I recently had the privilege of watching the IMAX re-release of Christopher Nolan’s Interstellar ten years after the movie was originally released. Some people didn’t like the ending of the movie and I think they didn’t understand it. I’ll try to explain it in detail. Regardless if you liked the film or not, it’s a marvel in film-making as Christopher Nolan typically avoids CGI and he’s well-renowned for his famous movie sets. Some things caught my attention when re-watching this film, especially at the end and I want to explain what I learned with an extra side of science (no charge). Spoiler alert!
Before I get to the ending, I want to revisit an overview of the film. One thing to keep in mind is that Christopher Nolan worked very closely with many scientists, specifically, Kip Thorne, an astrophysicist who is known for his theory on hoop conjecture. Basically, he’s an expert in black holes. I’ll provide a brief overview of the first 2/3 of the film as I feel it’s relevant to explain the ending. But, you can skip ahead to “Ending Explained” below.
The film starts on a bleak Earth where blight has ruined crops. Civilization has lost roughly 6 billion people due to many crops failing. Climate Change has caused an expansive dust bowl where many farming communities are torn by dust storms as crops struggle to survive a deadly pathogen that was accelerated by the heat from the earth. By the way, this was several years before Covid-19, but there are a lot of parallels between pathogens and the heating of the planet (source 1 and source 2).
Cooper, the main character, is a retired NASA flight engineer. In the film, we learn that his daughter, Murphy, is struggling in school. The essential scientific method is disregarded as schools have shifted to more “comfortable feelings”. We learn that the Apollo missions to the moon are no longer taught and NASA has since been defunded. Children are expected to become farmers to help keep life afloat on a dying planet.
Enter the “ghost” in Murphy’s room. Various books keep falling and she recognizes that they’re patterns of Morse code that read “STAY”. During an extreme dust storm, a pattern emerges out of the settled dust on Murphy’s floor which Cooper determines is binary code for latitude and longitudinal coordinates.
He and Murphy drive to the coordinates and discover that it’s a hidden NASA facility. While NASA has officially been “defunded”, it was still funded in secret with a single mission in mind: find another planet. There, we learn about a white hole that was discovered near Saturn and it leads to a shortcut in another solar system in another galaxy with several potentially habitable planets. A dozen scientists were sent to each planet individually and only three sent signals back: Dr. Miller, Dr. Mann, and Dr. Edmunds. For the rest of the film, each planet is named after the scientist.
Miller’s planet was determined to be the first planet the crew, now consisting of Cooper, Dr. Brand, and another guy who dies right away, is a giant water planet with gigantic waves reaching hundreds of meters in the sky. Of everything in this film, oddly enough, this is the most scientifically inaccurate part of the movie. Not the waves, but how destructive the waves are. In reality, most scientists agree that the waves would be more gentle and the ship would just keep floating near the bottom of the wave due to the gravitational force of the planet. Regardless, it makes for an intense moment and a major plot in the movie.
Miller’s planet is located extremely close to the black hole, Gargantua, it orbits. Due to the gravitational force of Gargantua, time is observed differently than on Earth. For context, Astronauts that are orbiting the Earth in the international space station are 0.014 seconds behind us on Earth per year. Since we’re on Earth, there’s more gravitational force than those orbiting it. Time is completely relative to the observer. A second is always a second to us no matter where we are, but observing the same second depending on the gravitational force will be observed differently. On Miller’s planet, the gravitational force from Gargantua causes time to dilate to a difference of about seven years to one hour. We can experience the time passing in the movie with every “click” during their excursion on the planet. Each click is equal to one year on Earth. While on the planet we hear 23 clicks, or the equivalent of 23 years on Earth.
From Cooper and Dr. Brand’s perspective, they’ve only been there for about 3.2 hours. On Earth, however, 23 years have passed because the gravitational forces on Earth are much less than on Miller’s planet. This is what Dr. Einstein’s theory of relativity is explaining. In other words, time is relative in a four-dimensional plane. We know it from a three-dimensional perspective: time is a linear constant; an hour from now will be an hour from now. With gravitational force, like a river, it can slow or be hastened, but it flows in one direction.
Cooper and Dr. Brand visit Mann’s planet next. He falsifies data and tries to kill Cooper and steal the landing ship so he can return to Earth. It goes disastrously wrong, but Cooper and Dr. Brand regain control of their space station again. Dr. Brand learns that her father has died and that their mission was allegedly doomed to fail from the start. However, they don’t give up and decide to continue to Miller’s planet with the caveat that they will not be able to leave with the remaining fuel they have due to Dr. Mann’s traitorous acts.
