Category Archives: Cinema

Cinema, My books & articles, Sciences

The Warped Science of Interstellar (6/6) : the final equation

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Sequel of the preceding post The Warped Science of Interstellar (5/6)

In november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.
This is the last one of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

Formules

The final equation

At the very end of the film, the scientist’s character called Murph begins to write an equation aimed to solve the problem of the incompatibility between general relativity and quantum mechanics. We can see blackboards covered by diagrams and equations supposed to be a possible way to the « ultimate equation » of a so-called « Theory Of Everything ». If discovered by the scientists, it would eventually help to solve all the problems of humanity. I will not discuss the naivety of such a view, but briefly discuss the question whether the equations on the screen have any meaning.

The complete unification of the four fundamental interactions can be achieved only at very high energy, conditions which prevailed in the very early universe during the so-called « Planck era ».
The complete unification of the four fundamental interactions can be achieved only at very high energy, conditions which prevailed in the very early universe during the so-called « Planck era ».

At first sight we can doubt because the unification of general relativity and quantum mechanics remains unsolved – even if various approaches, such as the loop quantum gravity[1], the string theory[2] (of which the Randall-Sundrum model referred above is a very particular solution) or the non-commutative geometry[3], are intensively explored by theoretical physicists all around the world. Continue reading →

Cinema, Sciences

The Warped Science of Interstellar (5/6) : Time machine and Fifth Dimension

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Sequel of the preceding post The Warped Science of Interstellar (4/6)

In november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.
This is the fifth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

TIME TRAVEL INSIDE GARGANTUA

Interstellar-FLprStills16-2nd-Batch

In the last part of the film, the main character, Cooper, plunges into Gargantua. There, beware the tidal forces breaking anything up ! Indeed in the Schwarzschild geometry, the tidal forces become infinite as r -> 0 ; so, even for a supermassive black hole like Gargantua, once past safely the event horizon and approaching the central singularity, everything will be ultimately destroyed. Happily for the continuation of the story, Gargantua has a high spin, and its lethal singularity has the shape of an avoidable ring. Thus the space-time structure allows Cooper to use the Kerr black hole as a wormhole ; he avoids the ring singularity and transports to another region of space-time. In the movie he ends up in a five-dimensional universe, in which he will be able to go backwards in time and communicate with his daughter by means of gravitational signals.

Inner structure of a rotating black hole with a ring singularity
Inner structure of a rotating black hole with a ring singularity

A lot of research has been done on whether the laws of physics permit travel back in time or not. Black hole physics gives interesting results but no firm answers. As seen in the post The Warped Science of Interstellar (1/6), according to Penrose-Carter diagrams a rotating black hole could connect myriads of wormholes to different parts of the space-time geometry. Since two events can differ in time as well as in space, it would be possible to pass from one given position at a given time, along a carefully chosen trajectory, through a wormhole, and arrive at the same position but at a different time, in the past or future. In other words, the black hole could be a sort of time travel machine.

Noneless a journey back through time is an affront to common sense. It is difficult to accept that a man could travel back through time and kill his grandfather before he has had the time to produce children. For the murderer could not have been born, and could not have murdered him, and so on… Such time paradoxes have been pleasantly presented in the celebrated series of movies Back to the future.

Continue reading →

Cinema, My books & articles, Sciences

The Warped Science of Interstellar (4/6) : Time dilation and Penrose process

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Sequel of the preceding post The Warped Science of Interstellar (3/6)

In november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.
This is the fourth of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

A HUGE TIME DILATION

The elasticity of time is a major consequence of relativity theory, according to which time runs differently for two observers with a relative acceleration – or, from the Equivalence Principle, moving in gravitational fields of different intensities. This well-known phenomenon, checked experimentally to high accuracy, is called « time dilation ».

The celebrated "smooth watches" by Salvador Dali are a nice metaphor of time elasticity predicted by Einstein's relativity theory.
The celebrated “smooth watches” by Salvador Dali are a nice metaphor of time elasticity predicted by Einstein’s relativity theory.

Thus, close to the event horizon of a black hole, where the gravitational field is huge, time dilation is also huge, because the clocks will be strongly slowed down compared to farther clocks. This is one of the most stunning elements of the scenario of Interstellar : on the water planet so close to Gargantua, it is claimed that 1 hour in the planet’s reference frame corresponds to 7 years in an observer’s reference frame far from the black hole (for instance on Earth). This corresponds to a time dilation factor of 60,000. Although the time dilation tends to infinity when a clock tends to the event horizon (this is precisely why no signal can leave it to reach any external observer), at first sight a time dilation as large as 60,000 seems impossible for a planet orbiting the black hole on a stable orbit.

As explained by Thorne in his popular book, such a large time dilation was a « non-negotiable » request of the film director, for the needs of the story. Intuitively, even an expert in general relativity would estimate impossible to reconcile an enormous time differential with a planet skimming up the event horizon and safely enduring the correspondingly enormous gravitational forces. However Thorne did a few hours of calculations and came to the conclusion that in fact it was marginally possible (although very unlikely). The key point is the black hole’s spin. A rotating black hole, described by the Kerr metric, behaves rather differently from a static one, described by the Schwarzschild metric. The time dilation equation derived from the Kerr metric takes the form:

1 – (dτ/dt)2 = 2GMr/c2rho2, where rho2 = r2 + (J/Mc)2cos2θ.

