Black Hole
Introduction
Today we explore one of the most fascinating aspects of Interstellar: Gargantua. It is the real protagonist of the film, the black hole. But what are the physical laws used to create Gargatua? Well, the coolest thing about black holes is that if we know the mass of it and how fast it spin, then from equations of General Relativity we can deduce all the hole's other properties, as size, gravitational pull, gravitational lensing etc everything. This is amazing! It's as though (using a quote from Kip Thorne) knowing my weight and how fast I can run, you could deduce everything about me, as my IQ colour of my skin, eyes and hair etc. So, let's see how Gargantua was conceived.
Gargantua's Mass
Let's start to analyze the mass of Gargantua: when it was conceived, it must had very specific mass, to allow the construction of the planets that orbit close to it. So, in Interstellar, Gargantua is a black hole with a mass between 100 and 200 millions Suns! Then, the dimension of a black hole is proportional to its mass, for Gargantua the horizon circumference is approximately the same as the Earth's orbit around the Sun, about 1 billion kilometres. While its radius (the radius of the event horizon) is about 150 million kilometres.
It would be 100 times bigger then Sagittarius A, the black hole at the centre of Miky Way!
Gargantua's Spin
At first, there is a maximum spin rate that any black hole can have. If it spins faster than the maximum, its horizon would disappear, leaving the singularity inside it wide open to see; that is, making it 'naked'. But this is probably forbidden by the laws of physics, because as the spin rate of the black hole increases, the spin rate of the accretion disk also increases exponentially. After a certain limit it would exceed the speed of light. However, Gargantua spin awfully fast, this because it's necessary for Miller's planet to orbit incredibly close to it, without falling in, it spins so fast that "one hour there is seven years back on Earth". So, this huge slowing of time requires Gargantua to spin almost as fast as the maximum. To make a great film often film-maker pushes things to extreme, but this is scientifically possible.
Other Objects
Fig 1:
This is the real simulation of Gargantua. In the film it has been slightly modified, to make it more spectacular.
Miller's Planet
■ The first planet (and the nearest to Gargantua) that Cooper and his crew visit is Miller's. The physics of this planet is absolutely awesome! It is so close to Gargantua that the black hole determines all its characteristics, in particular:
- Extreme slowing of time
- Gigantic water wave
- Huge tidal gravity
At first this planet represent the closest anything can live stably, without falling into a black hole. The entire accretion disk should be outside the orbit of Miller's planet! But in the film, Miller's planet is consciously outside the horizon event, otherwise Gargantua would have been simply .. a black spot (not so spectacular).
■ "Seven years on Earth is one hour on this planet". This is what Christopher Nolan wanted for his movie. But when I heard this for the first time I immediately thought it could not be true. But, instead, it's all scientific! This is due to the immense gravity of Gargantua. But being so close to it, Miller's planet is subject to enormous tidal gravity. So strong that deform the planet. In addition, it must keep the same face pointing toward Gargantua, otherwise first the planet would be crushed east-west and then north-south. So it would be torn apart! (Fig 2)
■ In fact, Miller's planet doesn't keep precisely the same face pointing toward Gargantua, but it rocks back and forth by a small amount (as shown in the picture). These Small fluctuations are responsible for spectacular and scary gigantic waves (at least 1 km high). Gargantua's tidal forces may not pulverize the crust of the planet, but they deform it and those and those deformations could easily produce gigantic heartquakes (or "millerquakes") and those one could easily produce gigantic Tsunmis! (Fig 3)
Mann's Planet
After discovering that Miller's planet is hopless for human colonization, Cooper and his crew travel to Mann's planet. The first peculiarity of this planet is its strange orbit (as shown in the image below). Indeed, it is similar to the orbit of Halley's comet in our Solar System. Then, once they land on the surface, they realize that there is no surface, but only ice cloud! This because the planet spend most of its life far from the warmth of Gargantua's acccretion disk (as we can see in Fig 4).
Possiblity of Life Near Black Holes
The physics of this strange planetary system is incredibly accurate, but in reality, is life on a planet orbiting a black hole possible? This question has no answer, but surely it would be incredibly difficult, much more than shown in the film. The main problems are:
- Few possibilities of presence of liquid water, because of extreme conditions.
- A planet too far from the black hole would be frozen and without energy, but another one too close would be strafe by radiations.
- Supermassive black holes are usually found in the centre of galaxies, areas of very high stellar density. With so many stars so close the dangers from possible supernovae is really high!
