1. The special significance of this film to the author: I am close to Interstellar:
1.1 I learned from my teacher and I am close to Interstellar:
When my wife and I were studying astrophysics in the United States, the tutor was Professor Clifford Will from Washington University. Kip Thorne, one of the executive producers of this film, is also Clifford Will's doctoral tutor, so although I am a little person in the field of relativity academically, I am Kip Thorne's direct disciple and grandson in terms of mentoring. In other words, to improve Bigger's words, "This is a movie produced by my master".
By the way: A few days ago, a friend said whether Sheldon from The Big Bang Theory knew Kip Thorne. I remember in one episode, Sheldon said that he was going to listen to Kip Thorne's lecture, so Sheldon should be the kind of admiration for Kip. Bar. In the physics world, Kip Thorne and Hawking are on the same level (actually they are also very good friends), and how nervous Sheldon was when he met Hawking, I remember playing it in one episode. Hey-hey.
1.2 "2006, it was a winter", and then put it on Interstellar almost:
In this circle of relativity, it is said that it is not too small, and it is not too big. I don't know when it started. When the more important scholars in this circle celebrated their 60th birthdays, everyone would get together to hold an academic conference and hold a birthday fest for them by the way. In my impression, Kip Thorne's birthday Kip Fest opened in 2000. And in 2006, just in time for my mentor's 60th birthday, we held a relativity meeting (2006 Midwest relativity meeting) at our school and held the Cliff Fest.
At the dinner that day, I happened to arrange a table with Kip and his wife Carolee. That should be the first time I had contact with Kip in an informal academic setting, and it was also the first time at the dinner table that I heard Kip talk about some time ago. Uncle Spielberg asked him to write a script. The goal, in Kip's words, is to make a movie that "time travels, parallel universes, but doesn't violate the laws of physics." Since Kip is a god-like figure in our circle, although I left the physics world in 2009 and came to the financial circle to make a living, I still pay attention to the progress of the movie from time to time. After 8 years of sharpening a sword, I really have to thank the flowers for waiting. Fortunately, from the producers, directors to the actors, none of the films are of low standard, which can be regarded as worthy of our hardships. Some of the explanations of strange physical phenomena in the film in simple terms are simply the reappearance of the scene when reading and doing research. Eight years later, things are different, and I almost shed tears after reading it. Far too far...
1.3 The relationship between Prof. Brand played by Michael Caine and Thorne
In Interstellar, when the male protagonist walked into the conference room of NASA, when Prof. Brand played by Michael Caine appeared for the first time, I immediately called out. It was like a Kip Thorne when he had hair. Image (it seems that after 2008, Kip Thorne began to shave his head, and the puppet called it "the grandfather of the turtle fairy"). Even think that Michael Caine is dressed according to Thorne's image. There have also been rumors that Kip may play a role in the film, and eventually it will be played by Michael Caine, which is not bad. Of course, like this matter, the benevolent sees the benevolent and the wise sees the wisdom.
2. Kip Thorne and the Wheeler Department of Theoretical Physics If
you want Kip Thorne, you have to start with his mentor John Archibald Wheeler. Wheeler himself is already a big man in research, but Wheeler has made two greater contributions to the theoretical physics community. The first is in the academic community's understanding of the theory of relativity, from "geometricalization" to "physicalization". The second is that the Wheeler family has cultivated a large number of apprentices and grandchildren of Niu X. Among Wheeler's students, in addition to Kip Thorne, there is also the famous Feynman.
2.1 Theory of Relativity: Mathematics or Physics?
[Note: This part has some physical content, which has nothing to do with Interstellar. It is mainly used for the later gossip Wheeler. Those who are not interested can skip it.]
In the history of the development of physical theory, mathematics has always played a very important role in it. For example, the development of classical mechanics is inseparable from the contributions of Newton, Leibniz and others to calculus. But at least in the entire classical theory, mathematics is more of an auxiliary role, and the origin of physics can still exist independently of mathematics. But when it comes to the old love's general theory of relativity, the situation changes.
A simple conclusion, the special theory of relativity has a theory about the world view, while the general theory of relativity is to extend this world view to the existence of gravity.
The so-called worldview of the special theory of relativity means that before the special theory of relativity, human beings understood the world from the perspective of "three-dimensional space + one-dimensional time". And Lao Ai's special theory of relativity, for the first time, put "space + time" together, allowing us to understand the world from the perspective of "four-dimensional space-time".
