Interstellar: inside a black hole and a tesseract. Science in the movie "Interstellar": wormholes, black holes, space-time There are huge waves on this planet

My name is Andrey Kolokoltsev. Due to my line of work, I have long been interested in stories about how famous directors, producers, and studios cope with the creation of certain visual films. For my first publication, I chose a movie that became an audiovisual revelation and a real emotional attraction for me (when watching in a movie on an IMAX screen, 2/3 of the impressions are lost at home on TV). You won't jump in surprise because you've already read everything in the title - this is Christopher Nolan's film Interstellar. Despite the fact that interest in it has long faded, I would like to present to your attention a free translation of Mike Seymour’s original article “Interstellar: inside the black art” dated November 18, 2014. This article talks about how the visualization of “Gargantua” and other scenes from the film was created - I think it will be interesting to readers even after 1.5 years.

Interstellar director Christopher Nolan explains the basics of quantum physics to Matthew McConaughey, the essence of the scene

Workers in the special effects and computer graphics department are often faced with the need to create a visualization of something that no one has ever seen before. Added to this is the demand of the modern film industry that it all look real, even despite the fact that, in fact, no one really has any idea what it might look like. In Christopher Nolan's Interstellar, special effects supervisor Paul Franklin and the Double Negative team had to create a rendering of things not in our dimension that would be as close as possible not only to quantum physics and relativistic mechanics, but also to our common understanding quantum gravity.

It was fortunate that among Double Negative's core team was Oliver James, a chief scientist with an Oxford education in optics and atomic physics, as well as a deep understanding of Einstein's relativistic laws. Like Franklin, he worked with supervising producer and scientific consultant Kip Thorne. Thorne had to calculate complex mathematical equations and send them to James to be translated into high-quality renders. The requirements for the film challenged James not only to visualize the calculations that would explain the arcing paths of light, but also to visualize the cross sections of the light rays changing size and shape as they traveled through the black hole.

James' code was just part of the overall solution. He worked hand-in-hand with art team lead and CG effects supervisor Eugen von Tanzelmann, who added the accretion disk and created the galaxy and nebula that distort as light from them passes the black hole. Equally challenging was the task of showing someone walking into a four-dimensional tesseract juxtaposed with the three-dimensional space of a little girl's room, all while making it clear to the viewer what was actually happening on screen.

In this article, we'll highlight some of the key frames Double Negative created, as well as the science behind them. Please note that the following material may contain spoilers.

Creation of a black hole

Perhaps one of the most significant achievements in achieving Nolan's goal of maximum realism is the depiction of the black hole Gargantua. After receiving input from Thorne, the filmmakers went to great lengths to show the behavior of light in a black hole and wormhole. For Double Negative, this challenge necessitated writing a completely new physical renderer.

A camera view of a black hole in a circular equatorial orbit, spinning at 0.999 times its maximum possible rotation speed. The camera is located at a distance of r=6.03 GM/c^2, where M is the mass of the black hole, G and c are Newton's constant and the speed of light, respectively. The event horizon of the black hole is at a distance of r=1.045 GM/c^2.

“Kip was explaining to me the relativistic curvature of space around a black hole,” says Paul Franklin. “Gravity, twisting through time, bends light away from itself, creating a phenomenon called the Einstein lens, a gravitational lens around a black hole. And at that moment I was thinking, how can we create such an image and are there any examples with a similar graphic effect that we could rely on.”

“I looked at the very basic simulations that the scientific community had created,” Franklin adds, “and I thought, OK, the movement of this thing is so complex that we'll have to make our own version from scratch. Kip then began working very closely with Oliver James, our chief scientist, and his department. They used Kip's calculations to derive all the light paths and ray tracing paths around the black hole. In addition, Oliver worked on the pressing questions of how to bring all this to life using our new DnGR (Double Negative General Relativity) renderer.”

The new renderer required setting all the critical parameters for their digital black hole. “We could set the speed, the mass and the diameter,” Franklin explains. “Essentially, these are the only three parameters that you can change in a black hole - that is, these are all we have to measure it. We've spent a huge amount of time working on how to calculate the paths of light beams around a black hole. All the work went quite intensively - the guys wrote software for six whole months. We had an early version of the black hole just in time for the film to finish pre-production."

A black hole at rest accelerates to a rotation speed of 0.999 of its possible speed; then the camera approaches the black hole from a radius of 10 GM/c^2 to a radius of r=2.60 GM/c^2, continuing to move along a circular equatorial orbit. The huge shadow of a black hole is distorted into a rectangular shape due to the conversion of the super image from the camera to the flat panel display.

These early images were used as huge paintings for the background of the outside of the ship - so the actors had something to look at while filming. That is, not a single green screen was used, it was just that Double Negative later replaced the early images used with the final ones, correcting some star clusters. “Most of the over-the-shoulder shots of astronauts that you see in the theatrical release,” Franklin notes, “are real footage. We had a lot of shots that didn't make it into the visual effects shots, even though a lot of work went into creating them."

