Black holes and time dilation: The science behind Interstellar! SPOILER ALERT!

 

Not quite long ago, the virtual sphere was abuzz with discussions on the Nolan brothers’ latest blockbuster flick, Interstellar. Within days of its release, the feature film attracted the attention of critics from the scientific realm and otherwise. The general opinion seemed to echo the fact that the movie is an absolute visual masterpiece and bears a multi-layered plot, characteristic of Christopher Nolan’s movies.

The plot of the film has been skilfully crafted through an augmented collaboration between an artist – Christopher Nolan, and world renowned theoretical astrophysicist – Kip Thorne. The plot features a giant black hole called Gargantua, wormholes that permit interstellar travel, spaceships that can escape gravitational fields 130% of Earth’s, to mention a few. Sounds excessively confusing right? However, insight into the science behind Interstellar reveals that most of the events depicted in the movie reel out under the constraints established by the universal physical laws.

Interstellar is set in a dystopian future, with the Earth riddled with famines and disasters and threatened by extinction. A crew of space explorers led by ex-engineer and pilot, Cooper [Matthew McConaughey], venture out to space in search of a planet that can sustain human life. A wormhole mysteriously appears in the solar system close to Saturn and the explorers use it to reach a distant part of the universe with planets which may be favourable for human life.

Wormholes, or Einstein-Rosen bridges, provide a shortcut across space and time. There is no observational evidence for wormholes but Einstein’s theory of general relativity permits for the possibility of wormholes. It is a widely accepted fact that wormholes would collapse as soon as matter would enter it; however, it is also accepted that it is possible to stabilize a traversable wormhole with exotic matter. In the movie, it is suggested that otherworldly beings have placed the wormhole for the scientists on Earth to find. Towards the end, Cooper has an epiphany where he realizes that these beings are humans from the future, who have discovered a way to cut across space and time to aid him and the others in their search for a new home. Scientists observe that in the very distant future, the technology available may permit the creation of warp drives and wormholes.

After two years of travel to the mouth of the wormhole and then through it, the crew successfully makes it to their destination. While passing through the wormhole, Dr. Brand [Anne Hathaway], experiences what she calls the “first handshake”. As revealed later in the movie, the handshake involves a future Cooper, who is now navigating the fifth dimension where time is a physical component. This is consistent with the theory that wormholes allow for time travel, thus enabling him to interact with a past version of his exploration crew. After making it through the wormhole, Cooper travels to Miller’s planet to assess its hospitability. However, the proximity of the planet to the giant black hole Gargantua results in severe gravitational time dilation: each hour on the planet is equivalent to seven years on Earth. On Cooper’s return to the mothership, Endurance, he finds that his crew on board has aged twenty eight years during his four hour visit to the planet. This particular facet is bound to have the audience confused and amused simultaneously.

So how exactly is this possible? To understand this would be to understand the phenomenon of gravitational time dilation. The following facts are critical and are to be noted:

1. Gravity can warp time: Processes close to a gigantic body move slowly [higher gravitational field] compared to processes further away from it. This occurs due to the inherent nature of gravity to morph the fabric of space-time, similar to a stretched out piece of cloth morphing when a heavy ball is placed on it.

2. The mass of a black hole is generally 102-105 times the mass of the sun. As gravity is directly proportional to mass, black holes have very powerful gravitational fields.

A black hole as large as Gargantua would have a gravitational field that is strong enough to cause a drastic time differential. To simplify this explanation, if you were to view the people on Miller’s planet and the people on Earth from an outside frame of reference, you’d see the people on Earth moving incredibly fast and the people on Miller’s planet moving incredibly slowly. This would manifest in the form of a greater extent of elapsed time on Earth as compared to Miller’s planet.

Although a field of this magnitude would generally cause the planets orbiting it to be ripped apart, Kip Thorne explains that it is possible for a planetary body in the vicinity to be sustained if the black hole itself were spinning fast enough. This gravitational force also seems to be the cause of giant waves on Miller’s planet. The tidal forces generated due to gravity would cause the formation of giant solitary waves.

A black hole is created when an object with a large mass is compressed to a tiny size, leading to a very high density. Black holes are characterised by an event horizon. You may have heard this term a few times in the movie itself with another term: singularity. Black holes generally have two layers:

1. The event horizon, a boundary beyond which events cannot affect outside observers. This simply means that the gravity at the boundary is strong enough to prevent even light from escaping.

