SPOILER ALERT: The purpose of this article is to provide explanations about the real, theoretical scientific concepts presented in the film, Interstellar (2014) so that people can have a greater understanding of this unusually complex film. If you haven't watched the film and you do not wish to know the specific details of the film, please stop reading and come back here later if you're interested to know more. 

If there are any mistakes found in this article, please kindly provide any comments below so I can rectify it.

- Saturday, 8 November 2014 -

 

• The more massive an object is, the greater the distortion (gravitational influence) it causes in the surrounding space.
• The distortion becomes weaker (amount of spatial warping decreases) as the distance between objects becomes larger.

Examples:
 

• In our solar system, the presence of mass (the sun) causes the fabric of space and time around it to warp (distorted). This distortion causes other surrounding objects (planets) to move around the sun and their motion is determined by the shape of the warp (elliptical orbit).
• Earth, being a massive object, also warps the fabric of space and time, but far lesser than the sun. This is how the Earth keeps the moon in orbit and each of us bound to its surface.

 

                                   

 

Earth causes the fabric of space and time to warp, the moon is kept in orbit around the Earth because it rolls along a valley in the warped spatial fabric. In more precise language, it follows a “path of least resistance” in the distorted region around the Earth.

 

The theory states that time goes more slowly in the presence of a gravity field (Gravitational time dilation) and that the universe is expanding, in some cases faster than the speed of light, because it’s the space itself that’s expanding, not objects within it.

 

Artificial Gravity

 

The effects of zero gravity in space is normally the big problem that we, as humans will face with long-term interstellar space travel. We were born on Earth and therefore our bodies are adapted to survive under gravity, but when we’re in space for long periods of time, our muscles will degrade.

 

 

To prevent this from happening, scientists have created different designs of installing artificial gravity on spaceships. One such way is to rotate the spacecraft, as shown in the film. The rotation creates a centrifugal force that pushes objects to the outer walls of the spacecraft. This push acts similar to how gravity would, but just in an opposite direction.

 

You experience this same form of artificial gravity when you’re driving around a tight curve and feel like you’re being pushed outward, away from the central point of the curve. For a spinning spacecraft, your wall becomes the floor on which you walk.

 

            

 

 

 

Gravitational Time dilation

 

In the film, Cooper tells his weeping 10-year-old daughter, Murph, before he flies off to space, “When I get back, we may be the same age.”

 

To understand time dilation, one must first understand the concept of a reference frame.

 

A reference frame is an imaginary coordinate system that specifies the location and time measurements of events with respect to a fixed origin. It can also be thought of as an imaginary map.

 

In space-time physics, every person (or observer) has his or her own reference frame in which he/she is the origin. Therefore, a person assigns spatial and time coordinates to events based on his or her position.

 

 

Time dilation is the difference between time measurements of two reference frames that are moving at different velocities with respect to one another. Two of the time dilations in Einstein’s Theory of Relativity have been experimentally proven. (the other one is Relative velocity time dilation)

 

According to Einstein’s Theory of General Relativity, time differs from place to place or time runs more quickly (the actual time speeds up) at higher altitudes because of a weaker gravitational force.

 

The effect of time passing at different rates in regions of different gravitational potential is called Gravitational time dilation. The lower the gravitational potential (closer to the centre of a massive object), the slower time passes.

Note: The gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of gravity to move an object to a fixed reference location. As we go closer to the centre of a massive object, the gravity gets stronger, meaning the gravitational potential needed to move an object becomes lesser.

 

In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of less than 1 meter (12 inches), using optical atomic clocks. The clock at a higher altitude was found to be running faster than the other.

 

It means that your head ages more quickly than your feet and that people living on the top floor of a tower block age more quickly than those on the ground floor. However, the effect is so small (negligible) that it would add just 90 billionths of a second to a 79-year life span.

 

 

In general relativity, the time dilation effect is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower and observers on the ground will agree about that. Gravitational time dilation is agreed upon by all stationary observers, independent of their altitude.

 

Einstein’s Theory of Special Relativity 

 

A theory of the structure of space and time developed by Albert Einstein in 1905, which states that:
All the laws of physics are equally valid for all observers in uniform motion (velocity) relative to one another. In other words, the speed of light and the relationship between force (energy), mass, and acceleration are the same for all observers (or reference frames) moving at constant velocity.

The speed of light from a uniformly moving source or in a vacuum is always the same for all observers; regardless of how fast (or slow) the light source or its observer is moving.

 

The consequences that follow from the special theory of relativity are:

 

Relativity of simultaneity - simultaneity is not absolute, but dependent on the observer's reference frame. It is impossible to say whether two events occur at the same time if those events are separated in space. So, the perception of Time is relative (dependent on the individual’s or observer’s point of view).

Things that appear to happen at the same time to stationary observer A may appear to happen at different times to moving observer B.

 

Example: Two plane crashes that happened at the same space. All observers in the same space will agree that both planes arrived at the point of impact at the same time. But where the events are separated in space, such as one plane crash in London and another in Chicago, the question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in others (in a different state of motion relative to the events) the crash in London may occur first, and in others the Chicago crash may occur first.

 

Length contraction - the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer. This contraction is usually only noticeable when objects are moving near the speed of light; to the direction in which the observed body is travelling.

 

Example:

 

At a speed of 13,400,000 m/s, the length is 99.9% of the length at rest; at a speed of 42,300,000 m/s, the length is still 99%.

 

Mass-energy equivalence

 

energy and mass are essentially the same thing, and transmutable into each other (neither one appears without the other). Energy always exhibits mass in whatever form the energy takes. The law of conservation of energy is relative to the law of conservation of mass.

The total internal energy, E of a body at rest is equal to the product of its rest mass, m (E = mc²).

Since c² is a big number, a little mass goes an extremely long way in producing energy.

 

Relativistic mass, m = E/c² for all particles moving at the speed of light. 

 

Einstein’s formula explains that nothing can travel faster than the speed of light. Nothing outruns electromagnetic radiation – photons (light, radio waves, microwaves, ultraviolet radiation, X-rays, gamma rays, infrared radiation). The faster something moves the more energy it has and from Einstein’s formula we see that the more energy something has the more massive it becomes.

 

 

 

Therefore, a slower-than-light particle with non-zero rest mass needs infinite (or vast amounts of) energy to accelerate to the speed of light; although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons - hypothetical).

 

Relative Velocity Time dilation

 

Time runs at different rates, depending on the relative velocity between two observers (clocks moving near the speed of light operate more slowly than stationary clocks).