These live-on-camera shots were made possible through the collaboration of Double Negative and Physics Ph.D. Hoyte Van Hoytema. Spotlights with a total luminous flux of 40,000 lumens per scene were used to illuminate the resulting background images.”

The same simulation, only bigger. Here the structure of light from the starry sky passed through a gravitational lens is clearly visible. At the edge of a black hole, the horizon moves toward us at close to the speed of light.

“We had to move and reconfigure the lights based on the needs of the scene,” Franklin continues. “In general, it could take a week to get everything right, but in some cases it had to be ready in 15 minutes. The guys worked so hard, because the spotlights are huge, unwieldy machines - each weighed about 270 kilograms. We had two specially made cages mounted on a large electric winch with the ability to move it along and across the pavilion, so we could use it to position the spotlights. Over the radio, I explained to the guys with the spotlights how to calibrate them, while simultaneously talking with the man operating the forklifts rushing over the densely packed area.”

Creating waves

In the film, Cooper (Matthew McConaughey), Amelia (Anne Hathaway), Doyle (Wes Bentley) and the AI robot CASE visit a planet completely covered in water, the waves of which, due to their very close location to Gargantua, reach extraordinary sizes. Viewers had already seen thirty-meter waves in other films, but according to history, this was not enough - according to the script, the waves were supposed to be more than a kilometer in height. To give the viewer a sense of this height, Double Negative had to rethink the standard approach to creating water. “When you take objects of this scale,” explains Franklin, “all the characteristics that you associate with waves, such as breakers and curls at the top, simply disappear because they become invisible relative to such a mass of water - that is, the wave becomes more like on a moving mountain made of water. That's why we spent a lot of time working on pre-visualization and thinking about how we could use the scale of the waves and the small spaceship Ranger being washed away by them. The most important moment of the scene is when the wave overtakes the Ranger and lifts him high above the surface. And you see how the ship moves up the wave, becomes smaller and smaller and suddenly gets lost on it. This was a key moment to sense the scale of what was happening.”

Anne Hathaway as Amelia on the Water Planet

Double Negative's artists manipulated the waves through deformer animations, effectively changing them at every keyframe. “This gave us a basic waveform,” says Franklin, “but to make it feel real, we have to add foam on the surface, interactive splashes, water swirls and splashes. To do this, we used our internal development called Squirt Ocean. And, of course, after that there was a lot of additional work in Houdini.”

The footage was created in high definition IMAX. This requirement somewhat limited the amount of time available for all possible iterations of Double Negative. “I'd look at the wave animation part, say, 'great, let's add everything else,'" Franklin laughs, "and then I'd have to wait about a month and a half for it all to come back to me, a long process due to the IMAX resolution. . As you understand, we couldn’t waste time, because usually the whole process is divided into many iterations, but this time we had a maximum of three.”

The robot CASE, which saves Amelia from the tidal wave, and its counterpart TARS, were in fact 80-pound metal puppets controlled by Icelandic artist Bill Irwin. Christopher Nolan wanted the film to have as many real elements as possible, and rather than just drawing him as many did, Double Negative needed to work on removing the performer behind the robot.

When CASE reconfigures itself to walk on water and then rolls towards Amelia, grabbing her and carrying her away, the frame combines two solutions: the practical and the digital. “In that shot,” Franklin says, “there was a small water rig built, mounted on an ATV. That is, we could ride “through” the water and get wonderful interactive splashes and splashes. We also had a special lift with robotic arms installed on the ATV, on which we could transport Anne Hathaway's double. That is, this whole structure drove and “cut” the water, and all we had to do was remove it from the image and replace it with a digital version of the robot.”

Double Negative tried to limit the number of moments with digital robots doing unusual things as much as possible. Such moments were running through water, landing a robot in a ship, running on a glacier and some moments with no gravity. “What we noticed a long time ago is that you can only make digital moments work if you combine them with real ones,” says Franklin, “For example, in the shots where the robot climbs into the ship at the very end of the segment we are already seeing a real version of the robot, not a digital one. That is, the scene ends with shots of reality, and this helps to feel the scene as really real.”

Inside the tesseract

In the film, "they" turns out to be "us", only advanced enough to help Cooper contact his daughter, who was on Earth years earlier. Since time travel is impossible in a universe of quantum and relativistic laws, history resolves this issue in such a way that Cooper leaves our three-dimensional space and enters a higher-order hyperspace. If our universe is displayed as a 2D disk or membrane, then hyperspace will be a box surrounding this membrane in three dimensions. The way to make sense of this is that each dimension requires 1 less dimension to represent it. Thus, three-dimensional space is drawn as a 2D disk, and the three-dimensional environment around this disk (physicists call it a brane) is one dimension above the membrane.