What's so special about "4-dimensional" space-time? Simply put, if we think that the essence of the world should be described by four-dimensional space-time (including 3-dimensional space + 1-dimensional time), then time is just the projection of a physical quantity on the time axis. As we learned in middle school analytic geometry, for a vector in the XY rectangular coordinate system, we can read the length of the projection of this vector on the two axes by means of vertical projection. But if we rotate the axis itself (clockwise or counterclockwise), the two projected lengths we read on the new axis change, although the vector itself does not change. In other words, in this problem, this vector is an essential thing, and its projection under each coordinate system will be different due to the different viewing angles and positions (coordinate systems), not the physical essence.
If we imagine the above Y axis as a time axis, what will happen? Understand? In short, the old love's special theory of relativity believes that we should use four-dimensional space-time to describe the world. Time is only the same as the x, y, and z dimensions of space. It is not the essence of physical phenomena, but physical phenomena (accurately, physical phenomena). event) a projection on the axes. When the coordinate system (observation system) of the observer is different, the distance (such as the long end of a ruler), and the time (or the speed of the clock) will be different.
In classical physics, gravitational and electromagnetic forces have relatively complete theories. However, Lao Ai did not consider gravity in the special theory of relativity. The special theory of relativity and classical electromagnetism combine very well, but when Lao Ai began to consider gravity into the framework of relativity, he began to encounter problems. The ultimate solution is to explain the nature of gravity through Riemannian geometry, the old favorite to use the curvature of spacetime.
Regarding the relationship between the curvature of spacetime and gravity, an example that often appears in popular science books: imagine a huge mattress, the surface of which is soft and smooth, and we roll glass balls on it. If there is nothing else on the mattress, and the mattress is flat, the glass ball will always move in a straight line on it (Newton's first law). Now imagine that we put a heavy bowling ball in the middle of this mattress, and at this time, the surface of the mattress bends (the middle sinks). If you play a glass ball on it at this time, the trajectory of the glass ball will involuntarily deviate towards the bowling ball in the middle. For glass balls that are slow or stationary at first, they will eventually fall next to the bowling ball (capture). If the initial speed of the glass ball is relatively fast and the angle is appropriate, the glass ball will revolve around the bowling ball several times (orbit); if the speed is faster, the trajectory of the glass ball will only be more obvious when passing the bowling ball. Bend, then run away (escape).
Now let's imagine that the bowling ball in the middle is the sun, the mattress is four-dimensional spacetime, and the little glass balls are the planets. Newton believed that the trajectories of the planets were influenced by the sun because of the "gravity" between the two. And Lao Ai believes that the essence of the relationship between the two can be explained by the curvature of space-time (mattress). The size of the mass determines the degree of curvature of space-time.
The above analogy is just a simplification of the old love theory in popular science books for readers to understand, but the actual situation is much more complicated. But the old love's general theory of relativity equates gravity with the curvature of space-time, which is its core idea. But this method of treatment also brings a trouble, that is, mathematics in the traditional sense fails in general relativity. Imagine how troublesome it is to bend space-time. For example, in a flat space-time, two parallel lines will not intersect, but curved space-time is different. For example, all the lines of longitude on the earth are parallel when they are at the equator, but they are compared at the north and south poles. This is because the earth's surface is a 2-dimensional surface. 2D surfaces are already so complex, now let's imagine a 4D surface. Therefore, in order to better describe the theory of relativity under the gravitational field, Riemannian geometry must be introduced.
2.2 Understanding Relativity from a Physical Perspective: Wheeler System and MTW
As mentioned earlier, general relativity has high requirements for mathematics, especially for the mathematics of non-flat space-time (Riemannian geometry). But as Li Zhengdao said, "There are only two kinds of mathematics books, one is the one you can't read after just one page, and the other is the one you can't read after reading the first sentence", although physicists seem to Both are nerds, but the nerds are still many orders of magnitude worse than the nerds of mathematicians. The advanced stuff of Riemannian geometry was still very new to physicists in the early 20th century, so after the birth of the old love theory, most of the old and young men in the physics world I don't know what to do except worship. Just like the classic joke Eddington was interviewed for: the reporter said "I heard that you are one of the three people in the world who really understand the theory of relativity", and Eddington replied "I have to think carefully about who the third person is".
