by Thorne, Kip
* * *
32 The table’s numerical values for the resonant frequencies are not in familiar units. To convert to familiar units, we must multiply by the cube of the speed of light and divide by 2πGM, where π = 3.14159..., G is Newton’s gravitational constant, and M is Gargantua’s mass. This conversion factor is approximately one vibration per hour, so the first predicted frequency in the table is about 0.67 vibrations per hour. The conversion factor for the die-out rate is the same.
19
Mann’s Planet
After discovering that Miller’s planet is hopeless for human colonization, Cooper and his crew travel to Mann’s planet.
The Planet’s Orbit and Lack of Sun
I have deduced a plausible orbit for Mann’s planet from two things in Interstellar:
First, Doyle says the trip to Mann’s planet will require months. From this I infer that, when the Endurance arrives at Mann’s planet, it must be far from Gargantua’s vicinity where the trip began. Second, almost immediately after the Endurance’s explosive accident in orbit around Mann’s planet, the crew find the Endurance being pulled toward Gargantua’s horizon. From this I infer that, when they leave Mann’s planet, the planet must be near Gargantua.
To achieve both requirements, the orbit of Mann’s planet must be highly elongated. And to avoid the planet’s being engulfed by Gargantua’s accretion disk as it nears Gargantua, the orbit, so far as possible, must be far above or below Gargantua’s equatorial plane, where the disk resides.
Fig. 19.1. A possible orbit for Mann’s planet, computed using a highly user-friendly web application written by David Saroff; see http://demonstrations.wolfram.com/3DKerrBlackHoleOrbits.
This dictates an orbit something like that shown in Figure 19.1, though extending much farther from Gargantua, to 600 Gargantua radii or more.33 Like the orbit of Halley’s comet in our solar system (Figure 7.5), the planet swings close around Gargantua then flies out to a large distance, then returns, swings around Gargantua, and flies out again. The whirl of space near Gargantua makes the planet fly around Gargantua once or twice on each swing by, and makes its orbit precess through a large angle from one outward excursion to the next, as shown in the figure.
Mann’s planet can’t be accompanied by a sun on its inward and outward journeys because, when near Gargantua, huge tidal forces would pry the planet and its sun apart, sending them onward in markedly different orbits. Therefore, like Miller’s planet, it must be heated and lit by Gargantua’s anemic accretion disk.
The Trip to Mann’s Planet
The Endurance’s trip to Mann’s planet begins near Gargantua and ends far from it. Such a trip—in my scientist’s interpretation of the movie—requires two gravitational slingshots (Chapter 7), one at the beginning of the trip and one at the end.
At the beginning, the challenges are twofold: In its parking orbit near Gargantua, the Endurance is moving at a third of light speed, c/3, in the wrong direction, a circumferential orbit around Gargantua; it must be deflected into radial motion, away from Gargantua. And the Endurance isn’t moving fast enough. Gargantua’s gravitational pull is so strong that, if the Endurance is deflected onto a radial trajectory but still has its starting speed of c/3, then Gargantua will pull it to a halt by the time it has traversed only a small fraction of the distance to Mann’s planet. To overcome Gargantua’s gravity and reach Mann’s planet moving with the same speed as the planet, roughly c/20, the first slingshot must accelerate the Endurance up to nearly half the speed of light. To achieve this, Cooper must find an intermediate-mass black hole (IMBH) at an appropriate location and moving with a suitable velocity.
Finding the necessary IMBH is not easy, and having found it, reaching it at the right point and moment in its orbit may not be easy. Most of the months’-long trip may be spent reaching the IMBH, and it might entail considerable waiting for the IMBH to arrive. Once the slingshot is completed, the trip to Mann’s planet, with speed about c/2 initially and gradual slowing to roughly c/20, will take roughly an additional forty days.
In the second slingshot, near Mann’s planet, the Endurance swings around a suitable IMBH and soars into a gentle rendezvous with the planet: a rendezvous that doesn’t require much rocket fuel.
Arrival at Mann’s Planet: Ice Clouds
In the movie, the Endurance parks in orbit around Mann’s planet, and then Cooper and his crew descend to the planet in a Ranger. The planet is covered with ice, as one might expect, since (in my interpretation) it spends most of its life far from the warmth of Gargantua’s accretion disk. As the Ranger nears the planet, we see it maneuver among what appear to be clouds, but then it scrapes along one (Figure 19.2) and we discover the cloud is actually made from some sort of ice.
Fig. 19.2. The Ranger scraping the edge of an “ice cloud” on Mann’s planet. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
Motivated by a conversation with Paul Franklin, I imagine that these clouds are largely frozen carbon dioxide, “dry ice,” and they are starting to be warmed as the planet is on its inward excursion toward the accretion disk, as in Figure 19.1. When warmed, dry ice sublimates—vaporizes—and so what appears to be clouds may be a mixture of dry ice and sublimating vapor; perhaps mostly vapor. At lower altitudes, where the Ranger lands, temperatures are higher and the ice on which they land is presumably all frozen water.