Image drawn by Kip Thorne explaining what a brane and membrane are

In the film, Michael Caine's character, Professor Brand, tries to unravel gravitational anomalies. The boards in the film clearly show an attempt to solve the problem in 4 and 5 dimensions. The film says that if Brand can understand these anomalies, they can be used to change gravity on Earth and lift a huge humanity-saving structure into space.

While going from 3D to 4D doesn't solve the problem of time travel, in the film it allows Cooper to send gravitational waves back in time. He can see any time, but can only cause ripples in these periods of time - gravitational ripples, which Cooper's daughter, Murphy, is trying to understand.

The Double Negative team's job was to visually demonstrate the four-dimensional tesseract that the future "us" provides to Cooper so that he can cause gravitational waves. This would be easily feasible if done in a symbolic sense or as a dream, but the Double Negative team decided to visualize the four-dimensional tesseract in a more expressive way, creating a concept that was, of course, a hypothesis, but could even be used for teaching . It was at this moment that Thorne reappeared.

Kip Thorne's formulas explaining gravity in four and five dimensions. Notice that here “our” brane is sandwiched between two alternate realities or other branes.

To understand the Double Negative solution, it is worth understanding the nature of higher order dimensions. If an object is at rest, say a ball, for two-dimensional space it is a circle; for one-dimensional – a line. If we look at this circle in three-dimensional space, we will see a ball (sphere). But what will happen to it if we move to four-dimensional space? One of the theories that was the basis for our daily thinking was to imagine the fourth space as time. Then it turns out that the same ball, but not at rest, but jumping, and in an infinitely small period of time is visible as the same ball. But along the way it creates a tube-like shape with hemispherical edges. That is, in four-dimensional space, the ball is a pipe, and the sphere is a three-dimensional projection of this four-dimensional figure.

If a cube in three-dimensional space changes its shape over time, for example, grows, then in four-dimensional space it will be depicted as a box, which over time grows into a large box, displaying all the states of the three-dimensional box during the entire time of its existence. It can animate and change shape as shown in this video:

According to the logic of the film, if you get into this tesseract, you will be able to see three-dimensional space at any moment in time of its existence, for example, in the form of lines going into the past and future. Moreover, if you take into account the assumption that there is an infinite number of parallel realities, you will see all the lines of all possible parallel realities going in an infinite number of directions. This is precisely the conceptual solution of the four-dimensional space with which the studio worked. The "threads" of time that Cooper sees look like strings, and by touching them, he can cause gravitational vibrations, thus communicating with his daughter. This is truly a brilliant piece of artistic scientific visualization!

But how to shoot it?

Nolan's insistence that actors interact with their surroundings when creating videos extended to the tesseract. After falling into a black hole, Cooper finds himself in a four-dimensional space in which he can see any objects and their “thread” of time. “Chris said that even though it was a very abstract concept, he really wanted to build something that we could actually film,” says Franklin. “He wanted to see Matthew physically interacting with the threads.” time, in real space, and not dangling in front of a green screen.”

This prompted Franklin to think about how to visualize the tesseract. “I spent a lot of time wondering how to implement all this in real space,” he says, “how to show all these temporal “threads” of all the objects in one room, and so that it was understandable in a physical sense. After all, the danger was that the space would turn out to be so cluttered with “threads” that you would have to figure out how to highlight the necessary moments among them. Plus, it was extremely important that Cooper not only saw the “threads” of time, but also saw their reverse reaction to the interaction, and at the same time could still interact with objects in his daughter’s room.”

The final "open lattice structure" design was inspired by the tesseract concept. “The Tesseract is a three-dimensional projection of a four-dimensional hypercube. It has a beautiful lattice-like structure, so we had a rough idea of what we were going to do. For a long time I looked at scans from long-exposure photographs (slit-scan photography) and how this technique allows you to display the same point in space at all points in time. Photography itself turns time into one of the dimensions of the final image. The combination of this shooting technique and the lattice structure of the tesseract allowed us to create these three-dimensional "threads" of time, as if flowing out of the object. Rooms are photographs, moments embedded in a lattice structure of time threads, among which Cooper can search for the ones he needs, moving them back and forth.”

“We ended up building one section of this physical model with four repeating sections around it,” Franklin says, “Then on the computer we multiplied those sections indefinitely so that no matter where you looked, they went on forever. We also used a lot of real projections during filming. We placed active “threads” of time under real sections using projectors. This gave us a feeling of trembling and febrile energy - all the information flowed along these "threads" from section to section and back again. But of course, every image of the final film also has an insane amount of digital effects built into the scene."

But some moments forced Double Negative to go completely digital visual effects - such as Cooper's movement through the tesseract tunnels. “We didn’t have enough tesseract sections to capture this movement, so we filmed Matthew with projection screens around him showing the pre-production rendering of the scene, so he had something to interact with,” says Franklin. The actors absolutely loved it because, as opposed to making a commercial or a green screen film, they had something to look at. Later we replaced this version with a high-quality final version, only leaving the pre-finish version in some moments, since it was simply out of focus and was not visible.”