 

However, the only way this can happen is if an observer’s space and time measurements of a system depend on the system’s velocity relative to that observer. This means that two observers can measure the time interval between the same two events and come up with different time measurements for these events, as long as one of the observers is moving at constant velocity with respect to the other. The faster the relative velocity, the slower time passes.

 

Therefore, when two people synchronize their clocks to read the same time, this synchrony remains as long as the two people remain at rest with respect to one another. However, if one person boards an airplane and flies a certain distance, that person’s clock will run at a slower rate than the person on the ground. This is called Relative velocity time dilation.

 

When a particle moves horizontally, the total speed of the constituent particles with respect to the rest frame is still equal to the speed of light. The difference, though, is that when the particle is moving horizontally, the total speed of the particle is made up of “orbital speed” and “horizontal speed” components, rather than just an orbital speed component as is the case when the particle is at rest.

The Standard Model of elementary particles shows that every particle consists of smaller particles that orbit each other at the speed of light. That is, each of these particles has an “orbital speed” that equals the speed of light.

 

Examples:

• Researchers in the 1970s used atomic clocks to test the theory. One clock remained on the ground, and the other clock flew on a jet at 600 miles per hour. As predicted by Einstein’s Special Theory of Relativity, the clocks ran at different rates. The airplane clock ran billionths of a second slower than the ground clock. (Atomic clocks are known to be so accurate that they lose or gain less than 1 second every 3.7 billion years.
• In 2010, relative velocity time dilation was observed at speeds of less than 10 meters per second using optical atomic clocks connected by 75 meters of optical fibre.
• In special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)

 

It is to note that special and general relativistic effects can combine:

 

Imagine for any two civilizations with an enormous distance between them (light years apart) and they communicate by transmitting radio waves that travel at the speed of light, the sender will be millennia ahead of the recipient by the time the message reaches the recipient.

Example: 

The satellite clocks are moving at 14,000 km/hr in orbits that circle the Earth twice per day, much faster than clocks on the surface of the Earth, and Einstein's theory of special relativity says that rapidly moving clocks tick more slowly, by about 7 microseconds per day. (relative velocity time dilation)

Also, the orbiting clocks are 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein's general relativity theory says that gravity curves space and time, resulting in a tendency for the orbiting clocks to tick slightly faster, by about 45 microseconds per day. (gravitational time dilation)

The net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day. At 38 microseconds per day, the relativistic offset in the rates of the satellite clocks is so large that, if left uncompensated, it would cause navigational errors that accumulate faster than 10 km per day! GPS accounts for relativity by electronically adjusting the rates of the satellite clocks, and by building mathematical corrections into the computer chips which solve for the user's location. Without the proper application of relativity, GPS would fail in its navigational functions within about 2 minutes. (James S. McDonnell)

 

Sources:

• Wikipedia
• Relativity: The Special and the General Theory – Albert Einstein 
• Einstein’s Theory of Relativity – Max Born
• Simply Einstein: Relativity Demystified - Richard Wolfson
  http://physicscentral.com/explore/writers/will.cfm
   

Things to know about Interstellar (2014) Explained - Part 2

 

 

Now, let's proceed to explain what quantum theory is about:

  Quantum mechanics/quantum physics/quantum theory

 

      Any theory of physics in which the Universe has no single history or even an independent existence and objects do not have single definite histories. It seeks to explain the Universe from a subatomic (microscopic) point of view. It is a branch of physics that provides a mathematical description of much of the dual particle-like and wave-like behaviour and interactions of energy and matter. It states that matter can be both a particle and a wave. It departs from classical mechanics primarily at the atomic and subatomic scales, the so-called quantum realm.

At quantum level, matter doesn't exist at a fixed state; instead it exists in a cloud of ‘probability’ called the ‘wave function’ where it exists in all states and in all locations. Only by ‘looking/observing’ at the particle, we collapse the ‘wave function’ and force it to exist in a certain location and in a certain state. Example: Light is made up of packets of energy called photons. 

 

Quantum uncertainty/Heisenberg uncertainty principle (Copenhagen interpretation) 

 

A finding in quantum physics by Werner Heisenberg that states that one cannot know both the exact position and exact momentum (or velocity) of a single particle at the same time (certain pairs of physical properties cannot be known simultaneously to arbitrary precision). You can only measure the position of a particle or measure its movement but you can never find out both.

 

 

In order to know where something is, you must be able to see it – and to see an object you must shine light on it. Light is made up of packets of energy called photons which although tiny, do possess some mass. Because particles are so small, the photons that you have used to see where it is will cause it to move. So, although you have measured its position, you can no longer know its velocity. The very act of observing a particle changes its physical attributes, so we can never know anything about it.

 

Quantum superposition

 

The quantum mechanical property of a particle to occupy its entire possible quantum states simultaneously. Due to this property, to completely describe a particle one must include a description of every possible state and the probability of the particle being in that state.

 

Example: In quantum physics, any living thing could exist simultaneously in various states, from completely alive to dead and all stages in-between. All of these states, known as superposition are possible outcomes before observation is performed on the living thing.

Note: Time is a dimension which isn't linear. At quantum level, every moment, past, present and future, exist simultaneously. Therefore there is no paradox. It's just that 3-dimensional beings like us don't/can't experience time in this way. We experience it in a linear fashion.

 

 

Quantum non-locality/Quantum entanglement

 

This phenomenon means that once two particles interact together, they become forever ‘entangled’ and that whatever affects one will instantly affect the other – no matter the distances involved, even if they are separated by light-years of space. So by affecting the properties of the first particle, you instantly affect the properties of the second, making measurement of the second particle meaningless.

 

“All things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.” – Richard Feynman

 

In particle physics, an elementary particle is a particle with no measurable internal structure; that is, it is not made up of smaller particles. Elementary particles are fundamental objects of quantum field theory. 

 

• Proton – A positively charged atomic particle that, along with the neutron, forms the nucleus of an atom.
• Neutron – An electrically neutral atomic particle that, along with the proton, forms the nucleus of an atom.
• Electron – An elementary particle with a negative charge that surrounds the nucleus of an atom and defines its chemical properties.

 

 

Protons and neutrons are each composed of three quarks.

 

Note: We tend to visualize an electron to be a tiny ball, in orbit around a larger cluster of balls representing protons and neutrons. That isn't what it is like. They don’t look like little balls. They are not like anything we recognize at all.

 

In Superstring Theory, each elementary particle is composed of a single string (each particle is a string), all strings are absolutely identical. Differences between particles arise because their respective strings undergo different resonant vibrational patterns. (Brian Greene)

 

All elementary particles are either bosons or fermions (depending on their spin). Spin is the intrinsic angular momentum of a subatomic particle. It is an important part of a particle’s quantum state. 

