出版社: W. W. Norton & Company
原作名: The Science of Interstellar
出版年: 2014117
页数: 336
定价: USD 24.95
装帧: Paperback
ISBN: 9780393351378
内容简介 · · · · · ·
A journey through the otherworldly science behind Christopher Nolan’s highly anticipated film, Interstellar, from executive producer and theoretical physicist Kip Thorne.
Interstellar, from acclaimed filmmaker Christopher Nolan, takes us on a fantastic voyage far beyond our solar system. Yet in The Science of Interstellar, Kip Thorne, the physicist who assisted Nolan on the sci...
A journey through the otherworldly science behind Christopher Nolan’s highly anticipated film, Interstellar, from executive producer and theoretical physicist Kip Thorne.
Interstellar, from acclaimed filmmaker Christopher Nolan, takes us on a fantastic voyage far beyond our solar system. Yet in The Science of Interstellar, Kip Thorne, the physicist who assisted Nolan on the scientific aspects of Interstellar, shows us that the movie’s jawdropping events and stunning, neverbeforeattempted visuals are grounded in real science. Thorne shares his experiences working as the science adviser on the film and then moves on to the science itself. In chapters on wormholes, black holes, interstellar travel, and much more, Thorne’s scientific insights—many of them triggered during the actual scripting and shooting of Interstellar—describe the physical laws that govern our universe and the truly astounding phenomena that those laws make possible.
Interstellar and all related characters and elements are trademarks of and © Warner Bros. Entertainment Inc. (s14).
作者简介 · · · · · ·
Kip Thorne is the Feynman Professor of Theoretical Physics Emeritus at Caltech, an executive producer for Interstellar, and the author of books including the bestselling Black Holes and Time Warps. He lives in Pasadena, California.
目录 · · · · · ·
Foreword
Preface
1 A Scientist in Hollywood: The Genesis of Interstellar
I. FOUNDATIONS
2 Our Universe in Brief
· · · · · · (更多)
Foreword
Preface
1 A Scientist in Hollywood: The Genesis of Interstellar
I. FOUNDATIONS
2 Our Universe in Brief
3 The Laws That Control
4 Warped Time and Space, and Tidal Gravity
5 Black Holes
II. GARGANTUA
6 Gargantua’s Anatomy
7 Gravitational Slingshots
8 Imaging Gargantua
9 Disks and Jets
10 Accident Is the First Building Block of Evolution
III. DISASTER ON EARTH
11 Blight
12 Gasping for Oxygen
13 Interstellar Travel
IV. THE WORMHOLE
14 Wormholes
15 Visualizing Interstellar’s Wormhole
16 Discovering the Wormhole: Gravitational Waves
V. EXPLORING GARGANTUA’S ENVIRONS
17 Miller’s Planet
18 Gargantua’s Vibrations
19 Mann’s Planet
20 The Endurance
VI. EXTREME PHYSICS
21 The Fourth and Fifth Dimensions
22 Bulk Beings
23 Confining Gravity
24 Gravitational Anomalies
25 The Professor’s Equation
26 Singularities and Quantum Gravity
VII. CLIMAX
27 The Volcano’s Rim
28 Into Gargantua
29 The Tesseract
30 Messaging the Past
31 Lifting Colonies off Earth
Where Can You Learn More?
Some Technical Notes
Acknowledgments
Figure Credits
Bibliography
Index of People
Index of Subjects
· · · · · · (收起)
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The Science of Interstellar的书评 · · · · · · ( 全部 22 条 )
请温和地走进科学的良夜
Why we are fanatic space lover
Just another physical dimension
这篇书评可能有关键情节透露
A very difficult book. In hindsight, this wouldn’t have been all that surprising had I known that it was Kip Thorne, the Nobelwinning theoretical physicist that worked on the science front of this movie: Black holes, gravitational slingshots, disks and j... (展开)> 更多书评 22篇
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我来写笔记
Einstein’s Law of Time Warps Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical...
20200630 06:24
Einstein’s Law of Time Warps
Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical formula that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there.
The greater the slowing of time, the stronger gravity’s pull. On Earth, where time is slowed by only a few microseconds per day, gravity’s pull is modest. On the surface of a neutron star, where time is slowed by a few hours per day, gravity’s pull is enormous. At the surface of a black hole, time is slowed to a halt, whence gravity’s pull is so humungous that nothing can escape, not even light.