Franklin also notes that a lot of digital effects, cable removal and a huge amount of rotoscoping (roto, rotopaint) were required to complete these scenes. There were also certain difficulties in implementing effects performed entirely using computer graphics. For example, in the part where the tesseract closes and begins to collapse. “We took the computer geometry of the tesseract and ran it through the rotation of a hypercube. The guys worked on how to implement the hypercube rotation transformation and apply it directly to the geometry of the tesseract we created. It was a special moment for me. When I saw the results, I knew it was perfect, exactly what I wanted." Add tags

More recently, science has become reliably aware of what a black hole is. But as soon as scientists figured out this phenomenon of the Universe, a new one fell on them, much more complex and confusing: a supermassive black hole, which cannot be called black, but rather dazzlingly white. Why? But because this is exactly the definition given to the center of each galaxy, which glows and shines. But once you get there, there is nothing left except blackness. What kind of puzzle is this?

A reminder about black holes

It is known for certain that a simple black hole is a once shining star. At a certain stage of its existence, it began to increase exorbitantly, while the radius remained the same. If earlier the star was “expanding” and growing, now the forces concentrated in its core began to attract all other components. Its edges “collapse” onto the center, forming an incredible collapse, which becomes a black hole. Such “former stars” no longer shine, but are completely outwardly invisible objects of the Universe. But they are very noticeable, since they literally absorb everything that falls within their gravitational radius. It is unknown what lies behind such an event horizon. Based on the facts, such a huge gravity will literally crush any body. However, recently, not only science fiction writers, but also scientists have been adhering to the idea that these could be a kind of space tunnels for traveling long distances.

What is a quasar?

A supermassive black hole has similar properties, in other words, the core of a galaxy, which has a super-powerful gravitational field that exists due to its mass (millions or billions of solar masses). The principle of formation of supermassive black holes has not yet been established. According to one version, the cause of this collapse is overly compressed gas clouds, the gas in which is extremely discharged and the temperature is incredibly high. The second version is an increase in the masses of various small black holes, stars and clouds to a single gravitational center.

Our galaxy

The supermassive black hole at the center of the Milky Way is not one of the most powerful. The fact is that the galaxy itself has a spiral structure, which, in turn, forces all its participants to be in constant and fairly fast motion. Thus, gravitational forces, which could be concentrated exclusively in the quasar, seem to dissipate and increase uniformly from the edge to the core. It is easy to guess that things are the opposite in elliptical or, say, irregular galaxies. On the “outskirts” the space is extremely rarefied, the planets and stars practically do not move. But in the quasar itself, life is literally in full swing.

Parameters of the Milky Way quasar

Using radio interferometry, the researchers were able to calculate the mass of the supermassive black hole, its radius and gravitational force. As noted above, our quasar is dim, it is difficult to call it super-powerful, but even the astronomers themselves did not expect that the true results would be like this. So, Sagittarius A* (that’s the name of the core) is equal to four million solar masses. Moreover, according to obvious data, this black hole does not even absorb matter, and the objects that are in its surroundings do not heat up. An interesting fact was also noticed: the quasar is literally buried in gas clouds, the matter of which is extremely rarefied. Perhaps the evolution of the supermassive black hole of our galaxy is just beginning, and in billions of years it will become a real giant that will attract not only planetary systems, but also other, smaller ones

No matter how small the mass of our quasar may be, what struck scientists most of all was its radius. Theoretically, such a distance can be covered in a few years on one of the modern spacecraft. The dimensions of the supermassive black hole are slightly larger than the average distance from the Earth to the Sun, namely 1.2 astronomical units. The gravitational radius of this quasar is 10 times smaller than the main diameter. With such indicators, naturally, matter simply will not be able to singularize until it directly crosses the event horizon.

Paradoxical facts

The galaxy belongs to the category of young and new star clusters. This is evidenced not only by its age, parameters and position on the map of space known to man, but also by the power possessed by its supermassive black hole. However, as it turned out, not only young ones can have “funny” parameters. Many quasars, which have incredible power and gravity, surprise with their properties:

Ordinary air is often more dense than supermassive black holes.
Once on the event horizon, the body will not experience tidal forces. The fact is that the center of the singularity is quite deep, and in order to reach it, you will have to go a long way, without even suspecting that there will be no way back.

Giants of our Universe

One of the most voluminous and oldest objects in space is the supermassive black hole in the quasar OJ 287. This is an entire lacertid located in the constellation Cancer, which, by the way, is very poorly visible from Earth. It is based on a binary system of black holes, therefore, there are two event horizons and two singularity points. The larger object has a mass of 18 billion solar masses, almost the same as a small full-fledged galaxy. This companion is static; only objects that fall within its gravitational radius rotate. The smaller system weighs 100 million solar masses and also has an orbital period of 12 years.