To get there, however, they need to use a gravity assist from Gargantua. This is commonly used in orbital mechanics where spacecrafts like the Voyager missions and New Horizons take advantage of the gravitational forces from planets to save fuel. In simple terms, a spacecraft travels in the vacuum of space at the same velocity as the last acceleration. When we drive a car we have to keep our foot on the acceleration because friction and gravity are opposing forces that will try to slow us down. In space, there is neither friction nor gravity. If you accelerate to 50 km/h, the car will continue moving at 50 km/h.
If you aim the car close enough to a planet to get a gravitational tug, but not enough of a tug to pull you into it, you can take advantage of that tug to accelerate the car to – for the sake of argument – 60 km/h. New Horizons, for example, used a flyby on Jupiter to increase its speed by 4 km/s to 83,000 km/h (or 21,000 mph). Again, this is relative to the sun. It shortened the voyage to Pluto by three years without using any fuel.
Ending Explained
Cooper and Dr. Brand couldn’t travel to Edmund’s planet on the fuel they had left. However, if using the gravitational force of Gargantua, they could accelerate enough using the correct orbital mechanic calculations for a gravity assist to get to Miller’s planet with some major caveats: 1) the gravitational force would cause them to lose decades relative to Earth’s time, and 2) they will need to leave something behind due to Newtonian physics.
Time being relative to the observer is an important factor here. From Earth, if I could watch the space station with an extremely powerful telescope, I would observe it going slower and slower to the point it looked like it wasn’t moving at all. If I stared at it for 80 years I might see it orbit the black hole once. In reverse, though, if I was on the space station and watched someone on Earth through an extremely powerful telescope, I would watch someone as if they were on fast-forward on the TV. I would see them go from school-aged to adulthood and eventually become a grandparent in a matter of seconds. This is due to the effects of gravity on spacetime.
During this scene they refer to Newton’s third law: for every action, there needs to be an equal opposing reaction. A football sitting on the field won’t move unless an action moves that ball. If you kick that ball, two actions are happening: one is moving the ball and the other is feeling an equal force on the foot. What isn’t relayed to Dr. Brand, however, is that the equal force is Cooper detaching from the space station in his ranger ship, while his robot counterpart, TARS, does the same. This leaves Dr. Brand by herself on her journey to Miller’s planet. During this scene, roughly 80 years have passed on Earth even though it was only about an hour for Dr. Brand and Cooper. Remember: the gravitational force of a black hole is greater the closer you get to it, so while one hour on Miller’s planet was roughly 7 years on Earth, going nearly to the event horizon of the black hole itself would expect time to bend even further.
Cooper “falls” into Gargantua where he ends up in a tesseract. During this moment, he requests TARS, his trusty robot marine sidekick, to collect data from the black hole. This tesseract is essentially a physical representation of the fifth dimension. Remember: the third dimension is where time is constant while the fourth dimension is where time can be bent. In the fifth dimension, time is a spatial dimension. In other words, all time exists in the fifth dimension. If you could physically harness it, like in the tesseract of the film, you can move freely through time. However, as the film mentions, the caveat is that you can only impact the gravitational forces.
This returns us to the scene in Murphy’s bedroom earlier in the film where she saw the “ghost” that books pushed off the shelves that turned out to be Morse code for “STAY”. Cooper wanted to tell his past self to never leave. This would obviously cause a paradox because if he never left then he wouldn’t be in the tesseract now. I’ll get into this later. In any case, he was able to manipulate the gravity of the dust from the sandstorm using gravity to relay the coordinates of the hidden NASA headquarters using binary. Finally, he asks TARS, the robot marine who also survived the black hole, to relay the data of the gravity from the black hole to him. Cooper finds the watch he gave Murphy before he left and forces it to tick using the calculations TARS relayed in Morse code once again. He chose the watch because of its sentimental value, its precision as a mechanical device, and its susceptibility to gravitational manipulation. Time is relative to gravity!
20 years later in Murphy’s timeline, she comes across the watch as she’s trying to force her brother and his family outside of a doomed household. When she notices the ticking, she discovers a eureka moment: it’s Morse code that solves Professor Brand’s gravitational equations from the data collected by TARS.
You can skip the nerdism section below if you don’t care about what that eureka moment is.
Start Nerdism:
This calculation is the reconciliation between quantum mechanics and gravity (also known as quantum gravity). Quantum mechanics (which governs the microscopic world) and general relativity (which describes gravity and the large-scale structure of spacetime) are incompatible theories. The reason we find them incompatible is because of extreme events such as black holes and the Big Bang theory. Dr. Einstein showed us that gravity is not a force but a curvature of spacetime. Quantum mechanics introduces another wrinkle: at the quantum level, time becomes “fuzzy” and uncertain, just like other quantum properties.
