The Science of Interstellar
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Why am I so pessimistic about natural wormholes?
We see no objects in our universe that could become wormholes as they age. By contrast, astronomers see huge numbers of massive stars that will collapse to form black holes when they have exhausted their nuclear fuel.
On the other hand, there is reason to hope that wormholes do exist naturally on submicroscopic scales in the form of “quantum foam” (Figure 14.7). This foam is a hypothesized network of wormholes that is continually fluctuating in and out of existence in a manner governed by the ill-understood laws of quantum gravity (Chapter 26). The foam is probabilistic in the sense that, at any moment, there is a certain probability the foam has one form and also a probability that it has another form, and these probabilities are continually changing. And the foam is truly tiny: the typical length of a wormhole would be the so-called Planck length, 0.000000000000000000000000000000001 centimeters; a hundredth of a billionth of a billionth the size of the nucleus of an atom. That’s small!!
Back in the 1950s John Wheeler gave persuasive arguments for quantum foam, but there is now evidence that the laws of quantum gravity might suppress the foam and might even prevent it from arising.
If quantum foam does exist, I hope there is a natural process by which some of its wormholes can spontaneously grow to human size or bigger, and even did so during the extremely rapid “inflationary” expansion of the universe, when the universe was very, very young. However, we physicists have no hint of any evidence at all that such natural enlargement can or did occur.
Fig. 14.7. Quantum foam. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]
The other tiny hope for natural wormholes is the big bang creation of the universe. It is conceivable, but very unlikely, that traversable wormholes could have formed in the big bang itself. Conceivable for the simple reason that we don’t understand the big bang well at all. Unlikely because nothing we do know about the big bang gives any hint that traversable wormholes might form there.
Can Wormholes Be Created by an Ultra-Advanced Civilization?
An ultra-advanced civilization is my only serious hope for making traversable wormholes. But it would face huge obstacles, so I’m pessimistic.
One way to make a wormhole, where previously there were none, is to extract it from the quantum foam (if the foam exists), enlarge it to human size or larger, and thread it with exotic matter to hold it open. This seems like a pretty tall order, even for an ultra-advanced civilization, but perhaps only because we don’t understand the quantum gravity laws that control the foam, the extraction, and the earliest stages of enlargement (Chapter 26). Of course, we don’t understand exotic matter very well either.
At first sight, making a wormhole seems easy (Figure 14.8). Just push a piece of our brane (our universe) downward in the bulk to create a thimble, fold our brane around in the bulk, tear a hole in our brane just below the thimble, tear a hole in the thimble itself, and sew the tears together. Just!
Fig. 14.8. Creating a wormhole. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]
In Interstellar, Romilly demonstrates the same thing with a sheet of paper and a pencil (Figure 14.9). As easy as this may look from the outside, playing with pencils and paper, it is horrendously daunting when the sheet is our brane and these manipulations must be carried out from within the brane, by a civilization that lives in our brane. In fact, I have no idea how to execute any of these maneuvers from inside our brane except the first, creating a thimble in our brane (which requires only a very dense mass, such as a neutron star). Moreover, if it is possible at all to tear holes in our brane, it can only be done with the help of the laws of quantum gravity. Einstein’s relativistic laws forbid tearing our brane, so the only hope is to make the tear where his laws fail, in a realm of quantum gravity. We then are back to the domain of terra almost incognita (Figure 3.2).
Fig. 14.9. Romilly explaining wormholes. Left: He bends a sheet of paper. Right: He punches a pencil (the wormhole) through the paper, joining its two edges. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
The Bottom Line
I doubt the laws of physics permit traversable wormholes, but this may be pure prejudice. I could be wrong. If they can exist, I doubt very much that they can form naturally in the astrophysical universe. My only real hope for forming them is artificially, in the hands of an ultra-advanced civilization. But we are extremely ignorant of how such a civilization could do it. And it appears more than daunting, at least from inside our brane (our universe), even for the most advanced of civilizations.
In Interstellar, however, the wormhole is thought to have been made, held open, and placed near Saturn by a civilization that lives in the bulk, a civilization whose beings have four space dimensions, like the bulk.
This is terra extremely incognita. Nevertheless, I discuss bulk beings in Chapter 22. In the meantime let’s talk about the wormhole in Interstellar.
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27 Energy is weird in relativistic physics; the energy one measures depends on how fast one moves and in what direction.
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Visualizing Interstellar’s Wormhole
The wormhole in Interstellar is thought to have been constructed by an ultra-advanced civilization, most likely one that lives in the bulk. In this spirit, when laying foundations for visualizing Interstellar’s wormhole, Oliver James28 and I pretended we were ultra-advanced engineers. We assumed that wormholes are allowed by the laws of physics. We assumed the wormhole’s builders had all the exotic matter they needed to hold the wormhole open. We assumed the builders could warp space and time in whatever way we wished them to, inside and around the wormhole. These are pretty extreme assumptions, so I labeled this chapter for speculation.
