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 is 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
I will try to answer a few questions that viewers have about the film.
1) Why does Gargantua's black hole look like this in the film?
The film Interstellar is the first feature film in the history of cinema to visualize a black hole based on a physical and mathematical model. The simulation was carried out by a team of 30 people (Paul Franklin's visual effects department) in collaboration with Kip Thorne, a world-renowned theoretical physicist known for his work in the theory of gravity, astrophysics and quantum measurement theory. About 100 hours were spent on one frame, and in total about 800 terabytes of data were spent on the model.
Thorne not only created a mathematical model, but also wrote specialized software (CGI), which made it possible to build a computer visualization model.
Here's what Thorne came up with:
Of course, it is fair to ask: is Thorne's simulation a first in the history of science? And is Thorne's image something never seen before in the scientific literature? Of course no.
Jean Pierre Luminet of the Paris-Mudon Observatory, Department of Relativistic Astrophysics and Cosmology, also internationally renowned for his work in the field of black holes and cosmology, is one of the first scientists to image a black hole using computer simulation. In 1987, his book “Black Holes: A Popular Introduction” was published where he writes:
“The first computer images of a black hole surrounded by an accretion disk were obtained by me (Luminet, J.-P. (1979): Astron. Astrophys.). More refined calculations were carried out by Marck (Marck, J.-A. (1993): Class. Quantum Grav) both for the Schwarzschild metric and for the case of a rotating black hole. Plausible images - that is, calculated taking into account the curvature of space, redshift and physical properties of the disk - can be obtained for an arbitrary point, even located inside the event horizon. A movie was even created showing how these distortions change as one moves along a timelike trajectory around a black hole (Delesalle, Lachieze-Rey and Luminet, 1993). The drawing is one of his frames for the case of movement along a suspended parabolic trajectory"
Explanation of why the image turns out this way:
“Due to the curvature of space-time in the vicinity of the black hole, the image of the system differs significantly from the ellipses that we would see if we replaced the black hole with an ordinary low-mass celestial body. The radiation from the upper side of the disk forms a direct image, and due to strong distortion we see "The entire disk (the black hole does not block the parts of the disk behind it from us). The lower part of the disk is also visible due to the significant bending of light rays."
Lumine's image is surprisingly reminiscent of Thorne's result, which he obtained more than 30 years after the Frenchman's work!
Why is it that in other numerous visualizations: both in articles and popular science films, a black hole can often be seen completely different? The answer is simple: computer “drawing” of a black hole based on a mathematical model is a very complex and time-consuming process that often does not fit into modest budgets, so the authors most often make do with the work of a designer rather than a physicist.
2) Why is Gargantua’s accretion disk not as spectacular as can be seen in numerous pictures and popular science films? Why couldn't the black hole be shown brighter and more impressive?
I'll combine this question with the following:
3) It is known that the accretion disk of a black hole is a source of very intense radiation. The astronauts would simply die if they approached the black hole.
And indeed it is. Black holes are the engines of the brightest, highest energy sources of radiation in the Universe. According to modern concepts, the heart of quasars, which sometimes shine brighter than hundreds of galaxies combined, is a black hole. With its gravity, it attracts huge masses of matter, forcing it to compress into a small area under unimaginably high pressure. This substance heats up, nuclear reactions take place in it, emitting powerful X-ray and gamma radiation.
Here's how the classic black hole accretion disk is often drawn:
If Gargantua were like that, then such an accretion disk would kill astronauts with its radiation. The accretion at Thorne's black hole is not so dense and massive; according to his model, the temperature of the disk is no higher than that of the surface of the Sun. This is largely due to the fact that Gargantua is a supermassive black hole, weighing at least 100 million solar masses, with a radius of one astronomical unit.
This is not just a supermassive, but an ultramassive black hole. Even the black hole in the center of the Milky Way has, according to various estimates, a mass of 4-4.5 million solar masses.
Although Gargantua is far from a record holder. For example, the hole in the galaxy NGC 1277 has the mass of 17 billion suns.