Where they can find other half of the answer? Simple, inside a black hole. So, in Interstellar, Cooper decides to throw himself into Gargantua, with his friend Tars. Looking up as he falls inward, Cooper sees the image of external universe reduced in size (due to aberration of the starlight), then we are rather ignorant of what goes on inside black holes. In interstellar, looking downward, Cooper should see light from objects that fell into Gargantua before him and are still falling inward. He can see them in reflected light from the accretion disk above and they are mostly interstellar dust (this explain the "fog" he encounters as he fall). Cooper can also overtake stuff that's infalling more slowly than him (this explain the white flakes that hit and bounce off his Ranger in the movie).
The Tesseract
As the ranger nears the singularity, Cooper ejects in the nick of time and tidal forces tear the Ranger apart. But at the singularity's edge a tesseract awaits Cooper, placed there probably by bulk beings. A standard tesseract is a hypercube, a cube in 4-space dimensions. Because Cooper is made of atoms held together by electric and nuclear forces, all of which can exist only in 3-space dimensions and 1-time, he is confined to reside in one of tesseract's 3-space-dimensioanl faces (a cube). But entering it, Cooper experiences a really complexified tesseract (this is a Nolan's visual choice, extreme is always better for audience!). However, a tesseract like this allow Cooper to carry messages into our brane's past, with gravitational forces (the force lines of the bulk field).
Messaging Murph
In the tesseract there is a one-way space-time barrier: light can travel toward the future from Murph to him, but not the vice versa. Only gravity can surmount that barrier, Cooper discovers. Moreover, he discovers that it can communicate (via electromagnetic waves) with Tars, because also him was saved somewhere in the tesseract. So, he decided to send quantum data collected from Tars to Murph. (Quantum data are referred to any data which could be obtained when gravity is studied at the quantum level, as in a black hole). In the movie we see Cooper pushing with his finger on a "world tube" of a watch's second hand, that produces a gravitational force. This force makes the second-hand of the watch in a Morse-encoded pattern that carries the quantum data. These will help Murph to find a Theory of Everything.
The Tesseract Revisited
The Bulk Beings
All the characters in Interstellar are convinced that bulk beings exist, though they use that name only rarely. Usually, the characters call the bulk beings “They.” A reverential They. Early in the movie, Amelia Brand (played by Anne Hathaway) says to widowed astronaut Cooper (Matthew McConaughey), “And whoever They are, They appear to be looking out for us. That wormhole lets us travel to other stars. It came along right as we needed it.”
One of Christopher Nolan’s clever and intriguing ideas is to imagine that They are actually our descendants: humans who, in the far future, evolve to acquire an additional space dimension and live in the bulk. Late in the movie, Cooper says to TARS (a robot voiced by Bill Irwin), “Don’t you get it yet, TARS? They aren’t beings. They’re us, trying to help, just like I tried to help Murph.” TARS responds, “People didn’t build this tesseract” (in which Cooper is riding). “Not yet,” Cooper says, “but one day. Not you and me but people, people who’ve evolved beyond the four dimensions we know.”
2D Brane and 3D Bulk
In 1844 Edwin Abbott wrote a satirical novella titled Flatland: A Romance of Many Dimensions. Though its satire on Victorian culture seems quaint today and its attitude toward women outrageous, the novella’s venue is highly relevant to Interstellar. I recommend it to you.
It describes the adventures of a square-shaped being who lives in a two-dimensional universe called Flatland. The square visits a one-dimensional universe called Lineland, a zero-dimensional universe called Pointland, and most amazing of all to him, a three-dimensional universe called Spaceland. And, while living in Flatland, he is visited by a spherical being from Spaceland.
In my first meeting with Christopher Nolan, we were both delighted to find the other had read Abbott’s novella and loved it.
In the spirit of Abbott’s novella, imagine that you are a two-dimensional being, like the square, who lives in a two-dimensional universe like Flatland. Your universe could be a tabletop, or a flat sheet of paper, or a rubber membrane. In the spirit of modern physics, I refer to it as a two-dimensional (2D) brane.
Being well educated, you suppose there is a 3D bulk, in which your brane is embedded, but you’re not certain. Imagine your excitement when one day you are visited by a sphere from the 3D bulk. A “bulk being,” you might call him.
At first you don’t realize it’s a bulk being, but after much observation and thought, you see no other explanation. What you observe is this: Suddenly, with no warning and no apparent source, a blue point appears in your brane (top left of Fig 1). It expands to become a blue circle that grows to a maximum diameter (middle left), and then gradually shrinks to a point (bottom left) and disappears completely.
You believe in conservation of matter. No object can ever be created from nothing, yet this object was. The only explanation you can find is shown in the right half of the figure above. A three-dimensional bulk being — a sphere — passed through your brane. As it passed through, you saw in your brane its changing two-dimensional cross section. The cross section began with a point at the sphere’s south pole (top right). It expanded to a maximal circle, the sphere’s equatorial plane (middle right). It then shrank to a point, the sphere’s north pole, and disappeared (bottom right).