 

 

All the particles of the Standard Model have been observed (experimentally verified), except Higgs boson ("tentatively confirmed") and graviton (theoretical).

 

Fermions:

 

• 6 ‘flavors’ of Quarks — up, down, charm, strange, top, bottom.
• 6 ‘flavors’ of Leptons — electron neutrino, electron, muon neutrino, muon, tau neutrino, tau.

 

Bosons:

 

• 12 Gauge bosons (force carriers) — eight gluons of the strong force, three W and Z bosons of the weak force, photon of electromagnetism.
• Other bosons — Higgs boson, graviton.

                                             

 

Standard Model of Particle Physics 

 

The Standard Model shown above explains the subatomic composition of the Universe and describes how three of the four forces stuck together (gravity is not included as graviton is not yet discovered). It explains how the Universe works at the subatomic level and is the basic understanding of matter for physicists.

Higgs boson and Higgs field

The Higgs Field is an energy field that exists everywhere in the universe. The Higgs field is not considered a force. It cannot accelerate particles, it doesn't transfer energy. The field is accompanied by a fundamental particle called the Higgs Boson, which the field uses to continuously interact with other particles. As particles (except the massless ones) pass through the field they are "given" mass. Different particles interact with the Higgs field with different strengths, hence some particles are heavier (have a larger mass) than others. (The Higgs particle does not interact with massless particles, such as a photon or a gluon. Since these particles don't interact with the Higgs field, the Higgs boson also doesn't interact with them.) The process of giving a particle mass is known as the Higgs Effect.

 

Elementary particle interactions 
 

Note: Mass itself is not generated by the Higgs field - the creation of matter or energy would conflict with the laws of conservation. However, mass is "imparted" to particles from the Higgs field, which contains the relative mass in the form of energy. Once the field has endowed a formerly massless particle the particle slows down because it has become heavier.

Note: The Higgs particle, like many other elementary particles, is not a stable particle. Once the Higgs particle has been created, it will eventually decay. Since it interacts with all kinds of other massive particles it can be created in collisions. If the Higgs field did not exist, particles would not have the mass required to attract one another, and would float around freely at light speed.

 

Four fundamental forces-mediating fields

 

• Strong Nuclear Force – Holds together the protons and neutrons inside the nucleus of an atom – and the protons and neutrons themselves. The strong force is the energy source for the Sun and nuclear power.
• Weak Nuclear Force – Causes radioactivity and plays a vital role in the formation of the elements in stars and the early Universe. We don’t come into contact with this or the strong force in our everyday lives.
• Electromagnetic Force – The long-range force much stronger than gravity, but acts only on particles with an electric charge. Electric forces between large bodies cancel each other out but dominate atoms and molecules.
• Gravity – The weakest of the four, but a long-range force that acts as an attraction on everything in the Universe. For large bodies, the gravitational forces add up and can dominate all others.   

 

 The four fundamental forces of nature

 

The following theory is important to understand the third act of the film, Interstellar.

 

Unified Field Theory (UFT) - coined by Einstein, who attempted to unify the general theory of relativity with electromagnetism, hoping to recover an approximation for quantum theory and to bring four fundamental force-mediating fields (Electromagnetism, Strong and weak nuclear force and gravity) together into a single framework (a single field). In short, the theory attempts to reconcile quantum mechanics and Einstein’s general relativity.

 

Our preoccupation with matter itself is incredibly skewed. We have this tendency to think that only solid, material ‘things’ are ‘really’ things at all. ‘Waves’ of electromagnetic fluctuation in a vacuum seem ‘unreal’. Most people think that waves had to be waves ‘in’ some material medium. Unfortunately, no such medium was known or discovered. We are more like waves than permanent ‘things’. 

 

For example: An experience from your childhood. Something you remember clearly, something you can see, feel, maybe even smell, as if you were really there. After all, you really were there at the time, weren't you? How else would you remember it? But the reality is: you weren't there at all.

Not a single atom that is in your body today was there when that event took place…Matter flows from place to place and momentarily comes together to be you. All your body cells at that time are dead and replaced by newly-formed body cells every day. Therefore, whatever you are now, you are not the stuff of which you are made in the past.

Humans live in ‘macroscopic levels’ of space-time dimensions that are bound by the four fundamental forces. They travel relative to one another at slow speeds, generally unaware of the distortions in the passage of time and perceive time linearly.

Before quantum mechanics, it was generally thought that all knowledge of the World could be obtained through direct observation, that things are what they seem, as perceived through our senses. But, quantum mechanics have shown that this is not the case, by remarkably accurate at predicting events on microscopic scales, while able to reproduce the predictions of the old classical theories when applied to events on macroscopic scales.


Sources:

• Wikipedia
• The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory – Brian Greene
• The Grand Design – Stephen Hawking and Leonard Mlodinow
• The Brief History of Time - Stephen Hawking
• The Fabric of the Cosmos: Space, Time and the Texture of Reality – Brian Greene
  Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension – Michio Kaku
  http://www.fnal.gov/pub/science/inquiring/questions/higgs_boson.html
   

Things to know about Interstellar (2014) Explained - Part 3

 

 

Now, let's explain what a wormhole and a black hole is:

Einstein-Rosen Bridge/Wormhole

A wormhole is a hypothetical space-time topology, a ‘shortcut’ that would allow travel between two points at apparently (closer to) faster-than-light speeds . The impossibility of faster-than-light relative speed only applies locally.

In reality, movement through a wormhole would not be faster-than-light, but rather moving at normal speed through folded space. Wormholes allow superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While travelling through a wormhole, subluminal (slower-than-light) speeds are used.

 

To explain what is a wormhole in simple terms, we have to first visualize space as a two-dimensional (2D) surface, let's say a paper. The normal route from Point A to Point B would be a straight line. But what if, we have something that generates a sudden enormous amount of energy strong enough to bend the paper (warp the fabric of space and time)?

A wormhole can be pictured as a hole in that surface that leads into a 3D tube (the inside surface of a cylinder). This tube then re-emerges at another location on the 2D surface (paper) with a similar hole as the entrance. An actual wormhole would be analogous to this but with the spatial dimensions raised by one - 4th dimensional space. For example, instead of circular holes on a 2D plane, a real wormhole's mouths are spheres in 3D space (perfectly round geometrical and circular object in three-dimensional space).


 

A wormhole as shown in Interstellar

If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole (e.g. running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it). However, light beam travelling through the wormhole would always beat the traveller.

Wormholes may connect an infinite series of parallel universes. Parallel universes may be graphically represented by two parallel planes. Normally, they never interact with each other. However, at times wormholes may open up between them, perhaps making communication and travel possible between them. Wormholes may connect a universe with itself, perhaps providing a means of interstellar travel. Since wormholes may connect two different time eras, they may also provide a means for time travel.