The idea of imagining such an experiment, in which people explore a black hole, has bothered Thorne since the 1980s. Already in his book “Black holes and folds of time. The Audacious Legacy of Einstein, published in 1990, Thorne examines a hypothetical model of interstellar travel in which researchers study black holes, wanting to get as close as possible to the event horizon to better understand its properties.
Researchers start with a small black hole. It does not suit them at all because the tidal forces it creates are too great and dangerous for life. They change the object of study to a more massive black hole. But she doesn’t satisfy them either. Finally, they head towards the giant Gargantua.
Gargantua is located near the quasar 3C273 - which allows you to compare the properties of the two holes.
Watching them, researchers wonder:
"The difference between Gargantua and 3C273 seems surprising: why doesn't Garnatua, at a thousand times its mass and size, have such a round donut of gas and giant quasar jets?"
Gargantua's accretion disk is relatively cool, not massive, and does not emit as much energy as a quasar does. Why?
"After telescopic research, Bret finds the answer: every few months, a star in the orbit of the central hole 3C273 comes close to the horizon and is torn apart by the tidal forces of the black hole. The remains of the star, with a mass of approximately 1 solar mass, are splashed in the vicinity of the black hole. Gradually, internal friction drives the spraying gas inside This fresh gas compensates for the gas that the donut is constantly supplying to the hole and the jets, so the donut and the jets maintain their gas reserves and continue to shine brightly.
Bret explains that the stars can come close to Gargantua. But because Gargantua is much larger than 3C273, its tidal forces above the event horizon are too weak to tear the star apart. Gargantua swallows stars whole without splashing their entrails into the surrounding donut. And without the donut, Gargantua cannot create jets and other features of the quasar."
For a massive radiating disk to exist around a black hole, there must be a building material from which it can form. In a quasar, these are dense gas clouds very close to the black hole of the star. Here is the classic model for the formation of an accretion disk:
In Interstellar, it is clear that there is simply nothing for a massive accretion disk to emerge from. There are no dense clouds or nearby stars in the system. If there was anything, it was all eaten long ago.
The only thing Gargantua is content with is low-density clouds of interstellar gas, creating a weak, “low-temperature” accretion disk that does not radiate as intensely as classical disks in quasars or binary systems. Therefore, the radiation from Gargantua's disk will not kill astronauts.
Thorne writes in The Science of Interstellar:
“A typical accretion disk has very intense X-ray, gamma-ray and radio emission. So strong that it will fry any astronaut who decides to be nearby. The Gargantua disk shown in the film is an extremely weak disk. “Weak” - not by human standards, of course, but by the standards of typical quasars. Instead of being heated to hundreds of millions of degrees, as quasar accretion disks are heated, Gargantua's disk is heated only a few thousand degrees, about the same as the surface of the Sun. It emits a lot of light, but emits almost no X-rays or gamma-rays. rays. Such disks can exist in the late stages of the evolution of black holes. Therefore, the Gargantua disk is quite different from the picture that you can often see on various popular astrophysics resources."
Is Kip Thorne the only one who suggested the existence of cold accretion disks around black holes? Of course no.
Cold accretion disks of black holes have been studied in the scientific literature for a long time:
According to some data, the supermassive black hole at the center of the Milky Way, Sagittarius A* (Sgr A*), has just the same cold accretion disk:
An inactive black hole may exist around our central black hole. cold accretion disk, remaining (due to low viscosity) from the “turbulent youth” of Sgr A*, when the accretion rate was high. Now this disk “sucks” hot gas, preventing it from falling into the black hole: the gas settles in the disk at relatively large distances from the black hole.