This slowing of time near a black hole plays a major role in Interstellar. Cooper despairs of ever seeing his daughter Murph again, when his travel near Gargantua causes him to age only a few hours while Murph, on Earth, is aging eight decades.
Human technology was too puny to test Einstein’s law until nearly half a century after he formulated it. The first good test came in 1959 when Bob Pound and Glen Rebca used a new technique called the Mössbauer effect to compare the rate of flow of time in the basement of a 73foot tower at Harvard University with time in the tower’s penthouse. Their experiment was exquisitely accurate: good enough to detect differences of 0.0000000000016 seconds (1.6 trillionths of a second) in one day. Remarkably, they found a difference 130 times larger than this accuracy and in excellent agreement with Einstein’s law: Time flows more slowly in the basement than in the penthouse by 210trillionths of a second each day.
The global positioning system (GPS), by which our smart phones can tell us where we are to 10 meters’ accuracy, relies on radio signals from a set of 27 satellites at a height of 20,000 kilometers (Figure 4.2). Typically only four to twelve satellites can be seen at once from any location on Earth. Each radio signal from a viewable satellite tells the smart phone where the satellite is located and the time the signal was transmitted. The smart phone measures the signal’s arrival time and compares it with its transmission time to learn how far the signal traveled—the distance between satellite and phone. Knowing the locations and distances to several satellites, the smart phone can triangulate to learn its own location.
This scheme would fail if the signal transmission times were the true times measured on the satellite. Time at a 20,000kilometer height flows more rapidly than on Earth by forty microseconds each day, and the satellites must correct for this. They measure time with their own clocks, then slow that time down to the rate of time flow on Earth before transmitting it to our phones.
Einstein was a genius. Perhaps the greatest scientist ever. This is one of many examples where his insights about the laws of physics could not be tested in his own day. It required a half century for technology to improve enough for a test with high precision, and another half century until the phenomena he described became part of everyday life. Among other examples are the laser, nuclear energy, and quantum cryptography.
The Warping of Space: The Bulk and Our Brane
Finally in November 1915, in a great Eureka moment, he formulated his “field equation of general relativity,” which encapsulated all his relativistic laws including space warps.
If space were flat, the roundtrip travel time would have changed gradually and steadily. It did not. When the radio waves passed near the Sun, their travel time was longer than expected, longer by hundreds of microseconds. The extra travel time is shown, as a function of the spacecraft’s location at the top of Figure 4.3; it went up and then back down. Now, one of Einstein’s relativistic laws says that radio waves and light travel at an absolutely constant, unchanging speed. Therefore, the distance from Earth to the spacecraft had to be longer than expected when passing near the Sun, longer by hundreds of microseconds times the speed of light: about 50 kilometers.
This greater length would be impossible if space were flat, like a sheet of paper. It is produced by the Sun’s space warp.
The shape that the team measured, for the Sun’s equatorial plane, is shown in Figure 4.4 with the magnitude of the warping exaggerated. The measured shape was precisely what Einstein’s relativistic laws predict—precise to within the experimental error, which was 0.001 of the actual warping, that is, a part in a thousand. Around a neutron star, the space warp is far greater. Around a black hole, it is enormously greater. Now, the Sun’s equatorial plane divides space into two identical halves, that above the plane and that below. Nonetheless, Figure 4.4 shows the equatorial plane as warped like the surface of a bowl. It bends downward inside and near the Sun, so that diameters of circles around the Sun, when multiplied by π (3.14159 . . . ), are larger than circumferences—larger, in the case of the Sun, by roughly 100 kilometers.
How can space “bend down”? Inside what does it bend? It bends inside a higherdimensional hyperspace, called “the bulk,” that is not part of our universe!
Let's make that more precise. In Figure 4.4 the Sun’s equatorial plane is a twodimensional surface that bends downward in a threedimensional bulk. This motivates the way we physicists think about our full universe. Our universe has three space dimensions (eastwest, northsouth, updown), and we think of it as a threedimensional membrane or brane for short that is warped in a higherdimensional bulk.
Now, it’s very hard for humans to visualize our threedimensional universe, our full brane, living and bending in a fourdimensional bulk. So throughout this book I draw pictures of our brane and bulk with one dimension removed, as I did in Figure 4.4.
