A Journey Into the Unkown: The Physics of Interstellar
Written By: Arman Momeni
Introduction:
Perhaps the most realistic imitation of a black hole can be found in Christopher Nolan’s 2014 masterpiece: Interstellar. A globally renown film, not just for its beautiful cinematography and clever storytelling, but also for its attention to detail and appreciation towards real-world physics. With several physicists such as Kip Thorne (awarded the 2017 Nobel Prize in Physics) and Neil DeGrasse Tyson (awarded nine honorary doctorates and the NASA Distinguished Public Service Medal) working on the project, director Christopher Nolan ensures that the storyline coincides with current understandings of general relativity and spacetime. Scientific realism persists so far in this film, that in fact, the movie was accompanied with a book by Kip Thorne, titled The Physics of Interstellar, which relates the jaw-dropping concepts of the movie to grounded real-world scientific studies. Nonetheless, Interstellar is a movie, which needs to skew away from scientific realism in order to create an intense and entertaining movie-going experience. Not everything portrayed in the movie is accurate and it is crucial to draw the line between science and fiction. This article from Science ReWired will explore the physics in Interstellar, focusing on the study of Black Holes and comparing the film to the real world.
Synopsis:
In the year 2060, mankind has destroyed earth; a global crop blight and second Dust Bowl render the planet uninhabitable, and humanity is on the brink of collapse. In a final effort to save the human race, NASA gathers a group of daring researchers to seek a habitable planet. The group must travel across the galaxy VIA a wormhole and explore three separate planets, in hopes of finding one that can support Earth’s population. The only problem, however, is that at the centre of this galaxy, resides a supermassive black hole, Gargantua, which causes a multitude of problems for the crew and their mission.
Black Holes and Gargantua:
A black hole is a region in space where a very large amount of matter has been densely squeezed into a very tiny space, which causes a prodigious and massive gravitational field to occupy the region. The gravitational field is so immense that not even light can escape, presenting it with the rightful name: black hole. A black hole can generally form in two distinct ways, either through the death of a super massive star (8 to 10 times the size of the sun) or from the direct collapse of a very large volume of gas.
In Interstellar, the black hole interrupting the crew’s mission is called Gargantua. Gargantua has been defined to be a supermassive black hole, categorizing it as an object that is millions or even billions of times as massive as the sun. Supermassive black holes have generally been proven to reside at the center of every galaxy, such as our own Milky Way. In the film, Gargantua is described as a rapidly spinning black hole, which is orbited by three planets that the crew seeks to visit: Miller’s planet, Mann’s planet, and Dr. Bran’s planet. The extreme size and gravitational pull of Gargantua causes extreme time dilation effects on the orbiting planets, which allows time to pass far slower on those planets relative to the earth (The Theory of General Relativity!).
Schwarzschild Radius:
In order to understand black holes, one must understand the fundamental concept of the Schwarzschild radius. The Schwarzschild radius essentially defines the parameters of any individual black hole. It is a measure from the center of a black hole all the way to its event horizon. The event horizon of a black hole is defined as the outer boundary of a black hole. If one was to travel beyond the event horizon, they would be trapped in a point of no return, as the gravitational field is so strong that any matter would be stuck within the field. One can presume they are past the event horizon of a black hole once the velocity required to escape the gravitational field exceeds the speed of light (SPOILER ALERT: you cannot go faster than the speed of light).
The Schwarzschild radius, however, can be applied to any object/matter, as it also expresses the radius below which the gravitational attraction between particles of any object will undergo irreversible gravitational collapse. All humans have a Schwarzschild radius, but it is far smaller than the nucleus of an atom. In hindsight, however, if you are able to compress any object so that its radius is smaller than its Schwarzschild radius, that object will collapse, becoming a black hole.
Calculating Gargantua’s Schwarzschild Radius:
Calculating the Schwarzschild radius of an object is straightforward and involves a very simplistic formula.
Calculation below:
Rs: The Schwarzschild radius
G: Newton’s gravitational constant
M: Mass of a black hole (Gargantua is 100 million solar masses)
c: The speed of light in a vacuum
After plugging in the variables, the Schwarzschild radius of Gargantua results to be 295,000,000 km, demonstrating that if one was to get any closer than 295,000,000 km from the centre of Gargantua, they would be sucked in and trapped forever.