Dangerous neighborhood

The galaxies OJ 287 and the Milky Way have been found to be neighbors - the distance between them is approximately 3.5 billion light years. Astronomers do not exclude the possibility that in the near future these two cosmic bodies will collide, forming a complex stellar structure. According to one version, it is precisely because of the approach to such a gravitational giant that the movement of planetary systems in our galaxy is constantly accelerating, and the stars are becoming hotter and more active.

Supermassive black holes are actually white

At the very beginning of the article, a very sensitive issue was raised: the color in which the most powerful quasars appear before us can hardly be called black. Even the simplest photograph of any galaxy can be seen with the naked eye that its center is a huge white dot. Why then do we think it is a supermassive black hole? Photos taken through telescopes show us a huge cluster of stars that are attracted to the core. Planets and asteroids that orbit nearby reflect due to their close proximity, thereby multiplying all the light present nearby. Since quasars do not pull in all neighboring objects at lightning speed, but only hold them in their gravitational radius, they do not disappear, but begin to glow even more, because their temperature is rapidly rising. As for ordinary black holes that exist in outer space, their name is completely justified. The dimensions are relatively small, but the force of gravity is colossal. They simply “eat up” the light, without releasing a single quantum from their banks.

Cinema and a supermassive black hole

Gargantua - humanity began to widely use this term in relation to black holes after the film “Interstellar” was released. Looking at this picture, it is difficult to understand why this particular name was chosen and where the connection is. But in the original script they planned to create three black holes, two of which would be called Gargantua and Pantagruel, taken from the satirical novel. After the changes were made, only one “rabbit hole” remained, for which the first name was chosen. It is worth noting that in the film the black hole is depicted as realistically as possible. So to speak, the design of its appearance was carried out by the scientist Kip Thorne, who was based on the studied properties of these cosmic bodies.

How did we know about black holes?

If it were not for the theory of relativity, which was proposed by Albert Einstein at the beginning of the twentieth century, no one would probably even pay attention to these mysterious objects. A supermassive black hole would be regarded as an ordinary cluster of stars in the center of the galaxy, and ordinary, small ones would go completely unnoticed. But today, thanks to theoretical calculations and observations that confirm their correctness, we can observe such a phenomenon as the curvature of space-time. Modern scientists say that finding a “rabbit hole” is not so difficult. Around such an object, matter behaves unnaturally; it not only contracts, but sometimes even glows. A bright halo forms around the black dot, which is visible through a telescope. In many ways, the nature of black holes helps us understand the history of the formation of the Universe. At their center there is a point of singularity, similar to the one from which the entire world around us previously developed.

It is not known for certain what can happen to a person who crosses the event horizon. Will gravity crush him, or will he end up in a completely different place? The only thing that can be said with complete confidence is that the gargantua slows down time, and at some point the clock hand finally and irrevocably stops.

The film Interstellar, released in early November, can rightfully be considered the main event of the season. And not only cinematic. The events shown in the film - space flights through hyperspace, falling into black holes and time travel - caused heated discussions both among science fiction fans and in pseudo-scientific circles. What is not surprising is that the famous theoretical physicist Kip Thorne acted as a consultant for the film. And where it comes to modern theoretical physics, it often turns out that what was just yesterday a frenzied fantasy today turns out to be a respectable scientific theory.
*Caution, the text contains spoilers.

Mole Hole

The main events of the film begin with the flight of the main characters through a wormhole that unfolded near Saturn. Physically, it is a tunnel connecting two remote regions of space-time. These areas can either be in the same universe or connect different points of different universes (within the concept of a multiverse). Depending on the possibility of returning through the hole, they are divided into passable and impassable. Impassable holes quickly close and prevent a potential traveler from making the return journey.

Solutions to wormhole-type general relativity equations were first discovered in 1916 by Ludwig Flamm. In the 1930s, Albert Einstein and Nathan Rosen became interested in them, and later John Wheeler. However, all of these wormholes were impassable. It wasn't until 1986 that Kip Thorne came up with a traversable wormhole solution.

From a mathematical point of view, a wormhole is a hypothetical object obtained as a special non-singular (finite and physically meaningful) solution to the equations of Albert Einstein’s general theory of relativity (GTR). Typically, wormholes are depicted as a bent two-dimensional surface. You can get from one side to the other by moving in the usual way. Or you can make a hole and connect both sides with a tunnel. In the visual case of two-dimensional space, it can be seen that this allows one to significantly reduce the distance.

In two dimensions, the throats of a wormhole - the holes from which the tunnel begins and ends - are shaped like a circle. In three dimensions (as in the film), the mouth of a wormhole looks like a sphere. Such objects are formed from two singularities in different regions of space-time, which in hyperspace (space of higher dimension) are pulled towards each other to form a hole. Since the hole is a space-time tunnel, you can travel through it not only in space, but also in time.

In Interstellar, the hole was traversable and connected different galaxies in the Universe. But in order to return back through it, the wormhole must be filled with matter with a negative average mass density, preventing the tunnel from closing. There are no elementary particles known to science that have such properties. However, they could probably be part of dark matter.