Fig. 4.4. Paths of Viking radio signals through the Sun’s warped equatorial plane.
In Interstellar, the characters often refer to five dimensions. Three are the space dimensions of our own universe or brane (eastwest, northsouth, updown). The fourth is time, and the fifth is the bulk’s extra space dimension.
Figure 4.5 is an extreme example of space warps. It is a fanciful drawing by my artist friend Lia Halloran, depicting a hypothetical region of our universe that contains large numbers of wormholes (Chapter 14) and black holes (Chapter 5) extending outward from our brane into and through the bulk. The black holes terminate in sharp points called “singularities.” The wormholes connect one region of our brane to another. As usual, I suppress one of our brane’s three dimensions, so the brane looks like a twodimensional surface.
Fig. 4.5. Black holes and wormholes extending out of our brane into and through the bulk. One space dimension is removed from both our brane and the bulk.
Tidal Gravity
Einstein’s relativistic laws dictate that planets, stars, and unpowered spacecraft near a black hole move along the straightest paths permitted by the hole’s warped space and time.
In Einstein’s relativity theory there is a mathematical quantity called the Riemann tensor. It describes the details of the warping of space and time. We found, hidden in the mathematics of this Riemann tensor, lines of force that squeeze some planetary paths together and stretch others apart. “Tendex lines,” my student David Nichols dubbed them, from the Latin word tendere meaning “to stretch.”
Fig. 4.7. Tendex lines
The green paths begin, on their right ends, parallel to each other, and then the red tendex lines stretch them apart. I draw a woman lying on a red tendex line. It stretches her, too; she feels a stretching force between her head and her feet, exerted by the red tendex line.
The purple paths begin, at their top ends, running parallel to each other. They are then squeezed together by the blue tendex lines, and the woman whose body lies along a blue tendex line is also squeezed.
This stretching and squeezing is just a different way of thinking about the influence of the warping of space and time. From one viewpoint, the paths are stretched apart or squeezed together due to the planetary paths moving along the straightest routes possible in the warped space and time. From another viewpoint it is the tendex lines that do the stretching and squeezing. Therefore, the tendex lines must, in some very deep way, represent the warping of space and time. And indeed they do, as the mathematics of the Riemann tensor taught us.
Fig. 4.8. Newton’s explanation for the tides on the Earth’s oceans.
What the Earth does feel is the redarrowed lunar pulls in the left half of Figure 4.8, with their average subtracted away; that is, it feels a stretch toward and away from the Moon, and a squeeze on its lateral sides (right half of Figure 4.8).
These felt forces stretch the ocean away from the Earth’s surface on the faces toward and away from the Moon, producing high tides there. And the felt forces squeeze the oceans toward the Earth’s surface on the Earth’s lateral sides, producing low tides there. As the Earth turns on its axis, one full turn each twentyfour hours, we see two high tides and two low tides. This was Newton’s explanation of ocean tides, aside from a slight complication: The Sun’s tidal gravity also contributes to the tides. Its stretch and squeeze get added to the Moon’s stretch and squeeze.
Because of their role in ocean tides, these gravitational squeezing and stretching forces—the forces the Earth feels—are called tidal forces. To extremely high accuracy, these tidal forces, computed using Newton’s laws of gravity, are the same as we compute using Einstein’s relativistic laws. They must be the same, since the relativistic laws and the Newtonian laws always make the same predictions when gravity is weak and objects move at speeds much slower than light.
Fig. 4.9. Relativistic viewpoint on tides: they are produced by the Moon’s tendex lines.
In the relativistic description of the Moon’s tides (Figure 4.9), the tidal forces are produced by blue tendex lines that squeeze the Earth’s lateral sides and red tendex lines that stretch toward and away from the Moon. This is just like a black hole’s tendex lines. The Moon’s tendex lines are visual embodiments of the Moon’s warping of space and time. It is remarkable that a warping so tiny can produce forces big enough to cause the ocean tides!
We now have three points of view on tidal forces:
•Newton’s viewpoint (Figure 4.8): The Earth does not feel the Moon’s full gravitational pull, but rather the full pull (which varies over the Earth) minus the average pull.
•The tendex viewpoint (Figure 4.9): The Moon’s tendex lines stretch and squeeze the Earth’s oceans; also (Figure 4.7) a black hole’s tendex lines stretch and squeeze the paths of planets and stars around the black hole.