2. The centre or the singularity, where the gravitational force of the black hole is strongest.

The event horizon is thus the point of no return where nothing can escape, not even light. If you were to observe someone approaching a black hole’s event horizon, the image of the person would appear to be redshifted over time, slow down and ultimately stop. From the perspective of the traveller, time would continue to pass at a normal speed, and would experience no strange effects on crossing the event horizon. They would be torn apart by tidal forces and the gravitational singularity as they fall into the black hole.

This is exactly what happens to Cooper after having detached his spaceship from Endurance, the space station, falls into Gargantua. Although it is impossible to perceive what exactly happens to matter that enters a black hole, it is logical to state that matter would be shredded to bits due to the insanely large amount of gravitational force.

Moreover, Gargantua is surrounded be an accretion disk. An accretion disk is a large disc comprised of dangerously hot gases, and highly energetic X-rays and gamma rays. The energy emanating from this disk provides light and heat for the orbiting planets. The temperature around the disk is immeasurable and the fatality due to this abundance of energy is incomprehensible. So why did Cooper and his spaceship not get fried? Kip Thorne answers this question with a seemingly plausible response, that Gargantua’s disk is anaemic, and not as dangerous as one might understand it to be. This disk is only a remnant of what was previously a hot, turbulent, menacing accretion disk. Although, such a quiescent and cooling disk would not stay stable for long, it was conveniently used in the movie to cater to its environment requirements.

Finally, the most appreciated and stunning component of the movie has scientists, critics, and aficionados quizzical. The questions are aplenty; answers, creatively subtle. Cooper enters the event horizon of Gargantua, and after an initial rough journey he ends up at the singularity of the black hole. This climactic sequence sees Cooper having an epiphany about the sequence of events that have taken place so far. He has entered a tesseract which is the fifth dimension. So what is this fifth dimension? It is easy to get lost amidst the visual spectacle that lies before us and lose track of what is really happening.

To understand this, I would like to review the four basic dimensions:

1. First dimension – A line extending infinitely or between two points is the simplest representation of a single dimension.

2. Second dimension – A plane or any flat surface lacking thickness [hypothetically], is the simplest representation of two dimensions.

3. Third dimension – Space or a stack of planes, with length, width and thickness, is the easiest representation of the three dimensions.

4. Fourth dimension – Time constitutes the fourth dimension. Although it is an abstract concept, time can be best understood by visualising it as a sequence of events which progresses linearly in one direction only.

5. Fifth dimension – In this dimension, time manifests as a physical quantity. Something that can be touched, felt and controlled like we normally manipulate space. As mentioned above, a timeline is a set of all chronological possibilities stretching out from a point of origin. In the fifth dimension, several such timelines are woven together intricately to give you a dimension rife with possibilities. A tad complex? Picture this. You have ten rupees with you and you walk into a candy store. You look around for candy that can be bought with the money you have. In this scenario, there are fifteen different types of candy you could choose from. Now comes the tricky part. For every candy you choose, there is a different scenario that would occur. So for the fifteen different possibilities, there are roughly fifteen different outcomes. This is exactly what the fifth dimension would entail. Possibilities originating from a rather common epicentre.

So, why the bookcase? Again, I would like to make a feeble attempt at explaining why Cooper ends up in the fifth dimensional manifestation of the timeline corresponding to the bookcase. Perhaps, when one has crossed into the fifth dimension, they can traverse to any point in time they would like. Cooper believes that love is the only thing which can cross the barriers of space and time. To him the event which led to this entire charade is most important. Therefore, that timeline appears in the tesseract. This idea of a hypercube with alternate possibilities as physical dimensions is far-fetched. Not to mention Cooper coding information regarding a black hole’s singularity into Murph’s [Jessica Chastain] watch placed on the bookshelf. It calls to reason that this facet may be the idea of an artist and not necessarily scientifically valid. Cooper also realises that the fifth dimensional beings are not extraneous, but humans from a far distant future who have transcended the four basic dimensions. This is known as a causality loop: a paradox. Another way of looking at it, would involve the consideration that the future has influenced the past. But again, it’s a paradox of its own. This strand of the film should be appreciated for the extent of thought it generates, a feature characteristic of Nolan’s movies.

The movie has to be lauded for its visual take on black holes and wormholes. The visual effects team used equations provided by Kip Thorne, to come up with their representation of Gargantua and the wormhole. Needless to say, the makers of the movie have exercised incredible caution in order to depict astronomical phenomena like never before. Endurance rotates at about 5.6 times per minute to generate Earth equivalent gravity aboard the ship. Some incredible notions aside, the movie is by far the most scientifically accurate description of interstellar travel and several prevalent physical phenomena. Hats off to the Nolan brothers for giving us something true, and most importantly, something beautiful.

 

Darshan Bamney (Mechanical Engineering)

This article was written by 19a

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