The Wormhole’s Gravity and Time Warping
Christopher Nolan wanted the wormhole to have a mild gravitational pull. Strong enough to hold the Endurance in orbit around itself, but weak enough that a modest rocket blast would slow the Endurance, letting it drop gently into the wormhole. This meant a gravitational pull much less than the Earth’s.
Einstein’s law of time warps tells us that the slowing of time inside the wormhole is proportional to the strength of the wormhole’s gravitational pull. With that pull weaker than the Earth’s pull, the slowing of time must be smaller than on Earth, which is only a part in a billion (that is, one second of slowing during a billion seconds of time, thirty years). Such slowing is so tiny that Oliver and I paid no attention to it at all when designing the wormhole.
“Handles” for Adjusting the Wormhole’s Shape
The ultimate decision about the wormhole’s shape was in the hands of Christopher Nolan (the director) and Paul Franklin (the visual-effects supervisor). My task was to give Oliver and his colleagues at Double Negative “handles” (or in technical language, “parameters”) that they could use to adjust the shape. They then simulated the wormhole’s appearance for various adjustments of the handles and showed the simulations to Chris and Paul, who chose the one that was most compelling.
I gave the wormhole’s shape three handles—three ways to adjust the shape (Figure 15.1).
Fig. 15.1. A wormhole viewed from the bulk and my three handles for adjusting its shape. (The inset on the left is the same wormhole, viewed from farther away in the bulk so we see its outer parts.)
The first handle is the wormhole’s radius as measured by an ultra-advanced engineer looking in from the bulk (analog of Gargantua’s radius). If we multiply that radius by 2π = 6.28318..., we get the wormhole’s circumference as measured by Cooper when he pilots the Endurance around or through it. Chris chose the radius before I began to work. He wanted the wormhole’s gravitational lensing of stars to be barely visible from Earth with the best large-tele
scope technology then available to NASA. That fixed the radius at about a kilometer.
The second handle is the wormhole’s length, as measured equally well by Cooper or by an engineer in the bulk.
The third handle determines how strongly the wormhole lenses the light from objects behind it. The details of the lensing are fixed by the shape of space near the wormhole’s mouths. I chose that shape similar to the shape of space outside the horizon of a nonspinning black hole. My chosen shape has just one adjustable handle: the width of the region that produces strong lensing. I call this the lensing width29 and depict it in Figure 15.1.
How the Handles Influence the Wormhole’s Appearance
Just as I had done for Gargantua (Chapter 8), I used Einstein’s relativistic laws to deduce equations for the paths of light rays around and through the wormhole, and I worked out a procedure for manipulating my equations to compute the wormhole’s gravitational lensing and thence what a camera sees when it orbits the wormhole or travels through it. After checking that my equations and procedure produced the kinds of images I expected, I sent them to Oliver and he wrote computer code capable of creating the quality IMAX images needed for the movie. Eugénie von Tunzelmann added background star fields and images of astronomical objects for the wormhole to lens, and then she, Oliver, and Paul began exploring the influence of my handles. Independently, I did my own explorations.
Eugénie kindly provided the pictures in Figures 15.2 and 15.4 for this book, in which we look at Saturn through the wormhole. (The resolutions of her pictures are far higher than my own crude computer code can produce.)
The Wormhole’s Length
We first explored the influence of the wormhole’s length, with modest lensing (small lensing width); see Figure 15.2.
When the wormhole is short (top picture), the camera sees one distorted image of Saturn through the wormhole, the primary image, filling the right half of the wormhole’s crystal-ball-like mouth. There is an extremely thin secondary, lenticular image on the left edge of the crystal ball. (The lenticular structure at the lower right is not Saturn; it is a distorted part of the external universe.)
Fig. 15.2. Left: The wormhole, with small lensing width (just 5 percent of the wormhole's radius), viewed from the bulk. Right: What the camera sees. Top to bottom: Increasing wormhole length: 0.01, 1, and 10 times the wormhole's radius. [From simulations by Eugénie von Tunzelmann’s team using Oliver James’ code based on my equations.]
As the wormhole is lengthened (middle picture), the primary image shrinks and moves inward, the secondary image also moves inward, and a very thin lenticular tertiary image emerges from the right edge of the crystal ball.
With further lengthening (bottom picture), the primary image shrinks further, all the images move inward, a fourth image emerges from the left edge of the crystal ball, a fifth from the right, and so forth.
These behaviors can be understood by drawing light rays on the wormhole as seen from the bulk (Figure 15.3). The primary image is carried by the black light ray (1), which travels on the shortest possible path from Saturn to the camera, and by a bundle of rays tightly surrounding it. The secondary image is carried by a bundle surrounding the red ray (2), which travels around the wormhole’s wall in the opposite direction to the black ray: counterclockwise. This red ray is the shortest possible counterclockwise ray from Saturn to the camera. The tertiary image is carried by a bundle surrounding the green ray (3), which is the shortest possible clockwise ray that makes more than one full trip around the wormhole. And the fourth image is carried by a bundle surrounding the brown ray (4): the shortest possible counterclockwise ray that makes more than one full trip around the wormhole.