•The straightestroute viewpoint (Figure 4.6): The paths of stars and planets around a black hole are the straightest routes possible in the hole’s warped space and time.
Peering at the puzzle first from one viewpoint and then from another can often trigger new ideas.
回应 20200630 06:24

Einstein’s Law of Time Warps Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical...
20200630 06:24
Einstein’s Law of Time Warps
Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical formula that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there.
The greater the slowing of time, the stronger gravity’s pull. On Earth, where time is slowed by only a few microseconds per day, gravity’s pull is modest. On the surface of a neutron star, where time is slowed by a few hours per day, gravity’s pull is enormous. At the surface of a black hole, time is slowed to a halt, whence gravity’s pull is so humungous that nothing can escape, not even light.
This slowing of time near a black hole plays a major role in Interstellar. Cooper despairs of ever seeing his daughter Murph again, when his travel near Gargantua causes him to age only a few hours while Murph, on Earth, is aging eight decades.
Human technology was too puny to test Einstein’s law until nearly half a century after he formulated it. The first good test came in 1959 when Bob Pound and Glen Rebca used a new technique called the Mössbauer effect to compare the rate of flow of time in the basement of a 73foot tower at Harvard University with time in the tower’s penthouse. Their experiment was exquisitely accurate: good enough to detect differences of 0.0000000000016 seconds (1.6 trillionths of a second) in one day. Remarkably, they found a difference 130 times larger than this accuracy and in excellent agreement with Einstein’s law: Time flows more slowly in the basement than in the penthouse by 210trillionths of a second each day.
The global positioning system (GPS), by which our smart phones can tell us where we are to 10 meters’ accuracy, relies on radio signals from a set of 27 satellites at a height of 20,000 kilometers (Figure 4.2). Typically only four to twelve satellites can be seen at once from any location on Earth. Each radio signal from a viewable satellite tells the smart phone where the satellite is located and the time the signal was transmitted. The smart phone measures the signal’s arrival time and compares it with its transmission time to learn how far the signal traveled—the distance between satellite and phone. Knowing the locations and distances to several satellites, the smart phone can triangulate to learn its own location.
This scheme would fail if the signal transmission times were the true times measured on the satellite. Time at a 20,000kilometer height flows more rapidly than on Earth by forty microseconds each day, and the satellites must correct for this. They measure time with their own clocks, then slow that time down to the rate of time flow on Earth before transmitting it to our phones.
Einstein was a genius. Perhaps the greatest scientist ever. This is one of many examples where his insights about the laws of physics could not be tested in his own day. It required a half century for technology to improve enough for a test with high precision, and another half century until the phenomena he described became part of everyday life. Among other examples are the laser, nuclear energy, and quantum cryptography.
The Warping of Space: The Bulk and Our Brane
Finally in November 1915, in a great Eureka moment, he formulated his “field equation of general relativity,” which encapsulated all his relativistic laws including space warps.
If space were flat, the roundtrip travel time would have changed gradually and steadily. It did not. When the radio waves passed near the Sun, their travel time was longer than expected, longer by hundreds of microseconds. The extra travel time is shown, as a function of the spacecraft’s location at the top of Figure 4.3; it went up and then back down. Now, one of Einstein’s relativistic laws says that radio waves and light travel at an absolutely constant, unchanging speed. Therefore, the distance from Earth to the spacecraft had to be longer than expected when passing near the Sun, longer by hundreds of microseconds times the speed of light: about 50 kilometers.
This greater length would be impossible if space were flat, like a sheet of paper. It is produced by the Sun’s space warp.
The shape that the team measured, for the Sun’s equatorial plane, is shown in Figure 4.4 with the magnitude of the warping exaggerated. The measured shape was precisely what Einstein’s relativistic laws predict—precise to within the experimental error, which was 0.001 of the actual warping, that is, a part in a thousand. Around a neutron star, the space warp is far greater. Around a black hole, it is enormously greater. Now, the Sun’s equatorial plane divides space into two identical halves, that above the plane and that below. Nonetheless, Figure 4.4 shows the equatorial plane as warped like the surface of a bowl. It bends downward inside and near the Sun, so that diameters of circles around the Sun, when multiplied by π (3.14159 . . . ), are larger than circumferences—larger, in the case of the Sun, by roughly 100 kilometers.