To understand the theory of relativity, you have to master Riemannian geometry. The main reason for not understanding the theory of relativity is that Riemannian geometry has not been learned well. From my own learning experience in the theory of relativity, this conclusion is correct, and the understanding of Riemannian geometry is indeed helpful to learn the theory of relativity well. But being too obsessed with mathematics seems to be a bit out of the essence of physics.
It should be said that in those early years, countless theoretical physics masters made great contributions in how to make the theory of relativity more physical and easier to be understood by new people in the physical world. And these essences were finally brought together into a more than 1,000-page Bible-level textbook on relativity - "gravitation" (translated into "gravitation" in Chinese). The three authors of this book are the aforementioned Wheeler, Kip Thorne, who is inextricably linked with Interstellar, and Misner, another student of Wheeler. The theoretical physics community likes to refer to the book by the last name of the three authors, Misner-Thorne-Wheeler, or MTW for short.
Although MTW brings together a lot of wisdom of predecessors, it cannot be said that all the contents are the contributions of the three authors, but its status in the field of relativity is the absolute No.1 textbook. Its greatest contribution is to put physics It is almost perfectly integrated with mathematics. I think people who read Interstellar will be impressed by the simple explanation of "A wormhole in three-dimensional space is a sphere". Now let's imagine that a few decades ago, when everyone didn't know how to get students into the theory of relativity, suddenly a textbook with more than 1,000 pages appeared, covering almost everything from the basics to the frontier. The relevant branches, and almost every incomprehensible physical phenomenon and formula are explained in simple terms similar to the previous "wormhole". How big is this impact, needless to say?
By the way, because MTW is too thick, Bernard F. Schutz, a PhD student of Thorne and director of the Max Planck Institute in Germany, published a thin version of "A first course in general relativity". , which can be regarded as the best choice for undergraduate students to study general relativity. In order to solve the problem of doing problems in the process of learning the theory of relativity, Lightman and Press, two other students of Thorne, published the best problem set for learning the theory of relativity. It can be said that basically most of the people in the circle of relativity grew up reading Schutz, MTW, and doing Lightman-Press topics.
Any physical problem must be explained in a language that ordinary people can understand. Why is the Wheeler department so important in the field of relativity and theoretical physics? I think it is indistinguishable from the characteristics of Wheeler and the great people in this department. Open (remember that in the movie margin calls, the boss of the investment bank said "speak to me as if I am a child, or a golden retriver", which is actually the same reason).
By the way, in the years when the United States engaged in physics, I really felt that many of the outstanding scholars in the United States were very good speakers. In other words, it is able to express "the most complex content in the most plain and easy-to-understand language". For example, in the first semester of my Ph.D., I was studying advanced mathematics and physics. At the beginning of a class, the Daniel teacher in our department said, "Let me take 10 minutes to explain quantum electrodynamics to you clearly", ten minutes After that, everyone understood. On this point, after I went to Germany as a postdoctoral fellow and returned to China, I deeply felt the particularity of the concept of the United States. Whether in Germany or in China, it seems that the more talented the scholars, the more "speaking like a book from heaven, and you are stupid if you don't understand" as the criterion. I don't know what is the reason for this.
Going a long way, it's still the same sentence, the road is simple, Wheeler is in the theory of relativity, and has brought this to the extreme. Why there are so many great people in the Wheeler line, I think it has a lot to do with it.
2.3 Wheeler, Thorne and "Black Hole", "Wormhole" and Space Travel
There are many names of celestial objects in Interstellar. Among them, the two that sound Bigger are higher, one is Black Hole and the other is Wormhole. . Wheeler was the first to publicly use the term black hole in the physics community, and he was also the first to coin the term "wormhole", pointing out that wormholes could be used for time travel. In Thorne's research, there is a lot of content related to this.