A wormhole may connect two regions that exist in different time periods. Thus, the wormhole may connect the present to the past. Since travel through wormhole is instantaneous, one could use the wormhole to go backward in time. It is not possible to travel to the future. However, vast amounts of energy may be required to generate a wormhole, which is beyond what will be technically possible for centuries to come. (Kip Thorne)

Note: Relative velocity time dilation takes place when travelling within a wormhole - time passes slowly when moving near speed of light (in a wormhole) compared to time on Earth.

Einstein's theory of relativity predicts that if traversable wormholes exist, they could allow time travel. This would be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation  would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone travelling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.

In short, Einstein’s theory states that time passes more slowly for a highly accelerated body. If one end of a wormhole were accelerated to close to the speed of light while another was stationary, a traveller entering into the stationary hole would emerge in the past from the accelerated hole. This type of wormhole would be called a closed time-like curve (a closed loop in space-time is formed) or a timehole.
 

 

Example of interstellar time travel:

• Suppose a traveller need to attend a 2-hour meeting at a different galaxy or universe. The traveller is from Universe 1/Galaxy 1. Consider two clocks at both holes both showing the date as 2004. After being taken on a trip at relativistic velocities, the accelerated hole reached Universe 2/Galaxy 2.
• The clock at the accelerated hole mouth of Universe 2/Galaxy 2 reads 2005 (assuming it takes 1 year for hyperspace travel due to extremely long distances between galaxies or universes) while the clock at the stationary hole mouth of Universe 1/Galaxy 1 reads 2010 (due to relative velocity and gravitational time dilation).
• The traveller attended the meeting for 2 hours and travel back to go home. The clock at the accelerated hole mouth of Universe 3 reads 2006.

Question arises: Is Universe 3 the same universe as Universe 1? Are Universe 1 and 3 two of the many universes in a quantum multiverse? The ‘original’ universe where the traveller comes from is actually Universe 1, which should be at least 2016 after the travel has taken place. If the two universes are the same and belongs in the same quantum multiverse, this means that the traveller had travelled back in time.

 

 

 

Infographics taken from

 

Black Hole

Note: Although solid mathematical calculations predict that black holes do exist, no one can ever confirm that it's the case until they really observed it in front of their eyes. The closest known black hole to Earth is thousands of light years away, making it impossible to travel into space (with our current technology) to 100% confirm that they do exist. Even if you have the chance to do so, would you dare enough to get near it? Despite the existence of multiple scientific theories to study and understand the nature of black holes, even today, what happens inside a black hole is still not completely known or understood by many physicists.
 

 

The theory of general relativity predicts that a sufficiently compact mass will distort space-time to form a black hole. General Relativity is essential in modern astrophysics and provides the basis for the current understanding of black holes - regions of space where gravitational attraction is so intense that not even light can escape. 
 

The mass of a neutron star cannot exceed about 3 solar masses. If a core remnant is more massive than that, nothing will stop its collapse, and it will become smaller and smaller and denser and denser. Once the gravitational collapse of the neutron core begins, there is no force known which is strong enough to stop the collapse. The collapse will continue forever.

Will our Sun become a black hole?
No. Stars like the Sun just aren't massive enough to become black holes. At the very minute, it is slowly expanding as the nuclear reactions in the core use up the hydrogen (converting it to helium - nuclear fusion) to generate energy. In several billion years, the Sun will cast off its outer layers, and its core will form a white dwarf - a dense ball of carbon and oxygen that no longer produces nuclear energy, but that shines because it is very hot. It will stay for billions of years longer before finally cooling down and fades away. A typical white dwarf is about as massive as the Sun, but only as big as Earth, which is one percent of the Sun's present diameter.  

Stationary black hole
From what is known about neutron stars, it is clear that a stellar black hole should be rotating very rapidly. However, the structure of a stationary black hole will be considered first. How rapid rotation affects the structure of a stellar black hole will then be considered.

A stationary black hole has three regions of interest:
 

1. Gravitational Singularity - General relativity predicts that no force can stop the gravitational collapse of a black hole. Mathematically, all of the mass is predicted to reside in an infinitely small point (infinite density) at the black hole's center. The gravitational field at the centre of a black hole would be infinite and any material object would be crushed. The electrons would be ripped off from atoms, and even the protons and neutrons within the nuclei themselves would be torn apart.
2. Event Horizon - Gravity is infinitely strong at the singularity. Gravity becomes weaker at distances further from the singularity. If a 3 solar mass black hole is considered, light (fastest elementary particle known to us) has no chance of escaping unless it is more than 9 km from the singularity. This location in the black hole is known as the event horizon. Karl Schwarzschild first calculated the size of the event horizon in 1916 using the General Theory of Relativity; therefore, the event horizon is also known as the Schwarzschild radius - the radius of a sphere such that, if all the mass of an object is compressed within that sphere, the escape speed from the surface of the sphere would equal the speed of light. Once a stellar remnant collapses below this radius, the singularity is no longer directly visible. Schwarzschild calculated that the size of the event horizon is directly proportional to the mass of the black hole. General relativity predicts that: At the event horizon of a black hole, the deformation of space-time caused by the singularity is so strong that there are no paths that can lead away from the black hole.
3. Photon Sphere - A spherical region of space where gravity is strong enough that photons (light) are forced to travel in orbits. The photon sphere corresponds to a distance at which light would orbit about the center of the black hole. The photon sphere is 1.5 times larger than the event horizon.

 

Note: Relativistic effects are strong in the vicinity of a black hole, so phenomena like length contraction and gravitational time dilation take place. As space contracts, time expands. To a distant observer, clocks near a black hole will appear to tick more slowly than those further away from the black hole. An object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it. Eventually, at a point just before it reaches the event horizon, the falling object becomes so dim that it can no longer be seen.

Note: The gravitational effects of a black hole are unnoticeable outside of a few Schwarzschild radii...black holes do not “suck in” material any more than an extended mass would.

Spinning black hole
 

Spinning neutron stars, that are dense enough, produce spinning black holes, which astronomers have observed, albeit indirectly. What you need to know about spinning black holes is that they warp the space around them differently than stationary black holes. This warping process is called frame dragging, and it affects the way a black hole will look and distort the space and, more importantly, the space-time around it. 

As a black hole begins to spin, its event horizon becomes smaller because the inward force of gravity is diminished to some extent by the outward force cause by the spinning.