How can space “bend down”? Inside what does it bend? It bends inside a higherdimensional hyperspace, called “the bulk,” that is not part of our universe!
Let's make that more precise. In Figure 4.4 the Sun’s equatorial plane is a twodimensional surface that bends downward in a threedimensional bulk. This motivates the way we physicists think about our full universe. Our universe has three space dimensions (eastwest, northsouth, updown), and we think of it as a threedimensional membrane or brane for short that is warped in a higherdimensional bulk.
Now, it’s very hard for humans to visualize our threedimensional universe, our full brane, living and bending in a fourdimensional bulk. So throughout this book I draw pictures of our brane and bulk with one dimension removed, as I did in Figure 4.4.
Fig. 4.4. Paths of Viking radio signals through the Sun’s warped equatorial plane.
In Interstellar, the characters often refer to five dimensions. Three are the space dimensions of our own universe or brane (eastwest, northsouth, updown). The fourth is time, and the fifth is the bulk’s extra space dimension.
Figure 4.5 is an extreme example of space warps. It is a fanciful drawing by my artist friend Lia Halloran, depicting a hypothetical region of our universe that contains large numbers of wormholes (Chapter 14) and black holes (Chapter 5) extending outward from our brane into and through the bulk. The black holes terminate in sharp points called “singularities.” The wormholes connect one region of our brane to another. As usual, I suppress one of our brane’s three dimensions, so the brane looks like a twodimensional surface.
Fig. 4.5. Black holes and wormholes extending out of our brane into and through the bulk. One space dimension is removed from both our brane and the bulk.
Tidal Gravity
Einstein’s relativistic laws dictate that planets, stars, and unpowered spacecraft near a black hole move along the straightest paths permitted by the hole’s warped space and time.
In Einstein’s relativity theory there is a mathematical quantity called the Riemann tensor. It describes the details of the warping of space and time. We found, hidden in the mathematics of this Riemann tensor, lines of force that squeeze some planetary paths together and stretch others apart. “Tendex lines,” my student David Nichols dubbed them, from the Latin word tendere meaning “to stretch.”
Fig. 4.7. Tendex lines
The green paths begin, on their right ends, parallel to each other, and then the red tendex lines stretch them apart. I draw a woman lying on a red tendex line. It stretches her, too; she feels a stretching force between her head and her feet, exerted by the red tendex line.
The purple paths begin, at their top ends, running parallel to each other. They are then squeezed together by the blue tendex lines, and the woman whose body lies along a blue tendex line is also squeezed.
This stretching and squeezing is just a different way of thinking about the influence of the warping of space and time. From one viewpoint, the paths are stretched apart or squeezed together due to the planetary paths moving along the straightest routes possible in the warped space and time. From another viewpoint it is the tendex lines that do the stretching and squeezing. Therefore, the tendex lines must, in some very deep way, represent the warping of space and time. And indeed they do, as the mathematics of the Riemann tensor taught us.
Fig. 4.8. Newton’s explanation for the tides on the Earth’s oceans.
What the Earth does feel is the redarrowed lunar pulls in the left half of Figure 4.8, with their average subtracted away; that is, it feels a stretch toward and away from the Moon, and a squeeze on its lateral sides (right half of Figure 4.8).
These felt forces stretch the ocean away from the Earth’s surface on the faces toward and away from the Moon, producing high tides there. And the felt forces squeeze the oceans toward the Earth’s surface on the Earth’s lateral sides, producing low tides there. As the Earth turns on its axis, one full turn each twentyfour hours, we see two high tides and two low tides. This was Newton’s explanation of ocean tides, aside from a slight complication: The Sun’s tidal gravity also contributes to the tides. Its stretch and squeeze get added to the Moon’s stretch and squeeze.
Because of their role in ocean tides, these gravitational squeezing and stretching forces—the forces the Earth feels—are called tidal forces. To extremely high accuracy, these tidal forces, computed using Newton’s laws of gravity, are the same as we compute using Einstein’s relativistic laws. They must be the same, since the relativistic laws and the Newtonian laws always make the same predictions when gravity is weak and objects move at speeds much slower than light.
Fig. 4.9. Relativistic viewpoint on tides: they are produced by the Moon’s tendex lines.