The Planck length is approximately 1.62x10 -35 meters, which is 2x10 20 times less than the “diameter” of a proton. The numerical value of Planck units (length, mass, time and others) is obtained from four fundamental physical constants and outlines the limit of applicability of modern physics.

It is believed that such a wormhole could be trapped in quantum foam, and then expanded and made potentially suitable for travel through hyperspace. Such foam represents fluctuations of space on Planck length scales, where the laws of classical general relativity do not work, since quantum effects must be taken into account.

Another way to create a wormhole is to stretch one region of space, forming a hole with a singularity that, in hyperspace, reaches another region of space. In both cases, it is proposed to maintain the passage of the hole by passing matter with a negative mass density through it. Such projects do not contradict GTR.

Exoplanets and time dilation

After flying through the wormhole, space travelers are sent to exoplanets that are potentially habitable according to information received from reconnaissance missions. For a planet to be at least potentially suitable for human life, it must have stable light, temperature and gravitational regimes similar to those on Earth. The pressure in the atmosphere must be comparable to that on Earth, and the chemical composition must be suitable for life for at least some terrestrial organisms. A prerequisite is the presence of water. All this imposes certain restrictions on the mass and volume of the planet, as well as its distance to the star and orbital parameters.

Currently, the most favorable time travel for humans has been created in Earth orbit. The longer cosmonauts and astronauts stay aboard the International Space Station, which orbits the planet at more than seven kilometers per second, the slower (compared to earthlings on the surface) they age. The time travel record belongs to Sergei Krikalev, who in more than 803 days moved into the future by approximately 0.02 seconds.

At the same time, the first of the planets (Miller) turned out to be located very close to the supermassive black hole Gargantua with a mass of 100 million suns and 10 billion light years away from Earth. The radius of the hole is comparable to the radius of the Earth's orbit around the Sun, and the accretion disk surrounding it would extend far beyond the orbit of Mars. Due to the black hole's strong gravitational field, one hour spent on the surface of Miller's planet is equivalent to seven years on Earth.

Not surprising, says theoretical physics, this is due to the effect of time dilation in the strong gravitational field of the black hole in which the planet is located. In the special theory of relativity (STR) - the theory of the motion of bodies at near-light speeds - time dilation is observed in moving objects. And in general relativity, which is a generalization of special relativity taking into account gravity, there is an equivalence of inertia and gravity, the long-term consequence of which is gravitational time dilation.

Supermassive black hole

After unsuccessful missions on exoplanets, the hero Matthew McConaughey (along with a robot) is sucked into a supermassive black hole by Gargantua. Moreover, neither McConaughey’s hero nor his robot were torn into a thousand little Matthews and robots by the monstrous gravity when approaching the hole. However, modern physics has an explanation here too.

Einstein based general relativity on the local equivalence of the fields of acceleration and gravity. It can be easily illustrated using the example of a laboratory inside a falling elevator. All objects inside such an elevator will fall with it with the same acceleration, and their relative accelerations will be zero. In this case, the situation can be described in two reference systems. In the first, inertial and connected to the Earth, the elevator falls under the influence of the Earth's gravity. In the second, associated with the elevator (non-inertial), there is no gravitational field. If there is an observer inside the elevator, then he is not able to determine in which field: acceleration or gravity, he is. It turns out that in the local sense (when the acceleration of gravity has approximately the same values in a given region of space, that is, the gravitational field is homogeneous) inertia and gravity are equivalent.

A black hole is a massive object, the gravitational attraction of which, according to the classical version of general relativity, does not allow matter to leave its boundaries. The hole's boundary with the surrounding space is called the event horizon. Having passed through it, the body, as it is believed, cannot return back (at least in the same way).

There are several scenarios for the formation of such objects. The underlying mechanism involves the gravitational collapse of certain types of stars or matter at the centers of galaxies. It is also possible that they formed during the Big Bang and during the reactions of elementary particles. The existence of black holes is beyond doubt among most scientists.

The strength of the gravitational field (in other words, the value of the acceleration due to gravity) of a black hole decreases with distance from it. This is not noticeable at large distances, where the black hole's field is local, uniform and significant at short distances: different parts of the same extended object fall into the hole with different accelerations, and the object is stretched.

This is exactly how the tidal force of a black hole works. However, there is a loophole here. The tidal force is directly proportional to the mass of the black hole and inversely proportional to the cube of the radius of the event horizon. The radius of the hole's event horizon grows in proportion to its mass. Therefore, in order of magnitude, the tidal force is inversely proportional to the square of the hole's mass. For ordinary black holes, enormous values of tidal forces are obtained, while for supermassive ones they are not so large, which is what the heroes of Interstellar took advantage of.

Hyperspace

Inside a spinning black hole, Matthew McConaughey's hero (and his robot) have discovered a fifth-dimensional universe. And here, frankly, they were lucky - if the black hole had not been rotating, the travelers would have continued moving towards its center - the singularity, and in this case the ending of the film would have been completely different.

