The Science of Interstellar

by Thorne, Kip

  16

  Discovering the Wormhole: Gravitational Waves

  How might humans have discovered Interstellar’s wormhole? As a physicist, I have a favorite way. I describe it here in an extrapolation of Interstellar’s story—an extrapolation that, of course, is my own and not Christopher Nolan’s.

  LIGO Detects a Burst of Gravitational Waves

  I imagine that decades before the movie begins, when Professor Brand was in his twenties, he was deputy director of a project called LIGO: The Laser Interferometer Gravitational Wave Observatory (Figure 16.1). LIGO was searching for ripples in the shape of space arriving at Earth from the distant universe. These ripples, called gravitational waves, are produced when black holes collide with each other, when a black hole tears a neutron star apart, when the universe was born, and in many other ways.

  One day in 2019, LIGO was hit by a burst of gravitational waves far stronger than any ever before seen (Figure 16.2). The waves oscillated with an amplitude that grew and fell several times, and then cut off suddenly. The entire burst lasted for only a few seconds.

  Fig. 16.1. Top: Aerial photograph of the LIGO gravitational wave detector at Hanford, Washington. Bottom: The LIGO control room where the detector is controlled and its signals are monitored.

  Fig. 16.2. The last 120 milliseconds (ms) of the gravitational waveform discovered by LIGO. [Drawing by Kip based on simulations by Yanbei Chen and by Foucart et al. (2011).]

  By comparing the waves’ shape (their “waveform”; Figure 16.2) with simulations performed on supercomputers, Professor Brand and his team deduced their source.

  Neutron Star Orbiting a Black Hole

  A neutron star, orbiting around a black hole, had emitted the waves. The star weighed 1.5 times as much as the Sun, the hole weighed 4.5 times the Sun, and the hole was spinning rapidly. The spin dragged space into motion, and the space whirl grabbed the star’s orbit, forcing it to precess slowly, like a tilted top. The precession modulated the waves, causing them to rise and fall in amplitude (Figure 16.2).

  The waves traveled out through the universe, carrying away energy (Figure 16.3). With its energy gradually decreasing, the star gradually spiraled inward toward the black hole. When the distance between the star and the hole had shrunk to 30 kilometers, the hole’s tidal gravity began tearing the star apart. Ninety-seven percent of the stellar debris was swallowed by the black hole, and 3 percent was thrown outward, forming a tail of hot gas that the hole then sucked back inward to form an accretion disk.

  Figure 16.4 shows a computer simulation of the last few milliseconds of the star’s life. At ten milliseconds before the end, the black hole is spinning around the red-arrowed axis, and the star is orbiting around the picture’s vertical axis. At four milliseconds the hole’s tendex lines are stretching the star apart. At two milliseconds, the hole’s whirling space has thrown the stellar debris up into the hole’s equatorial plane. At zero milliseconds, the debris is beginning to form an accretion disk.

  Fig. 16.3. Gravitational waves flowing out from the orbiting star and hole, as seen from the bulk. [Drawing by LIGO Laboratory artist based on my hand sketch.]

  Fig. 16.4. Computer simulation of the last few milliseconds of the neutron star’s life. [From a simulation by Francois Foucart, and colleagues. See http://www.black-holes.org/.]

  Discovering the Wormhole

  Looking back through LIGO’s data for the preceding two years, Professor Brand and his team discovered very weak waves emitted by the neutron star. The star had a tiny mountain, a centimeter high and a few kilometers wide (such mountains are thought likely). As the mountain was carried around and around by the star’s rotation, it produced waves that oscillated weakly but steadily, day after day after day.

  By analyzing these steady waves with care, Professor Brand learned the direction to their source. The direction was unbelievable! The waves were coming from something in orbit around Saturn. As the Earth and Saturn moved in their orbits, the source was always near Saturn!