In the relativistic description of the Moon’s tides (Figure 4.9), the tidal forces are produced by blue tendex lines that squeeze the Earth’s lateral sides and red tendex lines that stretch toward and away from the Moon. This is just like a black hole’s tendex lines. The Moon’s tendex lines are visual embodiments of the Moon’s warping of space and time. It is remarkable that a warping so tiny can produce forces big enough to cause the ocean tides!
We now have three points of view on tidal forces:
•Newton’s viewpoint (Figure 4.8): The Earth does not feel the Moon’s full gravitational pull, but rather the full pull (which varies over the Earth) minus the average pull.
•The tendex viewpoint (Figure 4.9): The Moon’s tendex lines stretch and squeeze the Earth’s oceans; also (Figure 4.7) a black hole’s tendex lines stretch and squeeze the paths of planets and stars around the black hole.
•The straightestroute viewpoint (Figure 4.6): The paths of stars and planets around a black hole are the straightest routes possible in the hole’s warped space and time.
Peering at the puzzle first from one viewpoint and then from another can often trigger new ideas.
回应 20200630 06:24

Einstein’s Law of Time Warps Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical...
20200630 06:24
Einstein’s Law of Time Warps
Einstein struggled to understand gravity on and off from 1907 onward. Finally in 1912 he had a brilliant inspiration. Time, he realized, must be warped by the masses of heavy bodies such as the Earth or a black hole, and that warping is responsible for gravity. He embodied this insight in what I like to call “Einstein’s law of time warps,” a precise mathematical formula that I describe qualitatively this way: Everything likes to live where it will age the most slowly, and gravity pulls it there.
The greater the slowing of time, the stronger gravity’s pull. On Earth, where time is slowed by only a few microseconds per day, gravity’s pull is modest. On the surface of a neutron star, where time is slowed by a few hours per day, gravity’s pull is enormous. At the surface of a black hole, time is slowed to a halt, whence gravity’s pull is so humungous that nothing can escape, not even light.
This slowing of time near a black hole plays a major role in Interstellar. Cooper despairs of ever seeing his daughter Murph again, when his travel near Gargantua causes him to age only a few hours while Murph, on Earth, is aging eight decades.
Human technology was too puny to test Einstein’s law until nearly half a century after he formulated it. The first good test came in 1959 when Bob Pound and Glen Rebca used a new technique called the Mössbauer effect to compare the rate of flow of time in the basement of a 73foot tower at Harvard University with time in the tower’s penthouse. Their experiment was exquisitely accurate: good enough to detect differences of 0.0000000000016 seconds (1.6 trillionths of a second) in one day. Remarkably, they found a difference 130 times larger than this accuracy and in excellent agreement with Einstein’s law: Time flows more slowly in the basement than in the penthouse by 210trillionths of a second each day.
The global positioning system (GPS), by which our smart phones can tell us where we are to 10 meters’ accuracy, relies on radio signals from a set of 27 satellites at a height of 20,000 kilometers (Figure 4.2). Typically only four to twelve satellites can be seen at once from any location on Earth. Each radio signal from a viewable satellite tells the smart phone where the satellite is located and the time the signal was transmitted. The smart phone measures the signal’s arrival time and compares it with its transmission time to learn how far the signal traveled—the distance between satellite and phone. Knowing the locations and distances to several satellites, the smart phone can triangulate to learn its own location.
This scheme would fail if the signal transmission times were the true times measured on the satellite. Time at a 20,000kilometer height flows more rapidly than on Earth by forty microseconds each day, and the satellites must correct for this. They measure time with their own clocks, then slow that time down to the rate of time flow on Earth before transmitting it to our phones.
Einstein was a genius. Perhaps the greatest scientist ever. This is one of many examples where his insights about the laws of physics could not be tested in his own day. It required a half century for technology to improve enough for a test with high precision, and another half century until the phenomena he described became part of everyday life. Among other examples are the laser, nuclear energy, and quantum cryptography.
The Warping of Space: The Bulk and Our Brane
Finally in November 1915, in a great Eureka moment, he formulated his “field equation of general relativity,” which encapsulated all his relativistic laws including space warps.