Imagine what would happen if a 3D human being, living in the 3D bulk, passed through your 2D brane. What would you see?
Bulk Beings From the Fifth Dimension, Passing Through Our 3D Brane
Suppose that our universe, with its three space and one time dimensions, really does live in a five-dimensional bulk (four space and one time). And suppose there are “hyperspherical beings” who live in the bulk. Such a being would have a centre and a surface. Its surface would consist of all points, in four space dimensions, that are some fixed distance from the centre, for example, 30 centimetres. The bulk being’s surface would have three dimensions and its interior would have four.
Suppose that this hyperspherical bulk being, traveling in the bulk’s out direction or back direction, were to pass through our brane. What would we see? The obvious guess is correct. We would see spherical cross sections of the hypersphere (see Fig 2).
A point would appear from nothing (1). It would expand to become a three-dimensional sphere (2). The sphere would expand to a maximum diameter (3), then contract (4), shrink to a point (5), and disappear.
Can you guess what we would see if a four-dimensional human being living in the bulk were to pass through our brane? To speculate about this, you need to imagine what a four-dimensional human being — with two legs, a torso, two arms, and a head — must “look like” in the bulk, with its four space dimensions. And what its cross sections must look like.
The Nature of Bulk Beings, and Their Gravity
If there are bulk beings, what are they made of? Certainly not atom-based matter like us. Atoms have three space dimensions. They can only exist in three space dimensions, not four. And this is true of sub-atomic particles as well. And it is true also of electric fields and magnetic fields and the forces that hold atomic nuclei together.
Some of the world’s most brilliant physicists have struggled to understand how matter and fields and forces behave if our universe really is a brane in a higher-dimensional bulk. Those struggles have pointed rather firmly to the conclusion that all the particles and all the forces and all the fields known to humans are confined to our brane, with one exception: gravity, and the warping of spacetime associated with gravity.
There might be other kinds of matter and fields and forces that have four space dimensions and reside in the bulk. But if there are, we are ignorant of their nature. We can speculate. Physicists do speculate. But we have no observational or experimental evidence to guide our speculations. In Interstellar, on Professor Brand’s blackboard, we see him speculating.
It’s a reasonable, half-educated guess that, if bulk forces and fields and particles do exist, we will never be able to feel them or see them. When a bulk being passes through our brane, we will not see the stuff of which the being is made. The being’s cross sections will be transparent.
On the other hand, we will feel and see the being’s gravity and its warping of space and time. For example, if a hyperspherical bulk being appears in my stomach and has a strong enough gravitational pull, my stomach may begin to cramp as my muscles tighten, trying to resist getting sucked to the centre of the being’s spherical cross section.
If the bulk being’s cross section appears and then disappears in front of a checkerboard of paint swatches, its space warp might lens the swatches, bending the image I see, as in the top half of Fig 3.
And if the bulk being is spinning, it might drag space into a whirling motion that I can feel and see, as in the bottom of Fig 3.
Cooper, Brand, and the crew of the Endurance never actually feel or see our bulk descendants’ gravity or their space warps and whirls. That, if it ever occurs, is left for a sequel to Interstellar. But older Cooper himself, riding through the bulk in the closing tesseract, reaches out to the Endurance’s crew and his younger self, reaches out through the bulk, reaches out gravitationally. Brand feels and sees his presence, and thinks he is They.
Introduction
Today we explore one of the most fascinating aspects of Interstellar: Gargantua. It is the real protagonist of the film, the black hole. But what are the physical laws used to create Gargatua? Well, the coolest thing about black holes is that if we know the mass of it and how fast it spin, then from equations of General Relativity we can deduce all the hole's other properties, as size, gravitational pull, gravitational lensing etc everything. This is amazing! It's as though (using a quote from Kip Thorne) knowing my weight and how fast I can run, you could deduce everything about me, as my IQ colour of my skin, eyes and hair etc. So, let's see how Gargantua was conceived.
Gargantua's Mass
Let's start to analyze the mass of Gargantua: when it was conceived, it must had very specific mass, to allow the construction of the planets that orbit close to it. So, in Interstellar, Gargantua is a black hole with a mass between 100 and 200 millions Suns! Then, the dimension of a black hole is proportional to its mass, for Gargantua the horizon circumference is approximately the same as the Earth's orbit around the Sun, about 1 billion kilometres. While its radius (the radius of the event horizon) is about 150 million kilometres.
It would be 100 times bigger then Sagittarius A, the black hole at the centre of Miky Way!