In fact, in both Newton's theory and relativity, there is such a problem. When the mass of a celestial body is too large, the gravitational force will cause itself to have a tendency to shrink. If there is not enough other force to counteract it, the inward collapse of the object will be unavoidable. Case in point: our sun. The sun's huge energy comes from nuclear fusion reactions, in other words, we can think of the sun as a huge hydrogen bomb. Due to the power brought by this fusion, the sun will not collapse yet (when the hydrogen bomb explodes, it will blow various substances from the inside to the outside, this force is the source of canceling the inward gravity of the sun), but when When it eventually runs out of fuel, it may collapse. If a star as massive as the sun collapses to a certain extent, it will eventually become a white dwarf or neutron star due to the degeneracy of electrons or neutrons. And if the mass of a star exceeds a value called the "Chandrasekhar limit", there is no force to counteract its collapse, and eventually the star will shrink to a point with a large mass but a volume of 0, so the mass density is infinite, which is a singularity. And in places that are relatively close to this point (the horizon mentioned in the movie, within the event horizon), due to the strong gravity, even light cannot escape. This is the common understanding of the term "black hole". (By the way, for a star as massive as the sun, the radius of the collapsed horizon is about 3 kilometers. The mass and radius are linearly related, so a black hole with a large horizon like the Gargantua in Interstellar, everyone. You can imagine how big it is)
The founder (promotion) of the word "black hole" is Wheeler. It is said that this is the case. In 1967, the old gentleman held an academic conference in New York. He was talking about the problem of gravitational collapse. I don't know which passer-by in the audience shouted, "Let's call this thing a black hole." The old man was very excited, so the name was born.
If you read MTW, there is a long explanation in it, why the term black hole is very appropriate. First of all, why are black holes black? Because light cannot escape. Secondly, why do we call it a "hole", the physical explanation is that if an astronaut falls into the viewport, he looks at his watch, and waits and waits, and finds that he can never fall into the middle one Singularity (hitting into any matter), that is, for astronauts, this is indeed the feeling of falling into a bottomless pit. How, is the name appropriate?
What about the actual situation? Anyway, just ask the French. The word "black hole" is a very obscene word in French slang (yes, don't doubt it, that's what you think it means). Even when the first time someone in the physics community used this word for a journal, the French editor-in-chief shouted, "Unless I die, I will never let such a wretched word appear in my journal." The final result? The word "black hole" spread rapidly among the otaku in the physics world, and in the end the editor-in-chief failed to stop the "torrent of history". A few years later, Mr. Wheeler coined another word - "black hole hairless"! ! ! From personal experience, not too few French people I know study astrophysics and relativity, and there are many who study gravitational waves, but it seems that there are not many who focus on the study of black holes.
The creator of the word wormhole is also Wheeler, in fact the word "wormhole" (1957) appeared earlier than "black hole" (1967). In 1921, Weyl proposed the concept of wormholes in a paper. From the current theory, due to the stable existence of a wormhole (that is, allowing an object to pass back and forth), there needs to be a stable circle of negative energy (but energy with a negative density) around it. So under the classic framework, there is no such wormhole. However, under the framework of quantum field theory, vacuum is not a vacuum, but is constantly created and annihilated by positive and negative particles, so there may also be huge negative energy at a certain point, so including Thorne, Hawking and others, It is believed that under this framework, there may be wormholes that allow to travel back and forth and exist stably. A lot of Kip Thorne's research is related to this, and one of my officemates when I was a Ph.D. student also did this research. However, this thing has never been found (if the wormhole needs negative energy, does it mean that the reason why this thing has not been found is because it is not conducive to "harmonious society"? :p), so that on his 60th birthday , and was also joked "You are in your 60s, it seems that time travel is no play, what should I do?".
2.4 Five-dimensional space-time, Brane theory, communication with ghosts in Interstellar
It should be said that in Interstellar, the way the ghost (the protagonist) communicates with his daughter should be the most dazzling part of the entire movie. In fact, this also implies very cutting-edge theoretical physics ideas. It is indeed in line with what kip said back then, "a movie about time travel, parallel universes, and not violating the laws of physics".
This keyword also appeared in the movie, Brane!
Brane (film) is a very hot word. In essence, there is a set of Brane-related theories in string theory. The more famous one is the Randall-Sundrum model co-created by MIT and Harvard double professors Lisa Randall and Raman Sundrum of the University of Maryland. (By the way, when Randall asked Sundrum to work on this theory together, Sundrum lost his confidence because he had been a postdoc for too long and decided to go to Wall Street, but he didn’t expect a blockbuster, so Wall Street lost one great man, and the University of Maryland gained one more. Full professor)
In simple terms, Randall-Sundrum is trying to solve the question: why is gravity so much weaker than other forces? For example, when we use a magnet to pick up an iron nail from the ground, on the one hand, the magnetism (electromagnetic force) of the magnet attracts the nail upward, and on the other hand, the whole earth is attracting the iron downward (through gravity). Nail, the result? The magnets won. The magnetic force generated by a small magnet can defeat an opponent the size of the entire earth. This is a very incredible phenomenon. In theoretical physics, this is called the "hierarchy problem" (how to translate? Hierarchy problem? Order of magnitude problem? Khan).