Continue reading →

Cinema, My books & articles, Sciences

The Warped Science of Interstellar (3/6) : Accretion Disk and Tidal Stress

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Sequel of the preceding post The Warped Science of Interstellar (2/6)

In november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.

This is the third of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

VISUALISATION OF THE ACCRETION DISK

Since a black hole causes extreme deformations of spacetime, it also creates the strongest possible deflections of light rays passing in its vicinity, and gives rise to spectacular optical illusions, called gravitational lensing. Interstellar is the first Hollywood movie to attempt depicting a black hole as it would actually be seen by an observer nearby.

For this, the team at Double Negative Visual Effects, in collaboration with Kip Thorne, developed a numerical code to solve the equations of light-ray propagation in the curved spacetime of a Kerr black hole. It allows to describe gravitational lensing of distant stars as viewed by a camera near the event horizon, as well as the images of a gazeous acccretion disk orbiting around the black hole. For the gravitational lensing of background stars, the best simulations ever done are due to Alain Riazuelo[i], at the Institut d’Astrophysique in Paris, who calculated the silhouette of black holes that spin very fast, like Gargantua, in front of a celestial background comprising several thousands of stars.

BH_LMC_APOD-BR
Gravitational lensing produced by a black hole in a direction almost centered on the Large Magellanic Cloud. Above it one easily notices the southernmost part of the Milky Way with, from left to right, Alpha and Beta Centauri, the Southern Cross. The brightest star, close to the LMC is Canopus (seen twice). The second brightest star is Achernar, also seen twice. © Alain Riazuelo, CNRS/IAP

But perhaps the most striking image of the film Interstellar is the one showing a glowing accretion disk which spreads above, below and in front of Gargantua. Accretion disks have been detected in some double-star systems that emit X-ray radiation (with black holes of a few solar masses) and in the centers of numerous galaxies (with black holes whose mass adds up to between one million and several billion solar masses). Due to the lack of spatial resolution (black holes are very far away), no detailed image has yet been taken of an accretion disk ; but the hope of imaging accretion disks around black holes telescopically, using very long baseline interferometry, is nearing reality today via the Event Horizon Telescope[ii]. In the meanwhile, we can use the computer to reconstruct how a black hole surrounded by a disk of gas would look. The images must experience extraordinary optical deformations, due to the deflection of light rays produced by the strong curvature of the space-time in the vicinity of the black hole. General relativity allows the calculation of such an effect. Continue reading →

Cinema, My books & articles, Sciences

The Warped Science of Interstellar (2/6)

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Sequel of the preceding post The Warped Science of Interstellar (1/6)

One year ago, in november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.

This is the second of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

THE FAST-SPINNING BLACK HOLE « GARGANTUA »

Once on the other side of the wormhole, the spaceship and its crew emerge into a three-planets system orbiting around a supermassive black hole called Gargantua. Supermassive black holes, with masses going from one million to several billion solar masses, are suspected to lie in the centers of most of the galaxies. Our Milky Way probably harbors such an object, Sagittarius A*, whose mass is (indirectly) measured as 4 million solar masses (for a review, see Melia[i]). According to Thorne, Gargantua would be rather similar to the still more massive black hole suspected to be located at the center of the Andromeda galaxy, adding up 100 million solar masses[ii]. Its size being roughly proportional to its mass, the radius of such a giant would encompass the Earth’s orbit around the Sun.

CGal_IR_1al
A view of the Galactic Center in X-rays

CGal_*Keck
The analysis of trajectories of stars orbiting around the Galactic Center leads to estimate the mass of the central black hole at about 4 millions solar masses.

m31
The Andromeda Galaxy (M31), located at 2.2 million light-years

coeurM31_HST
Detailed image of the core of Andromeda Galaxy by the Hubble Space Telescope. The central black hole would have 100 million solar masses.

Such enormous black holes are not a science-fiction exaggeration, since we have the observational clues of the existence of « Behemoth » black holes in faraway galaxies. The biggest one yet detected lies in the galaxy NGC 1277, located at 250 million light-years ; its mass could be as large as 17 billion solar masses, and its size would encompass the orbit of Neptune[iii]. Continue reading →

Cinema, Sciences

The Warped Science of Interstellar (1/6)

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One year ago exactly, in november  2014, the Hollywood blockbuster and science-fiction movie Interstellar was released on screens and  much mediatic excitation arose about it.