Dr. Mann’s Geological Data
In the movie, Dr. Mann has been searching for organic material on his planet and he claims to have found promising evidence. Promising but not definitive. He shows his data to Brand and Romilly.
The data consist of field notes that indicate where each rock sample was collected and the geological environment there, together with chemical analyses of the sample. Those chemical analyses are Dr. Mann’s evidence of organics.
Figure 19.3 shows a page from these data. The data were actually prepared for the movie by Erika Swanson, a talented geology PhD student at Caltech. Erika has done fieldwork and chemical analyses somewhat similar to Dr. Mann’s.
Fig. 19.3. Top: Romilly (played by David Oyelowo) and Brand (played by Anne Hathaway) discuss Dr. Mann’s geological data with him. Bottom: One page of data, prepared for the movie by Erika Swanson: the results of chemical analyses of rocks collected on the purported surface of the planet. Several rocks show promising evidence of organic material that could have arisen from living things. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
In the movie, it turns out that Dr. Mann has faked his data. That’s a bit ironic since, of course, Erika faked her data too. She has never made a field trip to Mann’s planet. Perhaps someday . . .
In this book I say nothing about the tragedy of Dr. Mann. It’s a human tragedy, involving little science. The tragedy’s climax is an explosion that severely damages the Endurance. The explosion, the damage, and the Endurance’s design: that’s the stuff of science and engineering, so let’s discuss them.
* * *
33 In the movie, when the Endurance is in orbit around Mann’s planet, we see Gargantua subtending about 0.9 degrees on the sky—nearly twice the size of the Moon as seen from Earth. From this I compute that Mann’s planet is about 600 Gargantua radii from the black hole. At this distance, the time required for the planet to travel inward to near Gargantua is at least forty days—a lot longer than the crew seem to spend on and near Mann’s planet, but reasonable for the outward trip to reach the planet; see Chapter 7.
20
The Endurance
Tidal Gravity and the Endurance’s Design
The Endurance has twelve modules linked in a ring, and a control module at the ring’s center (Figure 20.1). Two landers and Rangers dock onto the Endurance’s central module.
Fig. 20.1. The Endurance, with two Rangers and two landers docked onto its central, control module.
The Rangers are oriented out of the Endurance’s ring plane; the landers, parallel to it. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
In my scientist’s interpretation of the movie, the Endurance was designed to survive strong tidal gravitational forces. This was important for the Endurance’s trip through the wormhole. The Endurance ring’s diameter of 64 meters is nearly 1 percent of the wormhole’s circumference. Steel and other solid materials break or flow, when subjected to distortions bigger than about a few tenths of a percent, so the dangers were obvious. And little was known about what the Endurance would encounter on the Gargantua side of the wormhole, so it was designed to withstand tidal forces far stronger than the wormhole’s.
Now, a thin fiber can be bent around into complicated shapes without any portion of the fiber’s material being distorted by anything close to 1 percent. The key is the thinness of the fiber. You could imagine the Endurance’s strength relying on a huge number of thin fibers stretching around the ring, like the strands of a cable that hold up a suspension bridge and can bend as needed when a strong wind blows. But that would make the ring too flexible. The ring needs much resistance to being deformed, so it won’t deform so severely, when subjected to tidal forces, that the modules crash into each other.
The designers, in my interpretation, worked hard to make the Endurance resist deformation but be able to deform without breaking if it encounters tidal forces far stronger than anticipated.
Explosion in Orbit Above Mann’s Planet
This design philosophy really pays off when Dr. Mann unwittingly triggers a huge explosion that breaks the Endurance’s ring, destroys two of the ring modules, and damages two others (Figure 20.2).
Fig. 20.2. Left: The explosion on the Endurance, with the lander above and Mann’s planet below. (The ten radial light beams are lens flare due to scattering of light in the camera lens, not stuff from the explosion.) Right: The damaged Endurance after the explosion. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
The explosion sets the ring spinning so fast that its modules feel 70 gees (70 Earth gravities) of centrifugal force. Its broken ends swing apart from each other but don’t break, and the ring’s modules don’t crash into each other. This, in my scientist’s interpretation, is a great example of conservative design by clever engineers!
Incidentally, I’m impressed by the explosion in the movie. An explosion in space makes no sound, as there is no air to transmit the sound waves. The Endurance explosion has no sound. The flames in such an explosion must quench quickly, as the oxygen that feeds them is quickly disbursed into space. The flames in the movie quench quickly. Paul Franklin tells me that his team worked hard to achieve this, as the explosion was a real one, on a movie set, and not a computer-generated visual effect. Another example of Christopher Nolan’s commitment to science accuracy.
Our discussion of Gargantua’s environs has taken us from the physics of planets (tidal deformation, tsunamis, tidal bores, . . .), through Gargantua’s vibrations and the search for organic signs of life, to engineering issues (the Endurance’s robust design and its damaging explosion). As much as I enjoy these topics—and I’ve done research or textbook writing on most of them—they are not my greatest passion. My passion is extreme physics; physics at the edge of human knowledge and just beyond. That’s where I take us next.