 

1. Stationary limit - The boundary around a spinning black hole. At the poles of a spinning black hole, the stationary limit boundary touches the new (smaller) event horizon. At the equator of a spinning black hole, the stationary limit boundary is the size of the (bigger) event horizon of a stationary black hole.
2. Accretion disks - A spinning disk of extremely hot matter (gas and dust) surrounding an object with an intense gravitational field. It is formed of matter that's in the process of falling into the black hole. It is important to know that the photon sphere is inside the radius of the accretion disk and outside of the radius of the event horizon.
3. Ergosphere - The region between the stationary limit and the event horizon of a spinning black hole. Whether or not light can escape from the ergosphere depends on the direction in which it is traveling. 

Penrose process - The process wherein energy can be extracted from a spinning black hole. That extraction is made possible because the rotational energy of the black hole is located not inside the event horizon of the black hole, but in the ergosphere. All objects in the ergosphere become dragged by a rotating space-time. Although matter has to rotate in the same direction as the black hole within the ergosphere, particles can escape from it through this process.
In the film, Cooper and Amelia used this process to extract momentum from the black hole's spin to escape from it and give them a further boost to Edmund's planet.

 

Penrose Process works by extracting the energy from a black hole through use of a intermediary particle. This particle entering the spinning black hole breaks apart by some means sending one piece into the event horizon and the other out of the ergosphere with more energy than it originated with.

Gravitational lensing - An effect of Einstein's theory of general relativity – mass bends light. The gravitational field of a massive object will extend far into space, and cause light rays passing close to that object (and thus through its gravitational field) to be bent and refocused somewhere else. The more massive the object, the stronger its gravitational field and hence the greater the bending of light rays.

Note: General Relativity predicts that mass bends light. In strong gravitational fields, light will be significantly bent back towards the mass. A black hole is like a black body that reflects no light. So black holes cannot be observed directly. 

Moreover, quantum field theory in curved space-time predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it all but impossible to observe.

Despite its invisible interior, the presence of a black hole can be inferred through its interaction with other matter and with electromagnetic radiation such as light. Matter falling onto a black hole can form an accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbit can be used to determine its mass and location. 

Note: The shape of the event horizon of a black hole is always approximately spherical. In four dimensions, Hawking proved that the topology of the event horizon of a stationary black hole must be precisely spherical while for rotating black holes the sphere is somewhat oblate.  

Some theorists have proposed that the warped or curved spaces in spinning black holes form bridges to other parts of the Universe or other Universes.

Things to know about Interstellar (2014) Explained - Part 4

 

Note: Although Theory of Relativity (general and special) able to explain the world on a massive scale (vast universe), but it breaks down when it came to explain the world of the infinitesimally small (quantum realm). There are contradictions between Theory of Relativity and Quantum Theory. This is the reason why Superstring Theory, Supersymmetry Theory, M-Theory, Supergravity Theory, Unified Field Theory were proposed.

 

String/Superstring (Supersymmetric string) theory is a developing unified theory of the Universe in particle physics, proposing that fundamental ingredients of nature are not zero-dimensional point particles but patterns of vibration that have length but no height or width – like infinitely tiny one-dimensional filaments called strings.

The theory attempts to reconcile quantum mechanics and Einstein’s general relativity. Each of the five superstring theories requires 10 space-time dimensions (instead of the usual four), forces and matter are supersymmetrical, no tachyons (hypothetical particle that's faster than the speed of light), but have different size and shape of the extra spatial dimensions.  

Note: The existence of more than four dimensions would only make a difference at subatomic (quantum) level.

 

The theory suggested that the entire Universe was made up of tiny vibrating strings (The electrons and quarks within an atom are not 0-dimensional objects, but made up of 1-dimensional strings). Each particle took a separate form and had specific properties because its string or strings vibrated in a different way, equating the universe to a ‘cosmic symphony of superstrings’.

These strings can oscillate, giving the observed particles their flavor, charge, mass and spin. Among the modes of oscillation of the string is a massless, spin-two state—a graviton. The existence of this graviton state (remain unproven, theoretical) and the fact that the equations describing string theory include Einstein's equations for general relativity mean that string theory is a quantum theory of gravity. Since string theory is widely believed to be mathematically consistent, many hope that it fully describes our universe, making it a theory of everything.

Through mathematical equations, it shows that the way we had previously thought of particles as “points” or “little balls” of energy was inaccurate. Brian Greene explains that strings are so small that if a single atom were the size of our solar system, a string would only be the size of a tree. Strings make up all matter from the quantum level up.

The five different string theories are just different ways of curling up the extra dimensions and describing the same phenomena in four dimensions. Physicists found that adding an eleventh dimension mathematically explained all of the seemingly different string theories as different aspects of the same theory.

Compactification

In string theory, more dimensions are bound up in other ways. Space-time is viewed as a smooth "fabric" that can be bent and manipulated in various ways. It is suggested that the universe has an inherent curvature (the universe as a whole is curved in strange ways). The normal approach to string theory's extra dimensions has been to wind them up in a tiny, Planck length–sized shape. This process is called compactification. In the 1980s, physicists showed that the extra six space dimensions of superstring theory (other than the 4 dimensions we presently live in, 3 space and 1 time) could be compactified into Calabi-Yau spaces.

 

  At large distances, a two dimensional surface with one circular dimension looks one-dimensional

Example: Think of a garden hose. If you were an ant living on the hose, you would live on an enormous (but finite) universe. You can walk very far in either of the length directions, but if you go around the curved dimension, you can only go so far. However, to someone very far away, your dimension — which is perfectly expansive at your scale — seems like a very narrow line with no space to move except along the length.

If we got close enough to the garden hose, we'd realize that something was there, but we can't "get any closer" to explore extra compactified dimensions of the universe. We can't see the extra universes because they're so small that nothing we can do can ever distinguish them as a complex structure.

M-Theory predicts that these multiple universes were created out of nothing and arise naturally from various different physical laws and constants. It involves 11 space-time dimensions (a world of 10 dimensions, plus one for Time), which allows different Universes with different laws to exist; depending on how the internal space is curled. M-Theory has solutions that allow for many different internal spaces, perhaps as many as 10⁵⁰⁰ different universes, each with its own laws, which effectively supports The Multiverse Theory. Some of the universes, unlike ours, are quite unsuitable for the existence of any form of life. Only some would allow creatures like us to exist. (Stephen Hawking) 

Example: Think of black holes as points in the four dimensions we experience - three of space and one of time. These become "black strings" when extended into a fifth dimension of space. The researchers predict that braneworld black holes are about the size of an atomic nucleus but have masses similar to that of a tiny asteroid.