  A neutron star orbiting Saturn? Impossible! A black hole accompanying the neutron star, with both orbiting Saturn? Even more impossible! Saturn would long ago have been destroyed, and the star’s and hole’s gravity would long ago have disrupted the orbits of all the Sun’s planets, including Earth. With disrupted orbit, the Earth would have been carried close to the Sun and then far away. We would have been fried, frozen, and killed.

  But there the waves were. Unequivocally emerging from near Saturn.

  Professor Brand could find only one explanation: The waves must emerge from a wormhole that orbits Saturn. And their source, the black hole and neutron star, must be on the other end of the wormhole (Figure 16.5). The waves traveled outward from the star and hole. Small portions of the waves were captured by the wormhole, traveled through it, and then spread outward through the solar system with a small portion reaching Earth and passing through the LIGO gravitational wave detector.

  Fig. 16.5. Gravitational waves travel through the wormhole to Earth.

  Origin of This Story

  A brief variant of this story was in the original 2006 treatment for Interstellar that Lynda Obst and I wrote. However, gravitational waves did not play a significant role in the rest of our treatment, nor in the subsequent screenplay that Jonathan Nolan wrote and Chris rewrote. And even without gravitational waves, the amount of serious science in the movie was enormous. So when Chris sought ways to simplify Interstellar’s rich panoply of science, gravitational waves were a natural candidate for the ax. He jettisoned them.

  For me, personally, Chris’s decision was painful. I cofounded the LIGO Project in 1983 (together with Rainer Weiss at MIT and Ronald Drever at Caltech). I formulated LIGO’s scientific vision, and I spent two decades working hard to help make it a reality. And LIGO today is nearing maturity, with the first detection of gravitational waves expected in this decade.

  But Chris’s reasons to jettison gravitational waves were compelling, so I didn’t utter even a whisper of protest.

  Gravitational Waves and Their Detectors

  I indulge myself and tell you a bit more about gravitational waves before moving back to Interstellar.

  Figure 16.6 is an artist’s conception of some tendex lines emerging from two black holes that orbit each other counterclockwise, and collide. Recall that tendex lines produce tidal gravity (Chapter 4). The lines emerging from the holes’ ends stretch everything they encounter, including the artist’s friend, whom she has placed there. The lines emerging from the collision region squeeze everything they encounter. As the holes orbit around each other, they drag their tendex lines around, splaying outward and backward, like water from a whirling sprinkler.

  Fig. 16.6. Tendex lines from two black holes that collide while orbiting each other counterclockwise. [Painting by Lia Halloran.]

  The holes merge to form a single, larger black hole that is deformed and spinning counterclockwise, and that drags its tendex lines around and around. The tendex lines travel outward, like water from the sprinkler, creating the intricate pattern that I show in Figure 16.7. The red lines stretch. The blue lines squeeze.

  A person at rest far from the hole experiences an oscillating stretch then squeeze then stretch as the tendex lines travel outward through her. The tendex lines have become a gravitational wave. Wherever the lines in the plane of the picture are strongly blue (strongly squeezing), there are strongly red lines coming out of the picture, that stretch. And wherever the lines in the picture are strongly red (stretching), there are blue (squeezing) lines pointing in the third direction, out of the picture. As the waves flow outward, the hole’s deformation gradually grows weaker and the waves weaken.

  When these waves reach Earth, they have the form that I show in the upper part of Figure 16.8. They stretch along one direction and squeeze along the other. The stretch and
squeeze oscillate (from red right-left to blue right-left to red right-left, etc.) as the waves pass through the detector in the bottom part of Figure 16.8.

  The detector consists of four huge mirrors (40 kilograms, 34 centimeters in diameter) that hang from overhead supports at the ends of two perpendicular arms. The waves’ tendex lines stretch one arm while squeezing the other, and then squeeze the first while stretching the second, over and over and over again. The oscillating separation between mirrors is monitored with laser beams, by a technique called interferometry. Hence LIGO’s name: Laser Interferometer Gravitational Wave Observatory.

  Fig. 16.7. Tendex lines from a spinning, deformed black hole. [Drawing by Rob Owen.]