This is the first of a series of 6 posts devoted to the analysis of some of the scientific aspects of the film, adapted from a paper I published last spring in Inference : International Review of Science.

interstellar-posterInterstellar  tells the adventures of a group of explorers who use a wormhole to cross intergalactic distances and find potentially habitable exoplanets to colonize. Interstellar is a fiction, obeying its own rules of artistic license : the film director Christopher Nolan and the screenwriter, his brother Jonah, did not intended to put on the screens a documentary on astrophysics – they rather wanted to produce a blockbuster, and they succeeded pretty well on this point. However, for the scientific part, they have collaborated with the physicist Kip Thorne, a world-known specialist in general relativity and black hole theory. With such an advisor, the promotion of the movie insisted a lot on the scientific realism of the story, in particular on black hole images calculated by Kip Thorne and the team of visual effects company Double Negative. The movie also refers to many aspects of contemporary science, going from well-studied issues such as warped space, fast-spinning black holes, accretion disks, tidal effects or time dilation, to much more speculative ideas which stem beyond the frontiers of our present knowledge, such as wormholes, time travel to the past, extra-space dimensions or the « ultimate equation » of an expected « Theory of Everything ».

It is the reason why, beyond the subjective appreciations that everyone may have about the fiction story itself, many people – physicists and science journalists – have taken the internet to write articles lauding or criticizing the science shown in the movie. Kip Thorne has written a popular book, The Science of Interstellar [i], to explain how he tried to respect scientific accuracy, despite the sometimes exotic demands of Christopher and Jonah Nolan, ensuring in particular that the depictions of black holes and relativistic effects were as accurate as possible.

The aim of this article is not to write a (inevitably subjective) review of Interstellar as a fiction story, but to decipher some of the scientific notions, which support the framework of the movie.

AN ARTIFICIAL WORMHOLE IN THE SOLAR SYTEM ?

 In the first part of the film, we are told that a « gravitational anomaly », called a wormhole, has been discovered out near Saturn several decades ago, that a dozen habitable planets have been detected on the « other side » and a dozen astronauts sent to explore them. In particular, one system has three potentially habitable planets, and it is now the mission of the hero, Cooper, to pilot a spaceship through the wormhole and find which planet is more suitable for providing humanity a new home off the dying Earth. Continue reading →

Cinema, News, Sciences

Black Hole Imaging (2) : Heads and Tails

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 The thought experiments which have been described in my  previous post Back to the basics are more than an intellectual exercise, because if black holes really exist (and we have strong observational arguments to believe that), then there is a good chance that they will be illuminated by a natural light source. For a black hole or a planet the most obvious form of lighting is a star. This star could, for example, be bound to the black hole in a binary system. Although such systems are common throughout our Galaxy, the corresponding black holes would be impossible to detect by this effect, as their image  by reflected light would be drowned in the intense light of the direct image of the star itself.

A much more interesting situation from an observational point of  view is when the source of light comes from a series of rings of matter in orbit around the black hole.  It is believed that a number of black holes are surrounded by such structures, which are called accretion disks. Saturn’s rings are an excellent example of an accretion disk; they consist of amalgamated pieces of rock and ice which reflect the light of the distant Sun, whereas those of a black hole consist of hot gas brighting by itself (another important difference is that the accretion disk of a black hole is continually being supplied with gas, whereas that surrounding Saturn is the remnant of the primordial Solar System).

Planet Saturn and its rings. One can assume that a black hole accretion disc, although made of hot gas instead of rocks and ice, has a similar shape, namely circular thin rings.
Planet Saturn and its rings. One can assume that a black hole accretion disk, although made of hot gas instead of rocks and ice, has a similar shape, namely circular thin rings.

 The gases fall slowly into the black hole, like water in a whirlpool. As the gas falls towards the black hole it becomes hotter and hotter and begins to emit radiation. This is a good source of light: the accretion rings shine and illuminate the central black hole. One can then ask : what would be the apparent image of the black hole accretion disk ? Continue reading →

Cinema, Sciences

Black Hole Imaging (1/3): Back to the basics

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The centre of the black hearth,
of setting suns on the shore :
ah ! well of magic
Arthur Rimbaud (Illuminations)

As probably all of you already know, the Interstellar movie tells the adventures of a group of explorers who use a wormhole to cross intergalactic distances and find potentially habitable exoplanets to colonize. For the scientific part, the film director, Christopher Nolan,  has collaborated with a colleague of mine, the famous physicist Kip Thorne, a specialist in general relativity and black hole theory.

With such a scientific consultant, the promotion of the movie insisted a lot on the realism of the black hole images calculated by Kip Thorne and the team of visual effects company Double Negative. The most striking one shows a glowing accretion disk appearing above, below  and in front of the black hole.

The simulation of a black hole with thin accretion disk as shown in the Interstellar movie

As soon as the movie was displayed on the screens, a lot of physics blogs have commented in details the “Science of Interstellar”. Kip Thorne himself has published a such entitled popular book, to explain how he tried to respect scientific accuracy despite the sometimes odd demands of Christopher Nolan, ensuring in particular that the depictions of black holes and relativistic effects were as accurate as possible.

destinSince, as soon as 1979, I was the first researcher to perfom numerical calculations and publish the simulated image of a black hole surrounded by a thin accretion disk (you can upload the technical article here), to inaugurate this new blog I’ll devote a series of 3 posts to the basics of black hole imaging. A good part is adapted from a chapter of one of my books, published in French in 2006, Le destin de l’univers – unfortunately not yet available in English. Continue reading →