Gargantua's Spin
At first, there is a maximum spin rate that any black hole can have. If it spins faster than the maximum, its horizon would disappear, leaving the singularity inside it wide open to see; that is, making it 'naked'. But this is probably forbidden by the laws of physics, because as the spin rate of the black hole increases, the spin rate of the accretion disk also increases exponentially. After a certain limit it would exceed the speed of light. However, Gargantua spin awfully fast, this because it's necessary for Miller's planet to orbit incredibly close to it, without falling in, it spins so fast that "one hour there is seven years back on Earth". So, this huge slowing of time requires Gargantua to spin almost as fast as the maximum. To make a great film often film-maker pushes things to extreme, but this is scientifically possible.
Other Objects
Fig 1:
Miller's Planet
■ The first planet (and the nearest to Gargantua) that Cooper and his crew visit is Miller's. The physics of this planet is absolutely awesome! It is so close to Gargantua that the black hole determines all its characteristics, in particular:
- Extreme slowing of time
- Gigantic water wave
- Huge tidal gravity
At first this planet represent the closest anything can live stably, without falling into a black hole. The entire accretion disk should be outside the orbit of Miller's planet! But in the film, Miller's planet is consciously outside the horizon event, otherwise Gargantua would have been simply .. a black spot (not so spectacular).
■ "Seven years on Earth is one hour on this planet". This is what Christopher Nolan wanted for his movie. But when I heard this for the first time I immediately thought it could not be true. But, instead, it's all scientific! This is due to the immense gravity of Gargantua. But being so close to it, Miller's planet is subject to enormous tidal gravity. So strong that deform the planet. In addition, it must keep the same face pointing toward Gargantua, otherwise first the planet would be crushed east-west and then north-south. So it would be torn apart! (Fig 2)
■ In fact, Miller's planet doesn't keep precisely the same face pointing toward Gargantua, but it rocks back and forth by a small amount (as shown in the picture). These Small fluctuations are responsible for spectacular and scary gigantic waves (at least 1 km high). Gargantua's tidal forces may not pulverize the crust of the planet, but they deform it and those and those deformations could easily produce gigantic heartquakes (or "millerquakes") and those one could easily produce gigantic Tsunmis! (Fig 3)
Mann's Planet
After discovering that Miller's planet is hopless for human colonization, Cooper and his crew travel to Mann's planet. The first peculiarity of this planet is its strange orbit (as shown in the image below). Indeed, it is similar to the orbit of Halley's comet in our Solar System. Then, once they land on the surface, they realize that there is no surface, but only ice cloud! This because the planet spend most of its life far from the warmth of Gargantua's acccretion disk (as we can see in Fig 4).
Possiblity of Life Near Black Holes
The physics of this strange planetary system is incredibly accurate, but in reality, is life on a planet orbiting a black hole possible? This question has no answer, but surely it would be incredibly difficult, much more than shown in the film. The main problems are:
- Few possibilities of presence of liquid water, because of extreme conditions.
- A planet too far from the black hole would be frozen and without energy, but another one too close would be strafe by radiations.
- Supermassive black holes are usually found in the centre of galaxies, areas of very high stellar density. With so many stars so close the dangers from possible supernovae is really high!
The Wormhole
Beginning
In 1916 Ludwing Flamm discovered a solution of Einstein's equations that describe a wormhole. Nowadays we know that Einstein's equations allow many kinds of wormholes, but Flamm's is the only one that is precisely spherical and contain no gravitating matter. However, for a lot of years physicists paid little attention to Flamm's solution of Einstein's equations, but in 1935 Einstein’s himself and a physicist called Nathan Rose, rediscovered Flamm's solution and explored its properties. Other physicist, unaware of Flamm's work, began to call his wormhole the: "Einstein-Rosen Bridge". But now, let's go to see how the wormhole is created in Interstellar.
Construction
A lot of people think that a wormhole is 'static', forever unchanging, but in reality, it has a life: it is born, expands, contracts and dies. The starting point are two singularities in the space-time, if one of this reach the other through the bulk (this is an hypothetical higher-dimensional space within which the eleven dimensions of our universe may exist), a wormhole is created. Then, the wormhole can expand and then it shrinks and pinches off, leaving behind the two singularities. However these events happen so quickly that nothing, not even light, has the time to travel through it. But first things first.
Shape of a Wormhole
If a wormhole was created, what does it look like to people like us? There isn't a definitively answer (so I labelled this section as educated guess). If a wormhole can be held open (and later we will see if it's possible), the precise details of it are unknown, but scientists have assumed that it could be a sort of sphere where we can see a distorted image of the landscape on the other side (the entrances of the wormhole are called "mouth"). This is an examples of Images seen through a wormhole's two mouths. But why are they spherical?
