filings, and drive the needle to point as nearly along the force lines as possible. That’s how a compass works.
The Earth’s magnetic force lines are made visible by the Aurora Borealis (the Northern Lights; Figure 2.9). Protons flying outward from the Sun are caught by the force lines and travel along them into the Earth’s atmosphere. There the protons collide with oxygen and nitrogen molecules, making the oxygen and nitrogen fluoresce. That fluorescent light is the Aurora.
Neutron stars have very strong magnetic fields, whose force lines are donut-shaped, like the Earth’s. Fast-moving particles trapped in a neutron star’s magnetic field light up the force lines, producing the blue rings in Figure 2.10. Some of the particles are liberated and stream out the field’s poles, producing the two violet jets in the figure. These jets consist of all types of radiation: gamma rays, X-rays; ultraviolet, visual, infrared, and radio waves. As the star spins, its luminous jets sweep around the sky above the neutron star, like a searchlight. Every time a jet sweeps over the Earth, astronomers see a pulse of radiation, so astronomers have named these objects “pulsars.”
The universe contains other kinds of fields (collections of force lines) in addition to magnetic fields. One example is electric fields (collections of electric force lines that, for example, drive electric current to flow through wires). Another example is gravitational fields (collections of gravitational force lines that, for example, pull us to the Earth’s surface).
The Earth’s gravitational force lines point radially into the Earth and they pull objects toward the Earth along themselves. The strength of the gravitational pull is proportional to the density of the force lines (the number of lines passing through a fixed area). As they reach inward, the force lines pass through spheres of ever-decreasing area (dotted red spheres in Figure 2.11), so the lines’ density must go up inversely with the sphere’s area, which means the Earth’s gravity grows as you travel toward it, as 1/(the red spheres’ area). Since each sphere’s area is proportional to the square of its distance r from the Earth’s center, the strength of the Earth’s gravitational pull grows as 1/r2. This is Newton’s inverse square law for gravity—an example of the fundamental laws of physics that are Professor Brand’s passion in Interstellar and our next foundation for Interstellar’s science.
3
The Laws That Control the Universe
Mapping the World and Deciphering the Laws of Physics
Physicists have struggled from the seventeenth century onward to discover the physical laws that shape and control our universe. This has been like European explorers struggling to discover the Earth’s geography (Figure 3.1).
By 1506 Eurasia was coming into focus and there were glimmers of South America. By 1570 the Americas were coming into focus, but there was no sign of Australia. By 1744 Australia was coming into focus, but Antarctica was terra incognita.