  Fig. 16.8. Gravitational waves impinging on a LIGO detector.

  LIGO is now an international collaboration of 900 scientists in seventeen nations, headquartered at Caltech. It is currently led by David Reitze (director), Albert Lazzarini (deputy director) and Gabriella Gonzalez (spokesperson for the collaboration). And in view of its huge potential payoffs for our understanding of the universe, it is funded primarily by US taxpayers, through the National Science Foundation.

  LIGO has gravitational wave detectors in Hanford, Washington, and Livingston, Louisiana, and is planning to place a third in India. Scientists in Italy, France, and the Netherlands have built a similar interferometer near Pisa, and Japanese physicists are building one in a tunnel under a mountain. These detectors will all operate together, forming a giant worldwide network to explore the universe using gravitational waves.

  Having trained many scientists who work on LIGO, in 2000 I turned my own research in other directions. But I watch eagerly as LIGO and its international partners near maturity and near their first detections of gravitational waves.

  The Warped Side of the Universe

  Interstellar is an adventure in which humans encounter black holes, wormholes, singularities, gravitational anomalies, and higher dimensions. All these phenomena are “made from” warped space and time, or are tied intimately to that warping. This is why I like to call them the “warped side of the universe.”

  We humans, as yet, have very little experimental or observational data from the universe’s warped side. That’s why gravitational waves are important: they are made from warped space, and so they are the ideal tool for probing the warped side.

  Suppose you had only seen the ocean on a very calm day. You would know nothing of the heaving seas and breaking ocean waves that come with a huge storm.

  That is similar to our knowledge, today, of warped space and time. We know little about how warped space and warped time behave in a “storm”—when the shape of space is oscillating wildly and the rate of flow of time is oscillating wildly. For me this is a fascinating frontier of knowledge. John Wheeler, the creative coiner we met in earlier chapters, dubbed this “geometrodynamics”: the wildly dynamical behavior of the geometry of space and time.

  In the early 1960s, when I was Wheeler’s student, he exhorted me and others to explore geometrodynamics in our research. We tried, and failed miserably. We didn’t know how to solve Einstein’s equations well enough to learn their predictions, and we had no way to observe geometrodynamics in the astronomical universe.

  I’ve devoted much of my career to changing this. I cofounded LIGO with the goal of observing geometrodynamics in the distant universe. In 2000, when I turned my LIGO roles over to others, I cofounded a research group at Caltech aimed at simulating geometrodynamics on supercomputers, by solving Einstein’s relativistic equations numerically. We call this project SXS: Simulating eXtreme Spacetimes. It is a collaboration with Saul Teukolsky’s research group at Cornell University, and others.

  Fig. 16.9. Simulation of two black holes at their moment of collision. Top: The holes’ orbits and shadows as seen in our universe. Middle: The holes’ warped space and time as seen from the bulk, with arrows showing the dragging of space into motion and colors the warping of time. Bottom: The emitted gravitational waveform. This simulation is for identical, nonspinning black holes. [From a movie by Harald Pfeifer of a simulation by the SXS team.]

  A wonderful venue for geometrodynamics is the collision of two black holes. When they collide, the holes set space and time into wild gyrations. Our SXS simulations have now reached maturity, and are beginning to reveal relativity’s predictions (Figure 16.9). LIGO and its partners will observe the gravitational waves from colliding black holes within the next few years, and test our simulations’ predictions. It’s a wonderful era for probing geometrodynamics!

  Gravitational Waves from the Big Bang

  In 1975 Leonid Grishchuk, a dear Russian friend of mine, made a startling prediction: A rich plethora of gravitational waves was produced in the big bang, he predicted, by a previously unknown mechanism: Quantum fluctuations of gravity coming off the big bang were amplified enormously, he told us, by the universe’s initial expansion; and when amplified, they became primordial gravitational waves. If discovered, these gravitational waves could bring us a glimpse of our universe’s birth.