Discovery of the Wormhole
Now we know a possible structure of a wormhole, but how did they discover it in interstellar? Professor Brand and his team discovered very weak gravitational waves emitted by a neutron star and a black hole (probably with something similar to the current LIGO), but the direction of this source was... Saturn. Well, there aren't a neutron star and a black hole near Saturn! So, Professor Brand find only one explanation: the waves must emerge from a wormhole near Saturn (look at the image below).
Travelling Through the Wormhole
Once discovered the wormhole, Cooper and his crew reach it, after a long journey to Saturn. Once they reach it, they just have to go through it. The equations used for the film, to figure out what the entire wormhole would look like were solved by Kip Thorne. But there was a problem for Christopher Nolan. Using Kip Thorne's Equations for a long wormhole (as the one of Interstellar), it looked like traveling through a long tunnel with walls whizzing past too much like things we've seen in movies before (although in this case, it would have been much more accurate). So, in Interstellar we find a more abstract interpretation of the wormhole, not fully accurate, but it captures the spirit and much of the feel of a real wormhole and yes, it's spectacular.
Can They Really Exist?
In Interstellar Cooper says: "a wormhole isn't a naturally occurring phenomenon". And he was right. Probably. We are talking about speculations, but for all physicists in the word, even if a traversable wormhole is allowed by the laws of physics, it extremely unlikely it can exist in nature. We see no objects in our universe that could be become wormholes as they age. However there is a little hope that wormholes do exist naturally in submicroscopic scales in the form of "quantum foam". This is an hypothesized network of wormholes that is continually fluctuating in and out of existence. But we have no hint of any evidence at all that such natural enlargement can or did occur.
Can They be Created by Aliens?
An ultra-advanced civilization is the only serious hope for making traversable wormholes. But it would face huge obstacles! How to make a wormhole? Well, just push a piece of our universe (our brane) downward in the bulk (higher dimensions) to create a sort of thimble, then fold our brane around in the bulk, tear a hole in the thimble itself and saw the tears together. Nothing easier! We are extremely ignorant of how such a civilization could do it. However, in Interstellar, the wormhole is thought to have been made, well open and placed near Saturn by a civilization that lives in the bulk. Obviously, it's just speculation.
Extreme Physics
Introduction
In our Universe, space has 3 dimensions. But to schedule any event we must know 'when'. In this sense, time is a fourth dimension. However, time is different from space, because once an event has taken place, we cannot travel backward in time. We can only travel forward; the relativistic laws guarantee it. So, we live in a 4-dimensional space-time. But in interstellar there is a new idea of Universe, the bulk. Well, currently this is only a mathematical notion, a visual aid, not a real thing. But could it become real?
The 5th Dimension
At first, how can we know that a mathematical notion can be real? Well, it must influence things we measure. Nowadays we have no evidence of the existence of the bulk, but the superstring theory, hypothesizes the existence of a 10-dimensional bulk. In Interstellar is precisely this theory that becomes real (precisely the type II-B), but ten dimensions is a bit much for a science-movie, so Interstellar's bulk has only 5 dimensions. It shares 3 space dimensions and 1 time dimension with our brane (our Universe), and it has a fifth space dimension which extend "perpendicular" to our brane (imagining it as a flat sheet).
Gravitational Anomalies
Gravitational anomalies are something about gravity that doesn't fit our understanding of the universe, or our understanding of the physical law that control the universe. During universe history we have detected several gravitational anomalies, as "the anomalous orbit of galaxies around each other". Without delving into the topic, these anomalies have allowed us to correct our knowledge of gravity, in particular, the anomaly mentioned above was the one that made the discovery of dark matter possible. But there is still an anomaly that cannot be explained: "the anomalous acceleration of the Universe's expansion". There are two possibilities to explain this anomaly.
Gravity in Interstellar
The first is that there is something wrong with General Relativity, the second is the hypothetical existence of a sort of dark energy that repels gravitationally. The final verdict is not in. However, in Interstellar, the situation is different. Gravitational anomalies are startling for their weirdness and strength and professor Brand's team has collected a large trove data on the anomalies. Their explanation is that there is something unusual going on, that is probably related to the presence of the bulk and the new, extra-dimension (be attention, gravity is NOT the fifth dimension). This new knowledge about gravity are at the centre on the famous professor's equation.