VI
EXTREME PHYSICS
21
The Fourth and Fifth Dimensions
Time as the Fourth Dimension
In our universe, space has three dimensions: up-down, east-west, and north-south. But to schedule lunch with a friend, we must tell her not only where, but also when. In this sense, time is a fourth dimension.
However, time is a different kind of dimension than space. We have no trouble traveling westward as well as eastward; we make our choice and go. But having arrived at our luncheon, we cannot immediately, then and there, travel backward in time. No matter how hard we may try, we can only travel forward. The relativistic laws guarantee it. They enforce it.34
Nevertheless, time is a fourth dimension; it is the fourth dimension of our universe. The arena for our lives is four-dimensional spacetime, three space dimensions plus one time dimension.
When we physicists explore this spacetime arena by experiments and by mathematics, we discover that space and time are unified in several ways. At the simplest level, when we look out in space, we are automatically looking backward in time because of how long it takes light to reach us. We see a quasar a billion light-years away as it was a billion years ago, when the light that enters our telescope was launched on its journey to us.
At a much deeper level, if you move relative to me at high speed, then we disagree on what events are simultaneous. You may think that two explosions, one on the Sun and the other on Earth are simultaneous, while I think the Earth explosion was five minutes before the one on the Sun. In this sense, what you regard as purely spatial (the separation of the explosions) I see as a mixture of space and time.
This mixing of space and time may seem counterintuitive, but it is fundamental to the very fabric of our universe. Fortunately, we can pretty much ignore it in this book except for Chapter 30.
The Bulk: Is It Real?
Throughout this book, I visualize warped space by picturing our universe as a two-dimensional warped membrane, or brane, that resides in a bulk with three space dimensions—as in Figure 21.1, for example. Of course, in reality our brane has three space dimensions and the bulk has four, but I’m not very good at drawing that, so in my pictures I usually throw one dimension away.
Fig. 21.1. A small black hole spiraling into a large black hole, as viewed from the bulk with one space dimension removed. [Drawing by Don Davis based on a sketch by me.]
Does the bulk really and truly exist, or is it just a figment of our imaginations? Until the 1980s, most physicists, including me, thought it a figment.
How could it be a figment? Don’t we know for sure that our universe’s space is warped? Don’t the radio signals sent to the Viking spacecraft reveal its warpage to high precision (Chapter 4)? Yes. . . . And since our space is truly warped, doesn’t it have to be warped inside some higher-dimensional space, inside some bulk?
No. It is perfectly possible for our universe to be warped without there really existing a higher-dimensional bulk. We physicists can describe our universe’s warping, in mathematics, without the aid of a bulk. We can formulate Einstein’s relativistic laws, which govern the warping, without the aid of a bulk. In fact, that’s how we almost always do it, in our research. The bulk, for us, until the 1980s, was just a visual aid. An aid to give us intuition about what’s going on in our mathematics, and to help us communicate with each other and with nonphysicists. A visual aid. Not a real thing.
What would it mean for the bulk to be real? How can we test whether it’s real? The bulk is real if it can influence things we measure. And until the 1980s we saw no way it could influence our measurements.
Then in 1984 this changed. Radically. Michael Green at the University of London and John Schwarz at Caltech had a huge breakthrough in the quest to discover the laws of quantum gravity.35 But strangely, their breakthrough worked only if our universe is a brane embedded in a bulk that has one time dimension and nine space dimensions—a bulk with six more space dimensions than our brane. In the mathematical formalism that Green and Schwarz were pursuing, called “superstring theory,” the bulk’s extra dimensions influence our brane in major ways, in ways that can be measured in physics experiments when we have sufficiently advanced technology. In ways that may make it possible to reconcile the laws of quantum physics with Einstein’s relativistic laws.
Fig 21.2. Left: Michael Green (left) and John Schwarz hiking in Aspen, Colorado, in 1984, at the time of their breakthrough. Right: Michael Green (left) and John Schwarz (right) being awarde
d the three-million-dollar 2014 Fundamental Physics Prize for their breakthrough. In the middle are Yuri Milner (founder of the prize) and Mark Zuckerberg (Facebook cofounder).
Since the Green-Schwarz breakthrough, we physicists have taken superstring theory very seriously and have put great effort into exploring and extending it. And, consequently, we have taken very seriously the idea that the bulk truly exists and truly can influence our universe.
The Fifth Dimension
Although superstring theory says the bulk has six more dimensions than our universe, there is reason to suspect that, for practical purposes, the number of extra dimensions is really only one. (I explain this in Chapter 23.)
For this reason, and because six extra dimensions is a bit much for a science-fiction movie, Interstellar’s bulk has just one extra dimension, for a total of five dimensions in all. It shares three space dimensions with our brane: east-west, north-south, and up-down. It shares a fourth, time dimension, with our brane. And it has a fifth space dimension, out-back, which extends perpendicular to our brane, both above the brane and below, as depicted in Figure 21.3.
Fig. 21.3. Our universe as a brane with four spacetime dimensions, residing in a five-dimensional bulk. I have suppressed two dimensions from the diagram: time, and our universe’s up-down dimension.
