The Science of Interstellar

by Thorne, Kip

  Andromeda contains a gigantic black hole, 100 million times heavier than the Sun and as big across as the Earth’s orbit (the same weight and size as Interstellar’s Gargantua; Chapter 6). It resides in the middle of the central bright sphere in Figure 2.2.

  Fig. 2.2. The Andromeda galaxy.

  Solar System

  Stars are large, hot balls of gas, usually kept hot by burning nuclear fuel in their cores. The Sun is a fairly typical star. It is 1.4 million kilometers across, about a hundred times larger than the Earth. Its surface has flares and hot spots and cooler spots, and is fascinating to explore through a telescope (Figure 2.3).

  Eight planets, including the Earth, travel around the Sun in elliptical orbits, along with many dwarf planets (of which Pluto is the most famous) and many comets, and smaller, rocky bodies called asteroids and meteoroids (Figure 2.4). Earth is the third planet from the Sun. Saturn, with its gorgeous rings, is the sixth planet out and plays a role in Interstellar (Chapter 15).

  Fig 2.3. The Sun as photographed by NASA’s Solar Dynamics Observatory.

  Fig. 2.4. The orbits of the Sun’s planets and Pluto, and a region containing many asteroids.

  The solar system is a thousand times bigger than the Sun itself; light needs eleven hours to travel across it.

  The distance to the nearest star other than the Sun, Proxima Centauri, is 4.24 light-years, 2500 times farther than the distance across the solar system! In Chapter 13, I discuss the awful implications for interstellar travel.

  Stellar Death: White Dwarfs, Neutron Stars, and Black Holes

  The Sun and Earth are about 4.5 billion years old, about a third the age of the universe. After another 6.5 billion years or so, the Sun will exhaust the nuclear fuel in its core, the fuel that keeps it hot. The Sun then will shift to burning fuel in a shell around its core, and its surface will expand to engulf and fry the Earth. With the shell’s fuel spent and the Earth fried, the Sun will shrink to become a white dwarf star, about the size of the Earth but with density a million times higher. The white dwarf will gradually cool, over tens of billions of years, to become a dense, dark cinder.

  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.

  Fig. 2.5. A white dwarf (left), neutron star (middle), and black hole (right) that all weigh as much as 1.2 Suns. For the white dwarf I show only a tiny segment of its surface.

  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.

  Fig. 2.6. Magnetic force lines from a bar magnet, made visible by iron filings sprinkled on a sheet of paper. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]

  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.

  Fig. 2.7. The world’s first commerical magnetically levitated train, in Shanghai, China.

  Fig. 2.8. The Earth’s magnetic force lines.

  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.

  Fig. 2.9. The Aurora Borealis in the sky over Hammerfest, Norway.

  Fig. 2.10. Artist’s conception of a neutron star with its donut-shaped magnetic field and its jets.

  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 fu
ndamental laws of physics that are Professor Brand’s passion in Interstellar and our next foundation for Interstellar’s science.

  Fig. 2.11. The Earth’s gravitational force lines.

  * * *

  2 Google “gravitational waves from the big bang” or “CMB polarization” to learn about this amazing March 2014 discovery. I give some details at the end of Chapter 16.

  3 A light-year is the distance light travels in one year: about a hundred trillion kilometers.

  4 In more technical language, its mass is a million times that of the Sun’s or more, which means its gravitational pull, when you are at some fixed distance away from it, is the same as a million Suns’. In this book I use “mass” and “weight” to mean the same thing.

  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.

  Similarly (Figure 3.2), by 1690 the Newtonian laws of physics had come into focus. With concepts such as force, mass, and acceleration and equations that link them, such as F = ma, the Newtonian laws accurately describe the motion of the Moon around the Earth and the Earth around the Sun, the flight of an airplane, the construction of a bridge, and collisions of a child’s marbles. In Chapter 2 we briefly met an example of a Newtonian law, the inverse square law for gravity.

  By 1915 Einstein and others had found strong evidence that the Newtonian laws fail in the realm of the very fast (objects that move at nearly the speed of light), the realm of the very large (our universe as a whole), and the realm of intense gravity (for example, black holes). To remedy these failures Einstein gave us his revolutionary relativistic laws of physics (Figure 3.2). Using the concepts of warped time and warped space (which I describe in the next chapter), the relativistic laws predicted and explained the expansion of the universe, black holes, neutron stars, and wormholes.

  1506—Martin Waldseemuller

  1570—Abraham Ortelius

  1744—Emanuel Bowen

  Fig. 3.1. World maps from 1506 to 1744.

  By 1924 it was crystal clear that the Newtonian laws also fail in the realm of the very small (molecules, atoms, and fundamental particles). To deal with this Niels Bohr, Werner Heisenberg, Erwin Schrödinger, and others gave us the quantum laws of physics (Figure 3.2). Using the concepts that everything fluctuates randomly at least a little bit (which I describe in Chapter 26), and that these fluctuations can produce new particles and radiation where before there were none, the quantum laws have brought us lasers, nuclear energy, light-emitting diodes, and a deep understanding of chemistry.

  Fig. 3.2. The physical laws that govern the universe.