Professor's Equation-1
The professor convince himself that the anomalies are due to gravity from the fifth dimension, from the bulk, because the known laws work well in all situations, but the anomalies have no apparent source in our 4-dimensional universe. These anomalies must have a source and he thinks that the best way to explain them is that bulk field passing through our brane could produce changing in tidal gravity. A bulk field? A field is something that extends out through space exerts forces on things it encounters (as electric field, gravitational field and so on). A bulk field is a collection of force lines that reside in the five-dimension bulk, what kind of force lines, the professor doesn't know.
Professor's Equation-2
Bulk fields also play two other crucial roles: they hold the wormhole open and they could explain how to implement the professor's plan A: transport millions of people in a spaceship to save them from the dying Earth. But laws of physics are expressed in the language of maths. So, the famous professor's equation is the mathematical explanations of bulk fields and it's called: "Action". He managed to solve the equation, but "it's only half the answer".
Into Gargantua
Extreme Physics
Introduction
In our Universe, space has 3 dimensions. But to schedule any event we must know 'when'. In this sense, time is a fourth dimension. However, time is different from space, because once an event has taken place, we cannot travel backward in time. We can only travel forward; the relativistic laws guarantee it. So, we live in a 4-dimensional space-time. But in interstellar there is a new idea of Universe, the bulk. Well, currently this is only a mathematical notion, a visual aid, not a real thing. But could it become real?
The 5th Dimension
At first, how can we know that a mathematical notion can be real? Well, it must influence things we measure. Nowadays we have no evidence of the existence of the bulk, but the superstring theory, hypothesizes the existence of a 10-dimensional bulk. In Interstellar is precisely this theory that becomes real (precisely the type II-B), but ten dimensions is a bit much for a science-movie, so Interstellar's bulk has only 5 dimensions. It shares 3 space dimensions and 1 time dimension with our brane (our Universe), and it has a fifth space dimension which extend "perpendicular" to our brane (imagining it as a flat sheet).
Gravitational Anomalies
Gravitational anomalies are something about gravity that doesn't fit our understanding of the universe, or our understanding of the physical law that control the universe. During universe history we have detected several gravitational anomalies, as "the anomalous orbit of galaxies around each other". Without delving into the topic, these anomalies have allowed us to correct our knowledge of gravity, in particular, the anomaly mentioned above was the one that made the discovery of dark matter possible. But there is still an anomaly that cannot be explained: "the anomalous acceleration of the Universe's expansion". There are two possibilities to explain this anomaly.
Gravity in Interstellar
The first is that there is something wrong with General Relativity, the second is the hypothetical existence of a sort of dark energy that repels gravitationally. The final verdict is not in. However, in Interstellar, the situation is different. Gravitational anomalies are startling for their weirdness and strength and professor Brand's team has collected a large trove data on the anomalies. Their explanation is that there is something unusual going on, that is probably related to the presence of the bulk and the new, extra-dimension (be attention, gravity is NOT the fifth dimension). This new knowledge about gravity are at the centre on the famous professor's equation.
Professor's Equation-1
The professor convince himself that the anomalies are due to gravity from the fifth dimension, from the bulk, because the known laws work well in all situations, but the anomalies have no apparent source in our 4-dimensional universe. These anomalies must have a source and he thinks that the best way to explain them is that bulk field passing through our brane could produce changing in tidal gravity. A bulk field? A field is something that extends out through space exerts forces on things it encounters (as electric field, gravitational field and so on). A bulk field is a collection of force lines that reside in the five-dimension bulk, what kind of force lines, the professor doesn't know.
Professor's Equation-2
Bulk fields also play two other crucial roles: they hold the wormhole open and they could explain how to implement the professor's plan A: transport millions of people in a spaceship to save them from the dying Earth. But laws of physics are expressed in the language of maths. So, the famous professor's equation is the mathematical explanations of bulk fields and it's called: "Action". He managed to solve the equation, but "it's only half the answer".
Into Gargantua
Where they can find other half of the answer? Simple, inside a black hole. So, in Interstellar, Cooper decides to throw himself into Gargantua, with his friend Tars. Looking up as he falls inward, Cooper sees the image of external universe reduced in size (due to aberration of the starlight), then we are rather ignorant of what goes on inside black holes. In interstellar, looking downward, Cooper should see light from objects that fell into Gargantua before him and are still falling inward. He can see them in reflected light from the accretion disk above and they are mostly interstellar dust (this explain the "fog" he encounters as he fall). Cooper can also overtake stuff that's infalling more slowly than him (this explain the white flakes that hit and bounce off his Ranger in the movie).