(c) Close stars and an inactive accretion disc in Sgr A∗: eclipses and flares
Sergei Nayakshin1 and Rashid Sunyaev. // 1. Max-Planck-Institut fur Astrophysik, Karl-Schwarzschild-Str. Garching, Germany 2. Space Research Institute, Moscow, Russi
Or Cygnus X-1:
A spectral and temporal analysis of a large number of observations by the RXTE observatory of the accreting black holes Cygnus X-1, GX339-4 and GS1354-644 in a low spectral state during 1996-1998 was performed. For all three sources, a correlation was found between the characteristic frequencies of chaotic variability and spectral parameters - the slope of the spectrum of Comptonized radiation and the relative amplitude of the reflected component. The relationship between the amplitude of the reflected component and the slope of the Comptonization spectrum shows that the reflecting medium ( cold accretion disk) is the main supplier of soft photons to the field of Comptonization.
(c) Report at SPIE organization Conference "Astronomical Telescopes and Instrumentation", 21-31 March 2000, Munich, Germany
Interaction Between Stars and an Inactive Accretion Disc in a Galactic Core // Vladimır Karas. Astronomical Institute, Academy of Sciences, Prague, Czech Republic and
(c) Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic // Ladislav Subr. Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic
Quiet black holes are similar to the hole in the Andromeda Nebula, one of the first supermassive black holes discovered. Its mass is about 140 million solar masses. But they found it not by strong radiation, but by the characteristic movement of stars around this area. The characteristic “quasar” radiation from the core of these galaxies. And astrophysicists came to the conclusion that matter simply does not fall into this black hole. This situation is typical for “quiet” galaxies, like the Andromeda Nebula and the Milky Way.
Galaxies with active black holes are called active, or Seyfert, galaxies. Seyfert galaxies account for approximately 1% of all observed spiral galaxies.
How a supermassive black hole was found in the Andromeda Nebula is well shown in the BBC popular science film “Supermassive Black Holes.”
4) Black holes are known to have deadly tidal forces. Wouldn't they tear apart both the astronauts and Miller's planet, which in the film is too close to the event horizon?
Even the laconic Wikipedia writes about one important property of a supermassive black hole:
“Tidal forces near the event horizon are significantly weaker due to the fact that the central singularity is located so far from the horizon that a hypothetical astronaut traveling to the center of a black hole would not feel the effects of extreme tidal forces until he is very deep into it. »
Any scientific and popular sources that describe the properties of supermassive black holes agree with this.
The location of the point at which tidal forces reach such a magnitude that they destroy an object that falls there depends on the size of the black hole. For supermassive black holes, such as those located at the center of the Galaxy, this point lies within their event horizon, so a hypothetical astronaut can cross their event horizon without noticing any deformation, but after crossing the event horizon, his fall towards the center of the black hole is inevitable . For small black holes, whose Schwarzschild radius is much closer to the singularity, tidal forces will kill the astronaut before he reaches the event horizon
(c) Schwarzschild black holes // General relativity: an introduction for physicists. - Cambridge University Press, 2006. - P. 265. - ISBN 0-521-82951-8.
Of course, Gargantua's mass was chosen so as not to tear the astronauts apart by the tides.
It is worth noting that Thorne's 1990 Gargantua is somewhat more massive than in Interstellar:
“Calculations have shown that the larger the hole, the less thrust the rocket needs to keep it on a circumference of 1.0001 event horizon. For a painful but tolerable thrust of 10 Earth gs, the mass of the hole must be 15 trillion solar masses. The closest of these holes is called Gargantua, located 100,000 light-years from our galaxy and 100 million light-years from the Virgo galaxy cluster around which the Milky Way orbits. In fact, it is located near the quasar 3C273, 2 billion light years from the Milky Way...
By going into Gargantua's orbit and taking the usual measurements, you are convinced that its mass is indeed equal to 15 trillion solar masses and that it rotates very slowly. From this data you calculate that the circumference of its horizon is 29 light years. Finally, he calculates that this is a hole, the vicinity of which you can explore, experiencing permissible tidal forces and acceleration!"
In the 2014 book “The Science of Interstellar,” where Kip Thorne describes the scientific aspects of working on the film, he already gives a figure of 100 million solar masses - but noting that this is the minimum mass that a “comfortable” one can have in relation to tidal influences. black hole forces.