Mathematically, the concept of physical hyperspace arose at the end of 1910, when Theodor Kaluza embedded the four-dimensional space of General Relativity into the five-dimensional one, and thereby introduced a new dimension. Typically, in theories with extra dimensions, the dimensions of the observable universe along the new dimensions are so small that they have almost no effect on the other four.

General relativity allows for the possibility of solutions to Einstein's equations, for example, in the form of the Kerr metric, the analytical properties of which allow one to escape from the singularity. Such solutions have unusual properties, in particular, they imply the possibility of the existence inside a black hole of special space-time trajectories that violate the usual cause-and-effect relationships.

It can be assumed that McConaughey's hero (and his robot) managed to penetrate such a black hole, escape its singularity and travel inside it along a special trajectory that led him to a new universe. In it, the geometry turned out to be locally arranged in such a way that four dimensions are spatial and simultaneous. Formally, this does not contradict GTR.

And although a person, apparently, is capable of perceiving only three spatial and one time dimensions, in the film the main character in the new universe received the opportunity not only to travel through the time dimension, but also to observe projections of a four-dimensional one in three-dimensional space.

"The Gravity Equation"

While Matthew McConaughey (along with the robot) flies through exoplanets and into a black hole, the professor who remains on earth, played by Michael Caine, is trying to solve a certain “gravity equation” that would allow him to connect quantum mechanics and general relativity into one theory and thereby understand the physics of the wormhole and black hole.

Gribov-Hawking radiation suggests the evaporation of a black hole due to quantum fluctuations associated with the formation of pairs of virtual particles. One particle from such a pair flies away from the black hole, and the other - with negative energy - “falls” into it. For the first time, the Soviet theoretical physicist Vladimir Gribov spoke about the possibility of such a phenomenon. And in the first half of the 1970s, after a visit to the USSR, Stephen Hawking published a paper in which he predicted the existence of radiation from black holes (called Hawking radiation in English-language literature or Gribov-Hawking in Russian-language literature).

And, I must say, Michael Caine’s hero is not suffering alone. Creating a universal theory connecting general relativity and quantum mechanics is the main task of most modern mathematical physicists - specialists in string theory. The main task of the theory is to unify all four known interactions: strong, weak, electromagnetic and gravitational. The first three are described by quantum field theory (QFT), a mathematical model of modern particle physics, and the last by general relativity. At the same time, General Relativity as a whole does not contradict QFT, since it speaks of phenomena on other length and energy scales. But if GR deals with cosmological objects of huge masses, then QFT is applicable at the subatomic level.

The problem is that both theories conflict with each other on Planck scales, since on them quantum corrections need to be taken into account in general relativity. Thus, in a black hole, quantum effects lead to its evaporation. The quantum version of general relativity, obtained in a similar way to QFT, turns out to be non-renormalizable, that is, the observed quantities cannot be made finite. Most of the research in this area is devoted to solving this issue. String theory itself (M-theory) is based on the assumption of the existence on Planck scales of hypothetical one-dimensional objects - strings, the excitations of which are interpreted as elementary particles and their interactions.

Interstellar director Christopher Nolan explains the basics of quantum physics to Matthew McConaughey, the essence of the scene

In this article, we'll highlight some of the key frames Double Negative created, as well as the science behind them. Please note that the following material may contain spoilers.

Creation of a black hole

Creating waves

Anne Hathaway as Amelia on the Water Planet

Inside the tesseract

Image drawn by Kip Thorne explaining what a brane and membrane are

Kip Thorne's formulas explaining gravity in four and five dimensions. Notice that here “our” brane is sandwiched between two alternate realities or other branes.

But how to shoot it?

Nolan's insistence that actors interact with their surroundings when filming also applied to the tesseract. After falling into a black hole, Cooper finds himself in a four-dimensional space in which he can see any objects and their “thread” of time. “Chris said that even though it was a very abstract concept, he really wanted to build something that we could actually film,” says Franklin. “He wanted to see Matthew physically interacting with the threads.” time, in real space, and not dangling in front of a green screen.”

But some moments forced Double Negative to go completely digital visual effects - such as Cooper's movement through the tesseract tunnels. “We didn’t have enough tesseract sections to capture this movement, so we filmed Matthew with projection screens around him showing the pre-production rendering of the scene, so he had something to interact with,” says Franklin. The actors absolutely loved it all because, as opposed to shooting on a green screen, they had something to look at. Later we replaced this version with a high-quality final version, only leaving the pre-finish version in some moments, since it was simply out of focus and was not visible.”

Another challenging part, according to Franklin, was when Cooper interacts with the dust and draws binary code on the floor during the storm. “We had to work with Matthew's movements on the set in the volume of the tesseract and have them interact with something that actually made those shapes appear on the floor in the room in front of him.”