There are a few implications of quantum gravity: time granularity, time emergence, loop quantum gravity, and the holographic principle. Time Granularity is essentially stating that time is discrete units much like a pixel on a screen that can’t be seen from a distance and only up close. Time Emergence suggests that time itself is an emergent phenomenon much like temperature emerges from particle behavior. Loop Quantum Gravity is similar to Time Granulity, but time emerges from the prospect of a big bounce where the universe contracts and expands continuously. Holographic Principle arises from the string theory, suggesting that all information can be described by a boundary like a hologram.
In short, the quantum gravity calculations that Murphy used don’t exist in today’s theoretical physics. The data to complete this theory needs to come from inside a black hole, which is why the “eureka” moment had such an impact on the film.
:End Nerdism
Murphy’s calculations allowed her to create a device to harness electricity, which we see later in the film with the “Cooper Station” – the spaceship that the remaining Earth civilans used created by NASA to escape Earth. This is where we find Cooper, Murphy’s father, after the tesseract collapsed and he was picked up from being warped via the black hole of Gargantua to the white hole near Saturn. The worm hole, if you will.
Start Nerdism p2:
In fourth-dimensional spacetime, a black hole pulls everything past its event horizon while a white hole would do the opposite, ejecting matter. A white hole hasn’t been observed so it’s only theorized right now. A white hole would ultimately collapse under these conditions. The reason for this is the fundamental instabilities such as the matter accumulation problem (gravitational event horizon would cause the shell to collapse from the mass), thermodynamics (decrease in entropy), and quantum effects (particle creation would collide with outflowing particles).
The tesseract was a physical space in the fifth dimension, which in theory would pair the black hole with the white hole. Or, a theorized “worm hole”. As in, whatever goes in the black hole would ultimately be spit out of the white hole and vice versa since time could be manipulated in either direction. This means that the proposed “alien” civilization in the film, which is actually a future human civilization, can stabilize the wormhole while making it traversable. This requires the manipulation of gravity across time.
:End Nerdism p2
Murphy’s calculations to control gravity will ultimately allow Cooper Station to safely traverse the worm hole while also simulating Earth’s gravity for a comfortable ride for all the civilians on the ship.
Conversation between Murphy and Cooper
Murphy is celebrated and eventually reunited with her father. However, 113 years have passed for her since she was 10 years old when Cooper left and now she’s 123. Meanwhile, Cooper has only aged for several months. We see Cooper enter a hospital room where it’s filled with people, who we later discover include her kids, grandkids, and great-grandkids. The conversation with both Cooper and Murphy ultimately trades knowledge that she realized her father was the “ghost”, and Cooper says he was the “ghost” who acted in the fifth dimension and that he sent her the data required to complete the calculations for quantum gravity.
This, oddly enough, is a casuality loop (or temporal paradox). Cooper needed to go into the black hole to collect the data to send to his daughter via the tesseract so she could use that data to create the tesseract so he could fall into a black hole and send the data that she needed via the tesseract that she created. Confused? That’s why it’s a paradox.
The conversation shown between the two is brief and I think a lot of viewers got frustrated at how short it was. However, we have to keep a couple of things in mind: First, we experienced time from the perspective of the main character, Cooper. While several months passed for him without his daughter, she had spent over 100 years of her life without her father. I’m reaching nearly 40 and I can barely remember anyone from when I was 10. I can’t even fathom having a meaningful conversation with them now. Second, she continues talking as the movie reaches its conclusion. Therefore, we should assume that there was more to the conversation, but for the sake of brevity and having sat through a 3-hour movie, we should assume the conversation was discussing the same thing we just saw for the past three hours. In other words, the entire movie was their conversation.
As the movie concludes, Murphy tells Cooper to return to Dr. Brand.
Plan B
At the beginning of this lengthy article, I mentioned that NASA had a plan that was reliant on discovering a potentially habitable planet. NASA would then send people to that planet and re-civilize there. That was Plan A. Then, there was Plan B where humans failed to control gravity to escape the planet, and “they” – who created the wormhole – allowed only the scientists of Earth to find a potentially habitable planet and recreate civilization using DNA that was on the space station. Plan A succeeded because of the whole temporal paradox I mentioned earlier. The storyline of Cooper and Dr. Brand wouldn’t exist if Plan A failed.
This is where we find Dr. Brand at the end on Edmund’s planet. We find her at Dr. Edmund’s grave. He died potentially decades ago because she went near the event horizon of Gargantua while nearly a century passed for him. Remember: time is relative! As she walks back to the ship we see multiple buildings that have been constructed already. We can assume then that she has continued the DNA project on Edmund’s planet. What she doesn’t expect is Cooper on his way to the planet with a ranger he stole from Cooper station. Though, we don’t see them reunite in the film.
Either way, both Plan A and Plan B succeed. Civilians are able to safely leave Earth and are headed to Edmund’s planet to colonize, and Dr. Brand is working on Edmund’s planet to rebuild civilization using DNA.