 

          

Brane/Bulk/Hyperspace

In String Theory, the extra dimensions are curled up into what is called the internal space, as opposed to the 3-dimensional space that we experience in everyday life. The extra dimensions are highly curved, or curled, on a scale so small that we can’t see them. These internal spaces (hidden dimensions) have important physical significance. The exact shape of the internal spaces determines the values of physical constants, such as the charge of the electron, and the nature of the interactions between elementary particles.

 

 

The forces of Nature governing electricity, magnetism, radioactivity and nuclear reactions are confined to a 3-dimensional brane whilst gravity acts in all the dimensions and is correspondingly weaker.

 

This offered a new depiction of strings whereby, given enough energy, a string could stretch to become an extremely large floating membrane, or a brane for short. Branes can have different dimensional properties and grow as large as a universe. In fact, according to the theory, our entire universe exists on a floating brane - just one of several floating branes that each supports their own parallel universe. Each brane represents one slice of a higher dimensional space or bulk.

Just think that our four-dimensional space-time continuum as a type of membrane, or "brane," embedded in a "bulk" that takes in even more dimensions (also known as "hyperspace"). In the bulk model, at least some of the extra dimensions are extensive (possibly infinite), and other branes may be moving through this bulk. Interactions with the bulk, and possibly with other branes, can influence our brane and thus introduce effects not seen in more standard cosmological models.

For example, a point particle can be viewed as a brane of dimension zero, while a string can be viewed as a brane of dimension one.

 

The Randall-Sundrum braneworld model, named after the scientists who created it, states that the visible universe is a membrane embedded within a larger universe. Unlike the universe described by General Relativity-which has three dimensions of space and one of time-the braneworld universe contains an extra fourth dimension of space for a total of five dimensions.


 

Strings moving in the fifth dimension are represented in the everyday world by their projection onto the four-dimensional boundary of the five-dimensional space-time. The same string located at different positions along the fifth dimension corresponds to particles of different sizes in four dimensions: the further away the string, the larger the particle. The projection of a string that is very close to the boundary of the four-dimensional world can appear to be a point-like particle.

 

String theory predicts that strings can be open or closed. 

 

• Open-ended strings have at least one endpoint ‘attached’ to the brane on which they reside, keeping matter contained within that brane. Strings can move through the brane but cannot leave it, explaining why we can't physically see, reach into or interact with other dimensions. The atoms that make up our bodies are composed of open-ended strings that have attached endpoints to our 3-D membrane.
• Close-ended strings are like tiny rings, unattached to their brane and able to “leak” away from it.

 

Another way to look at it is to consider a movie screen. People on a screen appear to be three-dimensional, but they cannot actually reach off the screen into our 3-D world. They are stuck in their 2-D world, just as we are stuck in our 3-D world and cannot reach into neighbouring dimensions. 

Ever wonder why a tiny magnet can lift a paper clip, even though gravity is pulling it in the opposite direction?

The Standard Model already united three of the four forces in a unified theory, but gravity could not be reconciled with the three quantum forces. This is because gravity was such a weak force relative to the others. But, what if gravity on a parallel brane is as strong as the other forces, but is weaker here because it is only leaking into our dimension? 

String theory mathematically predicts that gravity is weak because it is only leaking here from a parallel universe. In other words, gravitons are leaking across the bulk into our own brane from an extra-dimensional brane nearby.

As a closed string or loop without attached endpoints, the other three forces (electromagnetism and the weak and strong nuclear forces) are localized on the brane, but gravity has no such constraint and propagates on the bulk. Much of the gravitational attractive power "leaks" into the bulk. As a consequence, the force of gravity should appear significantly stronger on small (subatomic or at least sub-millimetre) scales, where less gravitational force has "leaked". This would explain why gravity is many times weaker than the other forces.

 

 

The collision between two subatomic particles embedded in our 3-D universe (or "brane"). The collision produces other particles, including a graviton that escapes from our brane into the extradimensional "bulk" that lies beyond.

 

If the graviton, a massless theoretical particle responsible for transmitting gravity exists at the quantum level as a closed string, this would present a direct gravitational link to the theory of superstrings.

 

If our universe is a massive 10-brane, there might be other branes existing in a higher dimensional space. Brian Greene illustrates this by saying that it is as if the branes are slices of bread, and a multiverse is the loaf of all the slices together. He is saying that if branes are actually universes, then this might possibly imply the existence of a multiverse, called the braneworld scenario. However, there is no experimental evidence for this hypothesis.

 

 

Note: If they are present, why don’t we notice these extra dimensions?

According to string theory, they are curved up into a space of very small size.
Imagine a 2-dimensional plane. The plane is called two dimensional because the horizontal and vertical coordinates are needed to locate any point on it.

Another 2-dimensional space is the surface of a straw. To locate a point on that space you need to know the point along the straw’s length and the point along its circular dimension. If the straw is very thin, you can get a very good approximate position with only the coordinate that runs along the straw’s length, so the circular dimension might be ignored. If the straw were 10³⁰ of an inch in diameter, the circular dimension is not noticeable at all.

 

Note: The String Theory’s biggest obstacle is that much of it is not provable through observation. It is currently beyond the methodology of scientific investigation to confirm or disprove that other dimensions (floating branes and parallel universes) exist. Physicists can’t test other dimensions, study migrating gravitons, or observe the collision of floating branes to witness a Big Bang event.

 

For this reason, some scientists believe that without the ability to prove the theory, it is not true science at all. However, string theorists seem confident that proof of various sorts will come with technological progress and time.

 

4-dimensional Tesseract

A tesseract is the four-dimensional equivalent of a cube. It would only be a five-dimensional object if you're counting time as a dimension.
 

 

• a) A 3-dimensional cube appears 2-dimensional when seen in projection.
• b) A 4-dimensional cube appears 3-dimensional when viewed in projection and can be drawn in perspective on the page.
• c) Unfolding a cube.
• d) Unfolding a 4-dimensional cube.

The space we're familiar with has three dimensions all at right angles to another.
For example: up/down, forwards/backwards and left/right.
You can specify the location of any point in our 3D space by giving its coordinates in those directions. However, when you go to four dimension you've got another direction that is at right-angles to all three of the original ones. 

To draw a cube on paper, which is a projection of a 3-d object (cube) onto 2-d space (square), what you have to do is lay one square flat. Then put another square and hover it above the first one. The second square is separated from the first along the vertical direction, which you can see is at right angles to any line you can draw within the square. Now just connect the corners of one square and the corners of the other with lines. Make sure that the lines are the same length.
 

To draw a tesseract in 3-d space, it's the same. Get two cubes, separate them along the fourth dimension (which is at right angles to any line you can draw on a cube) and join the corners with lines.
 