The recently released visually arresting film Inrestellar is based on real-life scientificconcepts, such as rotating black holes, wormholes and time dilation.

But if you are not familiar with these concepts, you may be a little confused while watching.

In the film, a team of space explorers goes to extragalactic travel through a wormhole. On the other side, they find themselves in a different solar system with a rotating black hole instead of a star.

They are in a race against space and time to complete their mission. This kind of space travel may seem a little confusing, but it is based on basic principles of physics.

Here are the main ones 5 concepts of physics things you need to know to understand Interstellar.

Artificial gravity

The biggest problem we humans face during long-term space travel is weightlessness. We were born on Earth and our bodies have adapted to certain gravitational conditions, but when we are in space for a long time, our muscles begin to weaken.

The heroes in the movie Interstellar also face this problem.

To cope with this, scientists are creating artificial gravity in spacecraft. One way to do this is to spin up the spaceship, just like in the movie. The rotation creates a centrifugal force that pushes objects toward the outer walls of the ship. This repulsion is similar to gravity, only in the opposite direction.

This is a form of artificial gravity you experience when you are driving around a small radius curve and feel as if you are being pushed outward, away from the center point of the curve. In a spinning spaceship, the walls become your floor.

Rotating black hole in space

Astronomers, albeit indirectly, have observed in our Universe rotating black holes. Nobody knows what's at the center of a black hole, but scientists have a name for it -singularity .

Rotating black holes distort the space around them differently than stationary black holes.

This distortion process is called "inertial frame entrainment" or the Lense-Thirring effect, and it affects how the black hole will look by distorting space, and more importantly the space-time around it. The black hole you see in the movie is enoughvery close to the scientific concept.

The spaceship Endurance is heading towards Gargantua - fictional supermassive black hole with a mass 100 million times greater than the Sun.
It is 10 billion light years away from Earth and has several planets orbiting it. Gargantua spins at an astonishing 99.8 percent of the speed of light.
Garagantua's accretion disk contains gas and dust with the temperature of the Sun's surface. The disk supplies the Gargantua planets with light and heat.

The complex appearance of the black hole in the film is due to the fact that the image of the accretion disk is distorted by gravitational lensing. Two arcs appear in the image: one formed above the black hole, and the other below it.

Mole Hole

The wormhole or wormhole used by the crew in Interstellar is one of the phenomena in the film whose existence has not been proven. It is hypothetical, but very convenient in the plots of science fiction stories where you need to overcome a large space distance.

Just wormholes are a kind of shortest path through space. Any object with mass creates a hole in space, which means space can be stretched, warped, and even folded.

A wormhole is like a fold in the fabric of space (and time) that connects two very distant regions, which helps space travelers travel a long distance in a short period of time.

The official name for a wormhole is an "Einstein-Rosen bridge" since it was first proposed by Albert Einstein and his colleague Nathan Rosen in 1935.

In 2D diagrams, the mouth of a wormhole is shown as a circle. However, if we could see the wormhole, it would look like a sphere.
On the surface of the sphere, a gravitationally distorted view of space on the other side of the “hole” would be visible.
The dimensions of the wormhole in the film: 2 km in diameter and the transfer distance is 10 billion light years.

Gravitational time dilation

Gravitational time dilation is a real phenomenon observed on Earth. It arises because time relative. This means that it flows differently for different coordinate systems.

When you are in a strong gravitational environment, time moves slower for you compared to people in a weak gravitational environment.

If you are near a black hole, as in the movie, your coordinate system, and therefore your perception of time, is different from that of someone on Earth. This is because the gravitational pull of a black hole is stronger the closer you are to it.

According to Einstein's equation, time moves slower in higher gravitational fields. The same thing happens on a planet close to a black hole: the clock ticks slower than on a spacecraft orbiting further away.
The presence of mass bends the membrane, like a rubber sheet.
If enough mass is concentrated at one point, a singularity is formed. Objects approaching the singularity pass through the event horizon, from which they never return.

To you, a minute near a black hole would last 60 seconds, but if you could look at a clock on Earth, a minute would last less than 60 seconds. It means that you will age slower than people on Earth, and the stronger the gravitational field you are in, the more time slows down.

This plays an important role in the film when explorers encounter a black hole at the center of another solar system.

Fifth Dimensional Universe

Albert Einstein devoted the last 30 years of his life to developing " theories of everything", which would combine the mathematical concepts of gravity with the other three fundamental forces of nature: the strong force, the weak force and the electromagnetic force. He, like other physicists, failed to do this.

Some physicists believe that the only way to solve this mystery is to perceive our Universe as 5-dimensional, not 4-dimensional, as Einstein proposed in the theory of relativity, which combines three-dimensional space with one-dimensional time.

In the film, our Universe is presented in 5 dimensions, and gravity plays an important role in all of this.

Our three-dimensional Universe can be imagined as a flat membrane (or “brane”) floating in four-dimensional hyperspace.

Trailer "Interstellar" 2014