The Randall-Sundrum model explains this problem in this way. It believes that the four-dimensional space-time (3-dimensional space + 1-dimensional time) we are in is actually like a film (Brane) in the five-dimensional space-time, and at the same time, There are actually other similar Branes. If we think that a membrane is a universe, it can also be used as a theory of parallel universes. Interactions like electromagnetic force can only propagate on the same membrane (in other words, they can only exist in four-dimensional spacetime), while gravity can propagate between different membranes (i.e., gravity can propagate in five-dimensional spacetime) transmission).
If we believe that the Randall-Sundrum model is correct, it could explain why gravity is so much weaker than other interactions, such as electromagnetism. For example, the surface of a sheet of paper is a 2-dimensional plane. We use a small tube of ink. It is easy to fill a 10x10 cm sheet of paper, but if you want to fill a stack of 10 cm thick paper, it may be It will not be enough, because such a stack of paper has to be filled, adding one dimension (thickness) and becoming a three-dimensional object. If you have to fill it up and the ink is not enough, you have to dilute it with water, so the color per unit area will be lighter. Simply put, according to the membrane theory, the range of gravitational diffusion is five-dimensional space-time, which is larger than the interaction diffusion range of four-dimensional space-time, so it is weaker.
Going back to the movie, only the gravitational force can propagate between the membranes, which is why the ghost (the male protagonist) can only communicate with the daughter through the gravitational force, and the daughter cannot hear the shouting. Since only gravity can shuttle between his brane and his daughter's brane, shouting (sound propagation) is essentially based on electromagnetic interactions, confined to his own brane.
2.5 Gravity, gravitational waves, and watch hands.
Well, the above mentioned that gravity can be transmitted between Brane, which explains the communication between the ghost (the male protagonist) and the daughter, and also explains the strange way the sand falls, the book falls to the ground (the vertical downward Gravitational field, just become a horizontal gravitational field) Wait, but why did the hands of his daughter's watch go out of such a strange rhythm?
In fact, this is not surprising. There are two possible explanations: 1) The gravitational field causes the clock to change. The logic of this is the same as that of the clock on the Miller planet; 2) The gravitational wave causes the movement of the object, in short , when a gravitational wave passes through an object, it causes the object to wobble laterally.
In theory, both explanations make sense, but consider: 1) Kip Thorne's huge contribution to the study of gravitational waves (now waiting for the gravitational wave detector LIGO to detect gravitational waves, and then most likely to take Bell Award); 2) If it's a clock change, it's inevitable that the daughter of the protagonist who wears the watch will be affected. 3) If the clock changes, it should not be seen that the time goes back. To sum up, I still prefer this interpretation of gravitational waves.
2.6. Why do some other miscellaneous
Miller planets have such big waves?
tidal. Just as the moon revolves around the earth, causing tides on the earth, Miller is so close to the black hole that it brings huge tides during its rotation. It should not be the tides caused by the revolution, otherwise the tides are a bulge and will not move relative to the surface of Miller's planet. However, there is also a loophole in the theory of rotation, that is, if the tide is caused by rotation, it should appear once every day and night. Obviously, we did not see the darkness in the movie at that time. Movies, how to shoot Black Blondon, and you have to explain why you turn around in an hour. . .
Why didn't Miller's planet fall so close to the black hole?
This is also simple, just like the reason why the moon is so close to the earth and does not fall into it, after all, it does not pass through the view interface. It is said that it is worthwhile to calculate how close Miller is to the visual interface. In addition, it can also be calculated that due to the orbital attenuation caused by gravitational wave radiation, how long it will take for Miller's planet's orbit to shrink to fall into the horizon, etc. I haven't been doing physics for too long. Interested officials can check the relevant derivation. It should not be difficult.
The most conspicuous formula in the string theory and 10-dimensional space
film should be the formula written by the protagonist's daughter when she deduced the ultimate theory. At that time, a clear lens gave it, it was an integral in ten-dimensional space-time (in the integral there are d^10x). OK, string theory. Btw, many of the formulas on the blackboard in the movie were written by Kip Thorne and his students. Anyway, the formulas I have seen are reliable formulas. In fact, thinking about it, it seems more troublesome to have a physics giant sitting in the queue and writing messy formulas on the blackboard.
The robot on Mann planet is
OK, the name of this robot is KIPP, not Kip, but I prefer to believe that it is related to Kip.
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