5) How can Miller's planet exist so close to a black hole? Will it be torn apart by tidal forces?
Astronomer Phil Plaint, known as "Bad Astronomer" for his unbridled skepticism, simply couldn't get past Interstellar. Moreover, before that, he viciously destroyed many acclaimed films, for example “Gravity,” with his drilling skepticism.
“I was really looking forward to Interstellar... But what I saw was terrible. This is a complete failure. I really, really didn’t like it.”- he writes in his article dated November 6th.
Phil says that the scientific part of the film is complete bullshit. Which, even in a hypothetical framework, cannot correspond to modern scientific ideas. He especially traveled around Miller's planet. According to him, a planet can stably orbit such a black hole, but its orbit must be at least three times the size of Gargantua itself. The clock will run slower than on Earth, but only by 20 percent. The stability of a planet close to a black hole, as shown in the film, is an impossible fantasy. In addition, it will be completely torn apart by the tidal forces of the black hole.
But on November 9, Plaint appears with a new article. He calls her Follow-Up: Interstellar Mea Culpa. The incomparable scientific critic decided to repent.
“I screwed up again. But no matter the magnitude of my mistakes, I always try to admit them. In the end, science itself forces us to admit our mistakes and learn from them!”
Phil Plaint admitted that he made mistakes in his thinking and came to the wrong conclusions:
“In my review, I talked about Miller's planet orbiting close to a black hole. An hour spent on the planet is equal to seven Earth years. My claim was that with such time dilation, a stable planetary orbit would be impossible.
And this is true... for a non-rotating black hole. My mistake was this. that I didn't use the correct equations for a black hole that was spinning fast! This greatly changes the picture of space-time near the black hole. Now I understand that a stable orbit of this planet around a black hole may well exist, and so close to the event horizon that the time dilation indicated in the film is possible. In general, I was wrong.
I also stated in my original analysis that gravitational tides would tear this planet apart. I consulted a couple of astrophysicists who also said that Gargantua's tides would probably destroy the planet, but this has not yet been mathematically confirmed. They are still working on solving this problem - and as soon as it is solved, I will publish the solution. I myself cannot say whether I was right or wrong in my analysis - and even if I was right, my considerations still only applied to a non-rotating black hole, so they do not apply to this case.
To solve such a problem, many mathematical problems need to be discussed. But I don't know exactly how far Miller's planet was from Gargantua, and so it's very difficult to say whether the tides would have destroyed it or not. I have not yet read the book by physicist and executive producer of the film Kip Thorne “The Science of Interstellar” - I think it will shed light on this problem.
However, I was wrong about the stability of the orbit - and I now consider it necessary to cancel this complaint about the film.
So, to summarize: the physical picture shown in the movie near a black hole is actually consistent with science. I made a mistake for which I apologize.
Ikjyot Singh Kohli, a theoretical physicist from Yor University, provided solutions to equations on his page, proving that the existence of Miller's planet is quite possible.
He found a solution in which the planet would exist under the conditions demonstrated in the film. But he also discussed the problem of tidal forces, which should supposedly tear the planet apart. His solution shows that tidal forces are too weak to tear it apart.
He even substantiated the presence of giant waves on the surface of the planet.
Singh Kohli's thoughts with examples of equations are here:
This is how Miller Thorne shows the location of the planet in his book:
There are points at which the orbit will not be stable. But Thorne also found a stable orbit:
Tidal forces do not tear the planet apart, but deform it:
If a planet rotates around a source of tidal forces, then they will constantly change their direction, deforming it differently at different points in the orbit. In one position, the planet will be flattened from east to west and elongated from north to south. At another point in the orbit it is compressed from north to south and stretched from east to west. Since Gargantua's gravity is very strong, the changing internal deformations and friction will heat the planet, making it very hot. But as we saw in the film, Miller's planet looks very different.
Therefore, it would be fair to assume that the planet always faces one side towards Gargantua. And this is natural for many bodies that rotate around a stronger gravitating object. For example, our Moon, many satellites of Jupiter and Saturn are always turned to the planet with only one side.