The Tesseract
As the ranger nears the singularity, Cooper ejects in the nick of time and tidal forces tear the Ranger apart. But at the singularity's edge a tesseract awaits Cooper, placed there probably by bulk beings. A standard tesseract is a hypercube, a cube in 4-space dimensions. Because Cooper is made of atoms held together by electric and nuclear forces, all of which can exist only in 3-space dimensions and 1-time, he is confined to reside in one of tesseract's 3-space-dimensioanl faces (a cube). But entering it, Cooper experiences a really complexified tesseract (this is a Nolan's visual choice, extreme is always better for audience!). However, a tesseract like this allow Cooper to carry messages into our brane's past, with gravitational forces (the force lines of the bulk field).
Messaging Murph
In the tesseract there is a one-way space-time barrier: light can travel toward the future from Murph to him, but not the vice versa. Only gravity can surmount that barrier, Cooper discovers. Moreover, he discovers that it can communicate (via electromagnetic waves) with Tars, because also him was saved somewhere in the tesseract. So, he decided to send quantum data collected from Tars to Murph. (Quantum data are referred to any data which could be obtained when gravity is studied at the quantum level, as in a black hole). In the movie we see Cooper pushing with his finger on a "world tube" of a watch's second hand, that produces a gravitational force. This force makes the second-hand of the watch in a Morse-encoded pattern that carries the quantum data. These will help Murph to find a Theory of Everything.
The Tesseract Revisited
The Bulk Beings
All the characters in Interstellar are convinced that bulk beings exist, though they use that name only rarely. Usually, the characters call the bulk beings “They.” A reverential They. Early in the movie, Amelia Brand (played by Anne Hathaway) says to widowed astronaut Cooper (Matthew McConaughey), “And whoever They are, They appear to be looking out for us. That wormhole lets us travel to other stars. It came along right as we needed it.”
One of Christopher Nolan’s clever and intriguing ideas is to imagine that They are actually our descendants: humans who, in the far future, evolve to acquire an additional space dimension and live in the bulk. Late in the movie, Cooper says to TARS (a robot voiced by Bill Irwin), “Don’t you get it yet, TARS? They aren’t beings. They’re us, trying to help, just like I tried to help Murph.” TARS responds, “People didn’t build this tesseract” (in which Cooper is riding). “Not yet,” Cooper says, “but one day. Not you and me but people, people who’ve evolved beyond the four dimensions we know.”
2D Brane and 3D Bulk
In 1844 Edwin Abbott wrote a satirical novella titled Flatland: A Romance of Many Dimensions. Though its satire on Victorian culture seems quaint today and its attitude toward women outrageous, the novella’s venue is highly relevant to Interstellar. I recommend it to you.
It describes the adventures of a square-shaped being who lives in a two-dimensional universe called Flatland. The square visits a one-dimensional universe called Lineland, a zero-dimensional universe called Pointland, and most amazing of all to him, a three-dimensional universe called Spaceland. And, while living in Flatland, he is visited by a spherical being from Spaceland.
In my first meeting with Christopher Nolan, we were both delighted to find the other had read Abbott’s novella and loved it.
In the spirit of Abbott’s novella, imagine that you are a two-dimensional being, like the square, who lives in a two-dimensional universe like Flatland. Your universe could be a tabletop, or a flat sheet of paper, or a rubber membrane. In the spirit of modern physics, I refer to it as a two-dimensional (2D) brane.
Being well educated, you suppose there is a 3D bulk, in which your brane is embedded, but you’re not certain. Imagine your excitement when one day you are visited by a sphere from the 3D bulk. A “bulk being,” you might call him.
At first you don’t realize it’s a bulk being, but after much observation and thought, you see no other explanation. What you observe is this: Suddenly, with no warning and no apparent source, a blue point appears in your brane (top left of Fig 1). It expands to become a blue circle that grows to a maximum diameter (middle left), and then gradually shrinks to a point (bottom left) and disappears completely.
You believe in conservation of matter. No object can ever be created from nothing, yet this object was. The only explanation you can find is shown in the right half of the figure above. A three-dimensional bulk being — a sphere — passed through your brane. As it passed through, you saw in your brane its changing two-dimensional cross section. The cross section began with a point at the sphere’s south pole (top right). It expanded to a maximal circle, the sphere’s equatorial plane (middle right). It then shrank to a point, the sphere’s north pole, and disappeared (bottom right).
Imagine what would happen if a 3D human being, living in the 3D bulk, passed through your 2D brane. What would you see?
Bulk Beings From the Fifth Dimension, Passing Through Our 3D Brane
Suppose that our universe, with its three space and one time dimensions, really does live in a five-dimensional bulk (four space and one time). And suppose there are “hyperspherical beings” who live in the bulk. Such a being would have a centre and a surface. Its surface would consist of all points, in four space dimensions, that are some fixed distance from the centre, for example, 30 centimetres. The bulk being’s surface would have three dimensions and its interior would have four.