  By 1957 it became evident that the relativistic laws and the quantum laws are fundamentally incompatible. They predict different things, incompatible things, in realms where gravity is intense and quantum fluctuations are strong.5 These realms include the big bang birth of our universe (Chapter 2), the cores of black holes like Gargantua (Chapters 26 and 28), and backward time travel (Chapter 30). In these realms a “fiery marriage”6 of the incompatible relativistic and quantum laws gives rise to new laws of quantum gravity (Figure 3.2).

  We do not yet know the laws of quantum gravity, but we have some compelling insights, including superstring theory (Chapter 21), thanks to enormous effort by the world’s greatest twenty-first-century physicists. Despite those insights, quantum gravity remains terra almost incognita (an almost unknown land). This leaves much elbow room for exciting science fiction, elbow room that Christopher Nolan exploits with great finesse in Interstellar; see Chapters 28–31.

  Truth, Educated Guesses, and Speculations

  The science of Interstellar lies in all four domains: Newtonian, relativistic, quantum, and quantum gravity. Correspondingly, some of the science is known to be true, some is an educated guess, and some is speculation.

  To be true, the science must be based on well-established physical laws (Newtonian, relativistic, or quantum), and it must have enough basis in observation that we are confident of how to apply the well-established laws.

  In precisely this sense, neutron stars and their magnetic fields, as described in Chapter 2, are true. Why? First, neutron stars are firmly predicted to exist by the quantum and relativistic laws. Second, astronomers have studied in enormous detail the pulsar radiation from neutron stars (pulses of light, X-rays, and radio waves described in Chapter 2). These pulsar observations are beautifully and accurately explained by the quantum and relativistic laws, if the pulsar is a spinning neutron star; and no other explanation has ever been found. Third, neutron stars are firmly predicted to form in astronomical explosions called supernovae, and pulsars are seen at the centers of big, expanding gas clouds, the remnants of old supernovae. Thus, we astrophysicists have no doubt; neutron stars really do exist and they really do produce the observed pulsar radiation.

  Another example of a truth is the black hole Gargantua and the bending of light rays by which it distorts images of stars (Figure 3.3). Physicists call this distortion “gravitational lensing” because it is similar to the distortion of a picture by a curved lens or mirror, as in an amusement park’s fun house, for example.

  Fig. 3.3. The stars in Gargantua’s galaxy, as seen around Gargantua’s shadow. Gargantua bends the light rays coming from each star, thereby distorting enormously the appearance of its galaxy: “gravitationally lensing” the galaxy. [From a simulation for this book by the Double Negative visual-effects team.]

  Einstein’s relativistic laws predict, unequivocally, all the properties of black holes from their surfaces outward, including their gravitational lensing.7 Astronomers have firm observational evidence that black holes exist in our universe, including gigantic black holes like Gargantua. Astronomers have seen gravitational lensing by other objects (for example, Figure 24.3), though not yet by black holes, and the observed lensing is in precise accord with the predictions of Einstein’s relativistic laws. This is enough for me. Gargantua’s gravitational lensing, as simulated by Paul Franklin’s Double Negative team using relativity equations I gave to them, is true. This is what it really would look like.

  By contrast, the blight that endangers human life on Earth in Interstellar (Figure 3.4 and Chapter 11) is an educated guess in one sense, and a speculation in another. Let me explain.

  Throughout recorded history, the crops that humans grow have been plagued by occasional blights (rapidly spreading diseases caused by microbes). The biology that underlies these blights is based on chemistry, which in turn is based on the quantum laws. Scientists do not yet know how to deduce, from the quantum laws, all of the relevant chemistry (but they can deduce much of it); and they do not yet know how to deduce from chemistry all of the relevant biology. Nevertheless, from observations and experiments, biologists have learned much about blights. The blights encountered by humans thus far have not jumped from infecting one type of plant to another with such speed as to endanger human life. But nothing we know guarantees this can’t happen. That such a blight is possible is an educated guess. That it might someday occur is a speculation that most biologists regard as very unlikely.

  Fig. 3.4. Burning blighted corn. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]

  The gravitational anomalies that occur in Interstellar (Chapters 24 and 25), for example, the coin Cooper tosses that suddenly plunges to the floor, are speculations. So i
s harnessing the anomalies to lift colonies off Earth (Chapter 31).

  Although experimental physicists when measuring gravity have searched hard for anomalies—behaviors that cannot be explained by the Newtonian or relativistic laws—no convincing gravitational anomalies have ever been seen on Earth.

  However, it seems likely from the quest to understand quantum gravity that our universe is a membrane (physicists call it a “brane”) residing in a higher-dimensional “hyperspace” to which physicists give the name “bulk”; see Figure 3.5 and Chapters 4 and 21. When physicists carry Einstein’s relativistic laws into this bulk, as Professor Brand does on the blackboard in his office (Figure 3.6), they discover the possibility of gravitational anomalies—anomalies triggered by physical fields that reside in the bulk.

  We are far from sure that the bulk really exists. And it is only an educated guess that, if the bulk does exist, Einstein’s laws reign there. And we have no idea whether the bulk, if it exists, contains fields that can generate gravitational anomalies, and if so, whether those anomalies can be harnessed. The anomalies and their harnessing are a rather extreme speculation. But they are a speculation based on science that I and some of my physicist friends are happy to entertain—at least late at night over beer. So they fall within the guidelines I advocated for Interstellar: “Speculations . . . will spring from real science, from ideas that at least some ‘respectable’ scientists regard as possible” (Chapter 1).