Fig. 15.3. Light rays from Saturn, through the wormhole, to the camera.
Can you explain the fifth and sixth images? and explain why the images shrink when the wormhole is lengthened? and explain why the images appear to emerge from the edge of the wormhole’s crystal-ball mouth and move inward?
The Wormhole’s Lensing Width
Having understood how the wormhole’s length affects what the camera sees, we then fixed the length to be fairly short, the same as the wormhole’s radius, and varied the gravitational lensing. We increased the wormhole’s lensing width from near zero to about half the wormhole’s diameter and computed what that did to the images the camera sees. Figure 15.4 shows the two extremes.
With very small lensing width, the wormhole shape (upper left) has a sharp transition from the external universe (horizontal sheets) to the wormhole throat (vertical cylinder). As seen by the camera (upper right), the wormhole distorts the star field and a dark cloud in the upper left only slightly, near the wormhole’s edge. Otherwise it simply masks the star field out, as would any opaque body with weak gravity, for example a planet or a spacecraft.
In the lower half of Figure 15.4, the lensing width is about half the wormhole’s radius, so there is a slow transition from the throat (vertical cylinder) to the external universe (asymptotically horizontal sheet).
With this large lensing width, the wormhole strongly distorts the star field and dark cloud (lower right in Figure 15.3) in nearly the same way as does a nonspinning black hole (Figures 8.3 and 8.4), producing multiple images. And the lensing also enlarges the secondary and tertiary images of Saturn. The wormhole looks bigger in the lower half of Figure 15.3 than in the upper half. It subtends a larger angle as seen by the camera. This is not because the camera is closer to the mouth; it is not closer. The camera is the same distance in both pictures. The enlargement is entirely due to the gravitational lensing.
Fig. 15.4. Wormhole’s gravitational lensing of a star field and Saturn: influence of the lensing width which is 0.014 and 0.43 times the wormhole radius in the top and bottom images. [From simulations by Eugénie von Tunzelmann’s team using Oliver James’ code based on my equations.]
Interstellar’s Wormhole
When Chris saw the various possibilities, with varying wormhole length and lensing width, his choice was unequivocal. For medium and large length the multiple images seen through the wormhole would be confusing to a mass audience, so he made Interstellar’s wormhole very short: 1 percent of the wormhole radius. And he gave Interstellar’s wormhole a modest lensing width, about 5 percent of the wormhole radius, so the lensing of stars around it would be noticeable and intriguing, but much smaller than Gargantua’s lensing.
The resulting wormhole is the one at the top of Figure 15.2. And in Interstellar, after the Double Negative team had created for its far side a galaxy with beautiful nebulae, dust lanes, and star fields, it is marvelous to behold (Figure 15.5). To me it is one of the movie’s grandest sights.
Fig. 15.5. The wormhole as seen in a trailer for Interstellar. The Endurance is in front of the wormhole, near the center. Around the wormhole in pink I have drawn the Einstein ring, like that in Figure 8.4 for a nonspinning black hole. Primary and secondary images of gravitationally lensed stars move in the same way here as there. Looking at the trailer, can you identify some and trace their motion? [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
The Trip Through the Wormhole
On April 10, 2014, I got an urgent phone call. Chris was having trouble with visualizing the Endurance’s trip through the wormhole and he wanted advice. I drove over to his Syncopy compound where postproduction editing was underway, and Chris showed me the problem.
Using my equations, Paul’s team had produced visualizations for wormhole trips with various wormhole lengths and lensing widths. For the short, modest-lensing wormhole depicted in the movie, the trip was quick and uninteresting. For a long wormhole, it looked like traveling through a long tunnel with walls whizzing past, too much like things we’ve seen in movies before. Chris showed me many variants with many bells and whistles, and I had to agree that none had the compelling freshness that he wanted. After sleepin
g on it, I still had no magic-bullet solution.
The next day Chris flew to London and closeted himself with Paul’s Double Negative team, searching for a solution. In the end, they were forced to abandon my wormhole equations and, in Paul’s words, “go for a much more abstract interpretation of the wormhole’s interior,” an interpretation informed by simulations with my equations, but altered significantly to add artistic freshness.
When I experienced the wormhole trip in an early screening of Interstellar, I was pleased. Though not fully accurate, it captures the spirit and much of the feel of a real wormhole trip, and it’s fresh and compelling.
What did you think?
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28 Recall that Oliver James, chief scientist at Double Negative, wrote the computer code that underlies Interstellar’s visualizations of wormholes and black holes; see Chapters 1 and 8.
29 Most of the lensing occurs in the region where the wormhole’s shape in the bulk is strongly curved. This is the region where its outward slope is steeper than 45 degrees, so I define the lensing width to be the radial distance, in the bulk, from the wormhole throat to the location with 45-degree outward slope (Figure 15.1).