Suppose that this hyperspherical bulk being, traveling in the bulk’s out direction or back direction, were to pass through our brane. What would we see? The obvious guess is correct. We would see spherical cross sections of the hypersphere (see Fig 2).
Can you guess what we would see if a four-dimensional human being living in the bulk were to pass through our brane? To speculate about this, you need to imagine what a four-dimensional human being — with two legs, a torso, two arms, and a head — must “look like” in the bulk, with its four space dimensions. And what its cross sections must look like.
The Nature of Bulk Beings, and Their Gravity
If there are bulk beings, what are they made of? Certainly not atom-based matter like us. Atoms have three space dimensions. They can only exist in three space dimensions, not four. And this is true of sub-atomic particles as well. And it is true also of electric fields and magnetic fields and the forces that hold atomic nuclei together.
Some of the world’s most brilliant physicists have struggled to understand how matter and fields and forces behave if our universe really is a brane in a higher-dimensional bulk. Those struggles have pointed rather firmly to the conclusion that all the particles and all the forces and all the fields known to humans are confined to our brane, with one exception: gravity, and the warping of spacetime associated with gravity.
There might be other kinds of matter and fields and forces that have four space dimensions and reside in the bulk. But if there are, we are ignorant of their nature. We can speculate. Physicists do speculate. But we have no observational or experimental evidence to guide our speculations. In Interstellar, on Professor Brand’s blackboard, we see him speculating.
It’s a reasonable, half-educated guess that, if bulk forces and fields and particles do exist, we will never be able to feel them or see them. When a bulk being passes through our brane, we will not see the stuff of which the being is made. The being’s cross sections will be transparent.
On the other hand, we will feel and see the being’s gravity and its warping of space and time. For example, if a hyperspherical bulk being appears in my stomach and has a strong enough gravitational pull, my stomach may begin to cramp as my muscles tighten, trying to resist getting sucked to the centre of the being’s spherical cross section.
If the bulk being’s cross section appears and then disappears in front of a checkerboard of paint swatches, its space warp might lens the swatches, bending the image I see, as in the top half of Fig 3.
And if the bulk being is spinning, it might drag space into a whirling motion that I can feel and see, as in the bottom of Fig 3.
Cooper, Brand, and the crew of the Endurance never actually feel or see our bulk descendants’ gravity or their space warps and whirls. That, if it ever occurs, is left for a sequel to Interstellar. But older Cooper himself, riding through the bulk in the closing tesseract, reaches out to the Endurance’s crew and his younger self, reaches out through the bulk, reaches out gravitationally. Brand feels and sees his presence, and thinks he is They.
Curiosities
Introduction
As we have seen, physicists like Kip Thorne were asked to produce this film, who worked hard to make Interstellar as true and scientific as possible. In my opinion, with an excellent result. But there are still some curiosities, not really scientific, which are however worth knowing.
Real Corn Crop
For a scene in a cornfield, Christopher Nolan sowed more than 200 hectares of corn. The maize that grew after the shoot was sold and generated profit.
The Dust Bowl
Dust plays an important role in the film, because it's the cause of some of their health problems. The documentary "The Dust Bowl" of 2012 was the inspiration for the narrative system of Interstellar: the documentary tells of the terrible plague of the clouds of sand and dust that hit the moors of the northern United States in the 1930s, in the midst of Great Depression. So, the interviews we see on television in Interstellar are not recited and those are not actors. They are the real survivors of the real disaster of the 1930s and those are their authentic testimonies, present in the 2012 documentary and reused, with permission, by Christopher Nolan for Interstellar.
The Genius of Hans Zimmer
Hans Zimmer is the main creator of the background music in Interstellar. Obviously, his work has been subliming (as always). In particular, on the Miller's planet, the soundtrack in the background has a prominent ticking noise. These ticks happen every 1.25 seconds. Well, each tick we hear is a whole day passing on Earth. This is because we remember the time dilation due to Gargantua, so every hour spent there was seven years’ time on Earth.
Hans Zimmer is a genius.
Intentional Errors
Upon finding Miller's planet sterile, Amelia Brand argues for going next to a planet very far to Gargantua, Edmunds' planet, instead of the closer Mann's planet because: "accident is the first building block of evolution, but when you're orbiting a black hole, not enough can happen, it suck in asteroids, comets... We need to go further afield". Well, this is wrong, because is scientifically proved that the objects density near a black hole does not go down, it grows. So, the possible encounter with some asteroid is more likely and could have brought life to the planet. This is one of the few spots where the characters get the science wrong. However, Nolan knew that Brand's argument was wrong, but he chose to retain these lines from Jonah's draft of the screenplay. No scientists have perfect judgment.
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