 

This is a tesseract formed from a blue outer cube and a red inner cube. The corners are joined by more lines. The interesting thing is that the internal bits that look like pyramids with the tops cut off (highlighted yellow) are also cubes in four dimensional space, and all the new faces are squares. It's just because we can't properly represent a four-dimensional object in three dimensions that these cubes and squares look distorted.

 

Sources:

• Wikipedia
• http://news.discovery.com/space/black-holes-on-a-string-in-the-fifth-dimension.htm
  http://www.newscientist.com/article/mg21328474.500-naked-blackhole-hearts-live-in-the-fifth-dimension.html#.VFyQT_mUfON
  http://blogs.discovermagazine.com/cosmicvariance/2011/03/04/fractal-black-holes-on-strings/#.VF2t3fmUfoE
  http://www.nbcnews.com/id/13070896/ns/technology_and_science-science/t/physicists-probe-fifth-dimension/#.VFyCUfmUfOM
  http://screenrant.com/interstellar-ending-spoilers-time-travel/
• The Elegant Universe: Superstrings, Hidden Dimensions and the Quest for the Ultimate Theory – Brian Greene
• The Grand Design – Stephen Hawking and Leonard Mlodinow
• The Fabric of the Cosmos: Space, Time and the Texture of Reality – Brian Greene
• Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension – Michio Kaku

Things to know about Interstellar (2014) Explained - Part 5

Update: After a 2nd viewing on November 16, 2014, minor corrections are made to the answers provided below.
 

 

Q&A for Interstellar


1. What happened to Earth in the near future?

In the near future, Earth is too polluted and no longer able to sustain humanity. Earth's food supply is dwindling and crops are dying due to an unknown pathogenic organism (blight). However, a recently discovered wormhole provided hope for humanity to search and find a new habitable planet in a new galaxy. Humans need to leave the Earth or face the consequences: starve to death or slowly suffocate due to changes in the Earth's atmosphere due to blight (increase of nitrogen and lack of oxygen).


2. What the US government and NASA been trying to do in the past few years in the film?

US government has been secretly funding a NASA project (Lazarus Mission) to find a planet capable of sustaining human life by sending 13 astronauts through the wormhole. Each of the astronauts were required to set up a beacon upon arrival at their planet to indicate that their chosen planet was habitable or die at that planet alone without setting off the beacon. NASA has been tracking their beacons for nearly a decade, but only 3 beacons are active - Miller, Mann and Edmunds.


3. Cooper finds the secret NASA facility and it appears like the next day he blasts off into space with barely any training and preparation at all?

NASA had no money or resources and they're desperate. Humanity is at the brink of extinction. Cooper was the best astronaut NASA had ever had so they immediately signed him up.


4. What is the Endurance team's (Cooper, Amelia, Romilly and Doyle) mission?

To travel through the wormhole, visit all 3 planets and decide which planet (Miller, Mann or Edmunds) is suitable for human colonization and report back to Earth before it's too late.


5. What are the planets' proximity with each other?

Miller's planet (the first planet visited by the Endurance team) is the closest among the 3 promising planets, it's also the closest planet to Gargantua (black hole).
Mann's planet (the 2nd planet visited by the Endurance team) is the 2nd closest to the team after the exit from the wormhole. It's also quite close to Gargantua, but to a lesser extent compared to Miller's.
Edmunds' planet (the 3rd planet visited by Amelia) is the furthest among the 3 and quite far from Gargantua.


6. What are NASA's plans for survival of humanity?

Plan A - While the Endurance team is looking for habitable planets, Professor Brand will continue to work on unifying Einstein's Theory of Relativity and Quantum Theory that allows humans to manipulate gravity to build a colony in space. The NASA facility found by Cooper and Murph at the beginning of the film is actually a construction site for humanity's space-time traveling ark. If Brand succeeds at solving the equations and Cooper managed to find a habitable planet, humanity's survival is secured.

Plan B - If Brand failed in solving the equations, the 3 planets deemed uninhabitable or the Endurance team takes too long to secure a habitable planet to live in, NASA has collected a bank of fertilized human embryos to ensure humanity’s survival on board the Endurance, just in case everyone on Earth is wiped out. To ensure genetic diversity (to prevent genetic diseases), NASA collected sperms and eggs from a wide range of sources. Once the Endurance team managed to find a habitable planet, the team would settle down and raise the first generation of embryos, with each generation helping to raise a new set of embryos and reproduce naturally as well.


7. Why after the first mission, when the crew receives video messages from back home and we see that Cooper’s children, Tom and Murph have aged significantly and become full grown adults? 

When the Endurance team travelling in a wormhole, relative velocity time dilation takes place. Due to close proximity with a black hole, the time spent on Miller's planet is significantly slower due to gravitational time dilation effect. Both of these time dilation cost the team a total up to 23 Earth years.


8. It was revealed later on that Plan A was a lie. Why Professor Brand choose to do so?

Professor Brand has solved the equations many years back, but it was incomplete due to the lack of necessary quantum data which can only be collected from the singularity of a black hole. He was trying to ensure the survival of our species by convincing the world leaders to work together to build the necessary infrastructure to make Plan B succeed. He needed them to believe that there's still hope for their own survival.


9. Upon learning that Plan A was a lie, what did Cooper and Amelia decide to do?

They commit to Plan B on their final planetary option, where Amelia’s lover, Edmunds, who reports a positive beacon few years back. However, Cooper remains unconvinced that Plan A is impossible, so they use the nearby black hole to slingshot Endurance toward Edmunds’ planet (the Endurance sustained heavy damage after Mann chooses to open the airlock), Cooper sends TARS into the center of the black hole - in the hopes that it might able to translate the necessary quantum data that could help NASA to apply Professor Brand’s derived gravitational equations (or fix any miscalculations) on Earth.


10. In the film, the movement of the spaceship docking was way too fast to be believable. It didn't look like a several ton spacecraft moving in zero gravity. 

The spaceship doesn't have to move slowly. It's zero gravity so it has no weight. So once the thrusters kick in, it will start to move faster and faster unless reverse thrusters are activated.


11. Why Cooper choose to sacrifice himself?

Cooper and Amelia both decided to use the Penrose process to extract energy from the rotation of the black hole's spin to escape from it. Cooper sacrifices himself to reduce weight on the Endurance (reduce mass to increase acceleration), allowing the ship to leave the black hole so that Amelia can make it to Edmunds’ planet and enact Plan B should TARS fail. However, instead of dying alone in the black hole, Cooper is pulled inside the Tesseract that was created by the extra-dimensional beings.

Note: Newton's Third Law of Motion - For every force, there's a reaction force that is equal in size, but opposite in direction. Whenever an object pushes another object it gets pushed back in the opposite direction equally hard.


