Andrew’s film clips differ from what we see in Interstellar in several ways: First, for pedagogical purposes Andrew sometimes paints a grid of lines on the black hole’s horizon (there is no such grid for real black holes and none in Interstellar), and when he does so, he also replaces the star that imploded to form the black hole by a “past horizon.”[59] Second, in his “Journey into a Realistic Black Hole,” http://jila.colorado.edu/~ajsh/insidebh/realistic.html, Andrew endows the hole with a jet and an accretion disk. Gas from the disk falls into and through the horizon, and that infalling gas dominates what the camera sees at and beneath the horizon. In Interstellar, by contrast, there is no jet, and the accretion disk is so anemic that it is not currently sending any of its gas into and through the horizon, so the hole’s interior looks rather dark. However, in Interstellar Cooper encounters a dim fog of light and white flakes from stuff that fell in before him. These are not the result of simulations, but instead were put in by hand by the Double Negative artists.
When Christopher Nolan told me he was going to use a tesseract in Interstellar, I was delighted. At age thirteen I read about tesseracts in Chapter 4 of George Gamow’s marvelous book One, Two, Three, …Infinity (Gamow 1947), and that had a major role in making me want to become a theoretical physicist. You can find a detailed discussion of tesseracts in The Visual Guide to Extra Dimensions (McMullen 2008). Christopher Nolan’s complexified tesseract is unique; there is not yet any public discussion of it anywhere, except in this book and others connected to the movie Interstellar.
In Madeleine L’Engle’s classic science fantasy novel for children, A Wrinkle in Time (L’Engle 1962), children travel via a tesseract—they “tesser”—to find their father. My own interpretation of this is a journey through the bulk, riding in the face of a tesseract, like my interpretation of Cooper’s trip from Gargantua’s core to Murph’s bedroom, Figure 29.4.
For physicists’ current understanding of backward time travel in four spacetime dimensions without a bulk, see the last chapter of Black Holes & Time Warps (Thorne 1994), the chapters by Hawking, Novikov, and me in The Future of Spacetime (Hawking et al. 2002), and Time Travel and Warp Drives (Everett and Roman 2012). These are all by physicists who have contributed in major ways to the theory of time travel. For a historical account of modern research on time travel, see The New Time Travelers: A Journey to the Frontiers of Physics (Toomey 2007). For a comprehensive discussion of time travel in physics, in metaphysics, and in science fiction, see Time Machines: Time Travel in Physics, Metaphysics and Science Fiction (Nahin 1999). From Eternity to Here: The Quest for The Ultimate Theory of Time (Carroll 2011) is a wonderful discussion of almost everything physicists know, or speculate, about the nature of time.
I don’t know any good books or articles, for general readers, about time travel when our universe is a brane that lives in a higher dimensional bulk; but as I discuss in Chapter 30, Einstein’s laws extended to higher dimensions give basically the same predictions as without a bulk.
For some technical details of Cooper’s sending messages backward in time to Murph, see the appendix Some Technical Notes.
For Murph’s method (reducing G) for lifting the colonies off Earth, in my interpretation of Interstellar, see my remarks about Chapter 25, above.
In the early 1960s, when I was a PhD student at Princeton University, one of my physics professors, Gerard K. O’Neill, was embarking on an ambitious feasibility study for colonies in space, colonies somewhat like the one we see at the end of Interstellar. His study, augmented by a NASA study that he led, resulted in a remarkable book, The High Frontier: Human Colonies in Space (O’Neill 1978), which I highly recommend. But do pay attention to the book’s introduction by Freeman Dyson, which discusses why O’Neill’s dream of space colonies in his lifetime was shattered, but envisions them in the more distant future.
SOME TECHNICAL NOTES
The laws of physics that govern our universe are expressed in the language of mathematics. For readers comfortable with math, I write down a few formulas that come from the physical laws and show how I used them to deduce some things in this book. Two numbers that appear frequently in my formulas are the speed of light, c = 3.00 × 108 meters/second, and Newton’s gravitational constant, G = 6.67 × 10–11 meters3/kilogram/second2. I use scientific notation so 108 means 1 with eight zeros after it, 100,000,000 or a hundred million, and 10–11 means 0.[ten zeros]1, that is, 0.00000000001. I don’t aspire to accuracy any higher than 1 percent, so I show only two or three digits in my numbers, and when a number is very poorly known, only one digit.
The simplest, quantitative form of Einstein’s law of time warps is this: Place two identical clocks near each other, and at rest with respect to each other, separated from each other along the direction of the gravitational pull that they feel. Denote by R the fractional difference in their ticking rates, by D the distance between them, and by g the acceleration of gravity that they feel (which points from the one that ages the fastest to the one that ages the slowest). Then Einstein’s law says that g = Rc2/D. For the Pound-Rebca experiment in the Harvard tower, R was 210 picoseconds in one day, which is 2.43 × 10–15, and the tower height D was 73 feet (22.3 meters). Inserting these into Einstein’s law, we deduce g = 9.8 meters/second2, which indeed is the gravitational acceleration on Earth.
For a black hole such as Gargantua that spins extremely fast, the horizon’s circumference C in the hole’s equatorial plane is given by the formula C = 2πGM/c2 = 9.3 (M/Msun) kilometers. Here M is the hole’s mass, and Msun = 1.99 × 1030 kilograms is the Sun’s mass. For a very slowly spinning hole, the circumference is twice this size. The horizon’s radius is defined to be this circumference divided by 2π: R = GM/c2 = 1.48 × 108 kilometers for Gargantua, which is very nearly the same as the radius of the Earth’s orbit around the Sun.
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Stated more precisely and more technically, he has his camera fall into the maximally extended Schwarzschild solution or Reissner-Nordstrom solution of Einstein’s equations instead of into a black hole.