Calculating the Gravitational Force at the Event Horizon:
Using Newton’s law of universal gravitation and considering Gargantua and an average human (60 Kg) as the two systems, one can calculate the approximate gravitational force at the event horizon using the universal law of gravitation formula.
After plugging in the variables and the Schwarzschild radius calculated above, the approximate gravitational force at the event horizon is 9,150,000 N. The force of gravity that same person (mass of 60 Kg) would feel on earth is 589 N. The large difference in values shows that the force of gravity right outside the event horizon is 15500x stronger than that of Earth’s. Once an object or a person pass the event horizon, the gravitational force becomes exponentially larger, and can no longer be measured using simplistic arithmetic.
Time Dilation:
Time dilation is defined as the difference in time, which has elapsed when measured by two different clocks. It is essentially the slowing of time as perceived by one observer compared to another. Time, in fact, is not a constant throughout the universe and is instead, relative. The rate at which time passes depends on one’s frame of reference. There are two notable factors, which effect time dilation, one’s speed and one’s positioning within a gravitational field. Time will move slower for a person if they are travelling at very high speeds (near the speed of light) or if they experience a stronger gravitational field (eg. from a black hole). In Interstellar, the crew experiences effects of time dilation from the black hole, which relates to the theory of general relativity that was published by Albert Einstein in 1915.
Within the film, one of the most notable moments is when the crew is faced with the effects of time dilation. As they approach one of the possibly habitable planets (Miller’s planet in specific), they are dismayed with the fact that the planet is far closer to the black hole than they had predicted. The effects of the gravitational force from the black hole would cause time to flow extremely slow. The scientists explain that 1 hour on Miller’s planet would equate to 7 years back on earth (see clip below). The question arises: How plausible is such a strong factor of time dilation?
To answer this question, one must solve for the distance of the planet from the centre of the black hole and see whether it is plausible for a planetary object to reside at that distance.
One can use the time dilation formula for general relativity and rearrange it to solve for r (the distance between miller’s planet and the black hole). It can be inferred that the time dilation experienced is realistic if a plausible distance is calculated.
Step 1: The formula and the variables
Step 2: Rearranging the formula
Step 3: Plugging in variables and solving for the distance
After the calculation is complete, the distance between the center of Gargantua and Miller’s planet is calculated to be 295,000,000 km.
Surprisingly, the value for the distance from Miller’s planet to the center of Gargantua is the same value, which was calculated for the Schwarzschild radius. Due to the use of 3 significant digits, however, the calculated value is not 100% precise. What can be taken away from this calculation is that Miller’s planet resides is extremely close to the event horizon of Gargantua, which is also referenced in the movie (see image below).
Effects of the Distance:
If a planetary object were to reside this close to a black hole, essentially right at the event horizon, there are several effects that would be experienced on the planet. Firstly, one would experience a very strong gravitational force, much stronger than that of earths. Walking would be exhausting, as one would feel extremely heavy. Additionally, if there was water on the planet, there would be very strong tidal forces, creating extremely large waves. In the case of Interstellar, the waves on Miller’s planet rise to be 4000 feet tall. Finally, one would experience great effects of time dilation; the clock of the person on the planet would tick far slower than that of a clock on earth.
Verdict:
After examining the effects of time dilation on Miller’s planet and using that information to find the distance of Miller’s planet from the centre of the black hole, it was concluded that Miller’s planet could lie right at the event horizon, and up to 400,000 km away. It was also established that the effects of such a close distance to a black hole would essentially make the planet uninhabitable. The physics from the movie, however, all seem to line up, as the movie also concludes with the verdict that Miller’s planet is not suitable for life. However, if Miller’s planet was to truly lie right on the event horizon (exactly 295,000,000 km from the centre), then the planet would get sucked in past the horizon and into the endless abyss of the black hole. Overall, an A+ for effort to the filmmakers for depicting realistic effects of time dilation based on their approximate placement of Miller’s planet.
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