  In subsequent years, as our understanding of the big bang matured, it became evident that the waves would be strongest at wavelengths nearly as large as the visible universe itself, billions of light-years’ wavelength, and would likely be too weak for detection at LIGO’s far shorter wavelengths, hundreds and thousands of kilometers.

  In the early 1990s several cosmologists realized that these billion-light-years-long gravitational waves should have placed a unique imprint on electromagnetic waves that fill the universe, the so-called cosmic microwave background or CMB. A holy grail quickly emerged: search for that CMB imprint, from it infer the properties of the primordial gravitational waves that produced the imprint, and thereby explore the birth of the universe.

  In March 2014, while I was writing this book, the CMB imprint was discovered by a team assembled by Jamie Bock (Figure 16.10),30 a cosmologist down the hall from me at Caltech.

  Fig. 16.10. The Bicep2 instrument, built by Jamie Bock’s team, that discovered the imprint of primordial gravitational waves. Bicep2, at the South Pole, is here shown at twilight, which occurs only twice a year at the South Pole. It is surrounded by a shield to protect it from radiation from the surrounding ice sheet. The upper right inset shows the measured imprint on the CMB: a polarization pattern. The CMB’s electric field points along the short dashed directions.

  It was a fantastic discovery, but with a cautionary note: the imprint that Jamie and his team found might possibly be due to something else and not gravitational waves. As this book goes to press, intense efforts are underway to find out for sure.

  If the imprint is really due to gravitational waves from the big bang, then this is the type of cosmological discovery that comes along perhaps once every fifty years. It brings us a glimpse of the universe a trillionth of a trillionth of a trillionth of a second after the universe’s birth. It confirms theorists’ prediction that the expansion of the universe at that early moment was exceedingly fast, “inflationarily fast” in cosmologists’ jargon. It ushers in a whole new era for cosmology.

  Having indulged my passion for gravitational waves, having seen how they could be used to discover Interstellar’s wormhole—and having explored the properties of wormholes, especially Interstellar’s—I now take you on a tour of the other side of the Interstellar wormhole. A tour of Miller’s planet, Mann’s planet, and the Endurance, which carries Cooper there.

  * * *

  30 The formal leaders of the discovery team were Jamie and his former postdoctoral students John Kovac (now at Harvard) and Chao-Lin Kuo (now at Stanford), along with Clem Pryke (now at the University of Minnesota).

  V

  EXPLORING GARGANTUA’S ENVIRONS

  17

  Miller’s Planet

  The first planet that Cooper and his crew visit is Miller’s. The most impres
sive things about this planet are the extreme slowing of time there, gigantic water waves, and huge tidal gravity. All three are related, and arise from the planet’s closeness to Gargantua.

  The Planet’s Orbit

  In my interpretation of Interstellar’s science, Miller’s planet is at the blue location in Figure 17.1, very close to Gargantua’s horizon. (See Chapters 6 and 7.)

  Fig. 17.1. The warped space around Gargantua as seen from the bulk, with one space dimension omitted. Also, the orbits of Miller’s planet and the Endurance, parked and waiting for the crew to return.

  Space there is warped like the surface of a cylinder. In the figure, the cylinder’s cross sections are circles whose circumferences don’t change as we move nearer to or farther from Gargantua. In reality, when we restore the missing dimension, the cross sections are spheroids, whose circumferences don’t change as we move nearer or farther.

  So why is this location different from any other on the cylinder? What makes this location special?

  The key to the answer is the warping of time, which does not show up in Figure 17.1. Time slows near Gargantua, and the slowing becomes more extreme as we get closer and closer to Gargantua’s event horizon. Therefore, according to Einstein’s law of time warps (Chapter 4), gravity becomes ultrastrong as we near the horizon. The red curve in Figure 17.2, which depicts the strength of the gravitational force, turns sharply upward. By contrast, the centrifugal force that the planet feels (the blue curve) has a more gradually changing slope. As a result, the two curves cross at two locations. There the planet can travel around Gargantua with the outward centrifugal force balancing the inward gravitational force.