If space were flat, the roundtrip travel time would have changed gradually and steadily. It did not. When the radio waves passed near the Sun, their travel time was longer than expected, longer by hundreds of microseconds. The extra travel time is shown, as a function of the spacecraft’s location at the top of Figure 4.3; it went up and then back down. Now, one of Einstein’s relativistic laws says that radio waves and light travel at an absolutely constant, unchanging speed. Therefore, the distance from Earth to the spacecraft had to be longer than expected when passing near the Sun, longer by hundreds of microseconds times the speed of light: about 50 kilometers.
This greater length would be impossible if space were flat, like a sheet of paper. It is produced by the Sun’s space warp.
The shape that the team measured, for the Sun’s equatorial plane, is shown in Figure 4.4 with the magnitude of the warping exaggerated. The measured shape was precisely what Einstein’s relativistic laws predict—precise to within the experimental error, which was 0.001 of the actual warping, that is, a part in a thousand. Around a neutron star, the space warp is far greater. Around a black hole, it is enormously greater. Now, the Sun’s equatorial plane divides space into two identical halves, that above the plane and that below. Nonetheless, Figure 4.4 shows the equatorial plane as warped like the surface of a bowl. It bends downward inside and near the Sun, so that diameters of circles around the Sun, when multiplied by π (3.14159 . . . ), are larger than circumferences—larger, in the case of the Sun, by roughly 100 kilometers.
How can space “bend down”? Inside what does it bend? It bends inside a higherdimensional hyperspace, called “the bulk,” that is not part of our universe!
Let's make that more precise. In Figure 4.4 the Sun’s equatorial plane is a twodimensional surface that bends downward in a threedimensional bulk. This motivates the way we physicists think about our full universe. Our universe has three space dimensions (eastwest, northsouth, updown), and we think of it as a threedimensional membrane or brane for short that is warped in a higherdimensional bulk.
Now, it’s very hard for humans to visualize our threedimensional universe, our full brane, living and bending in a fourdimensional bulk. So throughout this book I draw pictures of our brane and bulk with one dimension removed, as I did in Figure 4.4.
Fig. 4.4. Paths of Viking radio signals through the Sun’s warped equatorial plane.
In Interstellar, the characters often refer to five dimensions. Three are the space dimensions of our own universe or brane (eastwest, northsouth, updown). The fourth is time, and the fifth is the bulk’s extra space dimension.
Figure 4.5 is an extreme example of space warps. It is a fanciful drawing by my artist friend Lia Halloran, depicting a hypothetical region of our universe that contains large numbers of wormholes (Chapter 14) and black holes (Chapter 5) extending outward from our brane into and through the bulk. The black holes terminate in sharp points called “singularities.” The wormholes connect one region of our brane to another. As usual, I suppress one of our brane’s three dimensions, so the brane looks like a twodimensional surface.
Fig. 4.5. Black holes and wormholes extending out of our brane into and through the bulk. One space dimension is removed from both our brane and the bulk.
Tidal Gravity
Einstein’s relativistic laws dictate that planets, stars, and unpowered spacecraft near a black hole move along the straightest paths permitted by the hole’s warped space and time.
In Einstein’s relativity theory there is a mathematical quantity called the Riemann tensor. It describes the details of the warping of space and time. We found, hidden in the mathematics of this Riemann tensor, lines of force that squeeze some planetary paths together and stretch others apart. “Tendex lines,” my student David Nichols dubbed them, from the Latin word tendere meaning “to stretch.”
Fig. 4.7. Tendex lines
The green paths begin, on their right ends, parallel to each other, and then the red tendex lines stretch them apart. I draw a woman lying on a red tendex line. It stretches her, too; she feels a stretching force between her head and her feet, exerted by the red tendex line.
The purple paths begin, at their top ends, running parallel to each other. They are then squeezed together by the blue tendex lines, and the woman whose body lies along a blue tendex line is also squeezed.
This stretching and squeezing is just a different way of thinking about the influence of the warping of space and time. From one viewpoint, the paths are stretched apart or squeezed together due to the planetary paths moving along the straightest routes possible in the warped space and time. From another viewpoint it is the tendex lines that do the stretching and squeezing. Therefore, the tendex lines must, in some very deep way, represent the warping of space and time. And indeed they do, as the mathematics of the Riemann tensor taught us.
Fig. 4.8. Newton’s explanation for the tides on the Earth’s oceans.
What the Earth does feel is the redarrowed lunar pulls in the left half of Figure 4.8, with their average subtracted away; that is, it feels a stretch toward and away from the Moon, and a squeeze on its lateral sides (right half of Figure 4.8).