Thorne also made another important point:
“If you look at Miller’s planet from Mann’s planet, you can see how it revolves around Gargantua with an orbital period of 1.7 hours, covering almost a billion kilometers during this time. That's about half the speed of light! Due to time dilation for the Ranger crew, this period is reduced to a tenth of a second. It's very fast! And isn't that much faster than the speed of light? No, because in the reporting system of the vortex-like moving space around Gargantua, the planet moves slower than light.
In my scientific model of the film, the planet is always turned to the black hole with one side, and rotates at breakneck speed. Will centrifugal forces tear the planet apart due to this speed? No: she is saved again by the rotating vortex of space. The planet will not feel destructive centrifugal forces, since space itself rotates with it at the same speed."
6) How are such giant waves possible on the surface of Miller’s planet?
Thorne answers this question like this:
“I made the necessary physical calculations and found two possible scientific interpretations.
Both of these solutions require that the position of the planet's rotation axis be unstable. The planet should wobble in a certain range, as shown in the figure. This occurs under the influence of Gargantua's gravity.
When I calculated the period of this rocking, I got a value of about an hour. And this coincided with the time that Chris chose - who had not yet known about my scientific interpretation!
My second model is a tsunami. The tidal forces of Gargantua can deform the crust of Miller's planet, with the same period (1 hour). These deformations can create very strong earthquakes. They can cause tsunamis that will far exceed any ever seen on Earth."
7) How are such incredible maneuvers of Endurance and Ranger in Gargantua orbit possible?
1) Endurance is moving in a parking orbit with a radius equal to 10 times the radius of Gargantua, and the crew heading to Miller is moving at a speed of C/3. Miller's planet moves at 55% of C.
2) The Ranger must slow down from C/3 to lower the orbit and approach Miller Point. It slows down to c/4, and reaches the outskirts of the planet (of course, here you need to follow strict calculations to get there. But this is not a problem for the computer)
The mechanism for such a significant change in speed is described by Thorne:
“Stars and small black holes revolve around giant black holes, like Gargantua. It is they who can create the determining forces that will deviate the Ranger from his circular orbit and direct him down towards Gargantua. A similar gravity maneuver is often used by NASA in the solar system, although it uses the gravity of planets rather than a black hole. The details of this maneuver are not revealed in Interstellar, but the maneuver itself is mentioned when they talk about using a neutron star to slow down the speed."
A neutron star is shown by Thorne in the figure:
Date with a neutron star allows you to change the speed:
“Such an approach can be very dangerous, i.e. The ranger must get close enough to the neutron star (or small black hole) to feel strong gravity. If the braking star or black hole is with a radius smaller than 10,000 km, then the people and the Ranger will be torn apart by tidal forces. Therefore, a neutron star must be at least 10,000 km in size.
I discussed this issue with Nolan during production of the script, suggesting a choice of a black hole or a neutron star. Nolan chose a neutron star. Why? Because he didn’t want to confuse the audience with two black holes.”
“Black holes, called IMBH (Intermediate-Mass Black Holes), are ten thousand times smaller than Gargantua, but a thousand times heavier than ordinary black holes. Cooper needs such a diverter. Some IMBHs are believed to form in globular clusters, and some are found in the cores of galaxies, where giant black holes are found. The closest example is the Andromeda Nebula, the closest galaxy to us. Hidden in the core of Andromeda is a hole similar to Gargantua - approximately 100 million solar masses. When the IMBH passes through a region with a dense stellar population, the effect of “dynamic friction” slows down the speed of the IMBH, and it falls lower and lower, getting closer to the giant black hole. As a result, IMBH finds itself in close proximity to a supermassive black hole. Thus, nature could well have provided Cooper with such a source of gravitational deflection."
For a real-life application of the “gravitational slingshot,” see the example of interplanetary spacecraft, for example, check out the history of the Voyagers.
The science
The recently released visually arresting film Inresttellar is based on real scientific concepts 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 that 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,” as 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 is 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.