These felt forces stretch the ocean away from the Earth’s surface on the faces toward and away from the Moon, producing high tides there. And the felt forces squeeze the oceans toward the Earth’s surface on the Earth’s lateral sides, producing low tides there. As the Earth turns on its axis, one full turn each twentyfour hours, we see two high tides and two low tides. This was Newton’s explanation of ocean tides, aside from a slight complication: The Sun’s tidal gravity also contributes to the tides. Its stretch and squeeze get added to the Moon’s stretch and squeeze.
Because of their role in ocean tides, these gravitational squeezing and stretching forces—the forces the Earth feels—are called tidal forces. To extremely high accuracy, these tidal forces, computed using Newton’s laws of gravity, are the same as we compute using Einstein’s relativistic laws. They must be the same, since the relativistic laws and the Newtonian laws always make the same predictions when gravity is weak and objects move at speeds much slower than light.
Fig. 4.9. Relativistic viewpoint on tides: they are produced by the Moon’s tendex lines.
In the relativistic description of the Moon’s tides (Figure 4.9), the tidal forces are produced by blue tendex lines that squeeze the Earth’s lateral sides and red tendex lines that stretch toward and away from the Moon. This is just like a black hole’s tendex lines. The Moon’s tendex lines are visual embodiments of the Moon’s warping of space and time. It is remarkable that a warping so tiny can produce forces big enough to cause the ocean tides!
We now have three points of view on tidal forces:
•Newton’s viewpoint (Figure 4.8): The Earth does not feel the Moon’s full gravitational pull, but rather the full pull (which varies over the Earth) minus the average pull.
•The tendex viewpoint (Figure 4.9): The Moon’s tendex lines stretch and squeeze the Earth’s oceans; also (Figure 4.7) a black hole’s tendex lines stretch and squeeze the paths of planets and stars around the black hole.
•The straightestroute viewpoint (Figure 4.6): The paths of stars and planets around a black hole are the straightest routes possible in the hole’s warped space and time.
Peering at the puzzle first from one viewpoint and then from another can often trigger new ideas.
回应 20200630 06:24
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这本书的其他版本 · · · · · · ( 全部3 )

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订阅关于The Science of Interstellar的评论:
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1 有用 霭船 20161025
物理学超性感！
0 有用 rainmaker 20141220
结合电影， 没有数学公式
2 有用 苍旻 20150504
science is the new black终于慢吞吞的读完了，很荣幸成为豆瓣上读过这本书的第66个人。这本书就像是一个引子，把一个未知的世界的索引展现。这也是S拿到我送的kindle后看的第一本，两个人一起看书的感觉真好
0 有用 [已注销] 20141228
书，比电影好看。其中许多概念，不陌生，不过贵在概念下的数学，像飘浮在半空的“悟”下面，一级级铺上来的台阶。听说、知道，跟会做能做，一个地上，一个天上。自己缺乏空间想象力，书里很多地方读不透。
1 有用 lewthonclitus 20150202
从比较基础的东西讲起，但看得还是挺累，有些也没看明白。黑洞行星的轨迹太牛了。
0 有用 Angle He 20210704
假装自己看过了这本神书 ——假如每一部好片背后，都有一部神书，该多好
0 有用 湖骗子 20210503
OMFG这本书太好读了吧，逻辑过于清晰，Kip Thorne永远滴神
0 有用 银河背包客 20210206
语言平实，图例生动，本领域外人士也能轻松看懂。现在197677年的Viking信号传输实验也是我最喜欢的证明time wrap的实验了。但毕竟是领域外人士，black hole lensing的相关部分还是有些没有想通，留给未来再读吧。plus，看完之后自觉对电影有了更深入的理解，想必再看一遍感受也会不同。
0 有用 大河 20200821
“Nothing in the bulk can go backward in local bulk time. However, when looking into our brane from the bulk, our brane’s time can look like just another physical dimension. “
0 有用 SchrödingerCat 20200709
读过书会对电影有更深的理解，之前觉得不太合理或没有解释的个别地方也都有说明。另外Kip 的文笔还挺流畅。这本书面对的是没啥物理基础的普通读者，非常易读，比较懂物理的读者可以读这本书里连接的深入阅读资料。