The universe is fraught with many mysteries. The structure and features of various objects and the possibility of interplanetary travel attract the attention of not only scientists, but also science fiction fans. Naturally, the greatest attractiveness is that which has unique properties, which, due to various circumstances, has not been sufficiently studied. Such objects include black holes.
Black holes have very high densities and incredibly strong gravitational forces. Even rays of light cannot escape from them. This is why scientists can “see” a black hole only due to the effect it has on the surrounding space. In the immediate vicinity of a black hole, matter becomes hot and moves at very high speed. This gaseous material is called an accretion disk, which looks like a flat, luminous cloud. Scientists observe X-ray radiation from the accretion disk using X-ray telescopes. They also record the enormous speed of movement of stars in their orbits, which occurs due to the high gravity of an invisible object of enormous mass. Astronomers distinguish three classes of black holes:
Black holes with stellar mass
Black holes with intermediate mass,
Supermassive black holes.
A star is considered to have a mass ranging from three to one hundred solar masses. Black holes with hundreds of thousands to several billion solar masses are called supermassive. They are usually located in the center of galaxies.
The second escape velocity or escape velocity is the minimum that must be achieved to overcome gravitational attraction and go beyond the orbit of a given celestial body. For the Earth, the escape velocity is eleven kilometers per second, and for a black hole it is more than three hundred thousand, that’s how strong its gravity is! 
The boundary of a black hole is called the event horizon. An object once inside it can no longer leave this area. The size of the event horizon is proportional to the mass of the black hole. To show how enormous the density of black holes is, scientists give the following figures: a black hole with a mass 10 times greater than the sun would have approximately 60 km in diameter, and a black hole with the mass of our Earth would be only 2 cm. But this only theoretical calculations, since scientists have not yet identified black holes that have not reached three solar masses. Everything that enters the region of the event horizon moves towards the singularity. A singularity, to put it simply, is a place where density tends to infinity. It is impossible to draw a geodesic line entering it through a gravitational singularity. A black hole is characterized by a curvature of the structure of space and time. A straight line, which in physics represents the path of light in a vacuum, becomes curved near a black hole. What physical laws work near the singularity point and directly in it is still unknown. Some researchers, for example, talk about the presence of so-called wormholes, or space-time tunnels, in black holes. But not all scientists agree to admit the existence of such wormhole tunnels.
The theme of space travel and space-time tunnels serves as a source of inspiration for science fiction writers, screenwriters and directors. In 2014, the film Interstellar premiered. A whole group of scientists worked on its creation. Their leader was the famous scientist, specialist in the field of gravity theory and astrophysics - Kip Stephen Thorne. This film is considered one of the most scientific among science fiction films and, accordingly, high demands are placed on it. There has been much debate about the extent to which various aspects of the film correspond to scientific facts. There was even a book published, “The Science of Interstellar,” in which Professor Stephen Thorne explains various scenes from the film from a scientific point of view. He said that much of the film is based on both scientific facts and scientific assumptions. However, there is also simply artistic fiction. For example, the Gargantua black hole is represented as a luminous disk that bends around light. This is not at odds with scientific knowledge, because... It is not the black hole itself that is visible, but only the accretion disk, and light cannot travel in a straight line due to powerful gravity and the curvature of space.
Gargantua's black hole contains a wormhole, which is a wormhole or tunnel through space and time. The presence of such tunnels in black holes is just a scientific assumption, which many scientists do not agree with. It is an artistic fantasy to be able to travel through such a tunnel and return back.
The black hole of Gargantua is a fantasy of the creators of Interstellar, which largely corresponds to real space objects. Therefore, for particularly ardent critics, I would like to remind you that the film is, after all, science fiction, and not popular science. It shows the beauty and greatness of the world that surrounds us, and reminds us of how many unsolved problems we still have. And to demand that a science fiction film accurately reflect scientifically proven facts is somewhat unfair and naive.
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 for me an audiovisual revelation and a real emotional attraction (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 the 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 upward along 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 entire 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 truly 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