12. Who actually created the wormhole and Tesseract within the black hole?

In Interstellar's third and final act, it was revealed that the extra-dimensional beings responsible for creating the wormhole near Saturn and Tesseract within the black hole are '5-dimensional beings' or 'bulk beings' mentioned by TARS. Cooper was convinced that these beings are in fact a future form of humanity who have evolved to live in higher dimensions and have come back in time to ensure humanity's survival. They've built the Tesseract to allow Cooper to locate the precise and suitable moment to deliver the quantum data collected by TARS in the singularity to Murph to solve the equations that allow humanity to manipulate gravity.


13. Black holes are regions of space where gravitational attraction is so strong that not even light can escape. Then why Cooper is not immediately teared apart by the black hole's strong gravitational pull?

The gravitational singularity of a black hole is a 'place' where the laws of space and time become infinite - all spatial dimensions of size zero, infinite density, infinite temperature and infinite space-time curvature (from the viewpoint of an observer outside the black hole, time stops as gravity becomes infinitely strong). When Cooper sacrifices himself to ensure Plan B, he is caught in the black hole’s gravitational pull but, instead of dying, he ejects from his ship and actually landed inside The Tesseract, a 5-dimensional place preventing Cooper from experiencing spaghettification. However, it is unknown to us as to how the extra-dimensional beings manage to construct the Tesseract within the black hole. It is also revealed that the source that creates the wormhole near Saturn is actually from the gravitational singularity of Gargantua.

Note: Spaghettification - the effect of extreme gravitational pressure on any particle or body of matter, in particular when exposed to the extreme forces of the black hole.


14. What happened actually when Cooper enters the black hole?

At some point near the climax of the film, TARS said that "The bulk beings are closing the Tesseract..." The black hole leads Cooper to what TARS refers to as the bulk. The bulk is a higher-dimensional space (within the black hole, space-time is bending into a different dimension). TARS calls the beings living there 5-dimensional beings. Cooper seems convinced that these beings are humans from the future who have evolved to live in higher dimensions (rather than the 4 dimensions we presently live in, 3 space and 1 time).

Inside the bulk, these beings have constructed what TARS calls a Tesseract, the thing that allows Cooper to communicate with Murph. The film showed how Cooper was able to interact with multiple dimensions of space-time (limited only to Murph's room) inside the Tesseract near the centre of the black hole. After they close the Tesseract, Cooper is sent back near Saturn through a wormhole (which allows Cooper to "shake" Amelia's hand during the initial travel within the wormhole). A black hole is not a wormhole. In the movie, Thorne and Nolan both hypothesize that the black hole leads to the bulk.

The Tesseract is a 5-dimensional object that has 3-dimensional visibility specifically tuned to Murph's room, allowing Cooper to visit his daughter at any point in time. It has 3-dimensional structures specifically tuned to Murph's room (as TARS explains to Cooper) that the beings of the bulk have made so that Cooper could comprehend it, since at that point Cooper is in a 4-dimensional space and we cannot visualize things in more than 3 spatial dimensions. There is also one dimension of time, which is why TARS calls them 5-dimensional beings.

Note: Time is relative. Time is a dimension which isn't linear. Every moment exist simultaneously. Cooper is not there to change the past. Whatever happened, happened and couldn't have happened any other way. Therefore there is no paradox. It's just that 3-dimensional beings like us experience time in a linear fashion.


15. Why Cooper was sure that Murph will soon realize that the 'ghost' that has been communicating with her in the past is actually him and know the data needed to solve the equation is found in the watch that he gave her? 

Love transcends space and time. If everything in the universe is simply information, then love does transcend time and space by facilitating the preservation of information. When you love someone, you never forget them, even after they've died. Even after all those years, Murph still loves her father enough to remember the memories of him and her together. Sooner or later, she will able to connect the dots together and realize the answer lies within the watch that Cooper gave to her years ago. It's possible that information can travel through space-time.

She made a detailed recording of the timeline of her and her father's life, which is shown in the beginning of the film. This recording is passed onto future generations so that humans in the future able to construct the Tesseract that's specifically tuned to Cooper and allows him to transmit the necessary data back to Murph through Morse Code. It is only Cooper who can do it because he was heavily tangled with his daughter's timeline. The bond shared between Cooper and Murph allows him to locate the precise, suitable moment in time to provide Murph the data needed to solve the equations. 


16. How Cooper managed to save humanity in the end?

When inside the Tesseract, gravity "leaks" through all the other dimensions in space-time, allowing Cooper to spell out a message (“S-T-A-Y”) by pushing books off of Murph’s shelf in the past, communicate map coordinates to the past version of himself by spreading dust across the floor (in binary language) using gravity and the 5th-dimensional communication through gravity (made visible by 3-dimensional objects back on Earth) enables Cooper to gently manipulate the hands on Murph’s watch – transferring the data that TARS acquired with morse-coded watch ticks. Subsequently, translating that coded data gives Murph all the information she needs to drastically advance humanity’s understanding of space and time – as well as to complete Plan A.


17. Were any of the 3 planets (Miller, Mann or Edmunds) habitable?

Miller's planet is considered uninhabitable due to the constant strong tidal waves generated by the black hole gravitational pull and no land was found in sight after landing. Mann's planet is also considered uninhabitable as well due to extreme cold temperatures, toxic gases in the air and the lack of food resources. It was revealed at the end of the film that Edmunds' planet was habitable (due to existence of sun, land and water) but Edmunds didn't survive in the end, leaving Amelia alone at the planet.


18. How Cooper survives his time inside the Tesseract, and how he intends to reunite with Amelia? 

Time moves slower near the gravitational pull of the black hole. Cooper’s ejection from the Tesseract and entering through the wormhole to reach Saturn should not take long for him (time stops due to strong gravity near the centre of the singularity), but over half a century for the rest of humanity (around 80-90 years since Cooper is said to be 124 years old and Murph is estimated to be over 120 years old) when Cooper wakes up from bed.

Cooper survived and finally reunited with Murph, who was living on the faster moving side of the wormhole. However, knowing that Cooper has nothing left for him to live for here (his son, Tom is probably dead by now and Murph will join him soon), Murph reminds her father that, through the wormhole (if it still exists), Amelia is just beginning to set-up Plan B on Edmunds' planet and Cooper should join her to start a new life.

Even though around 80-90 years have passed since the Endurance first set out, time on the other side of the wormhole is moving much slower compared to our solar system – meaning that his trip through the wormhole again should allow him to reunite with Amelia on Edmunds' planet in only a short time after Cooper first sacrificed himself and dropped into the singularity. We don’t actually see the reunion, but it's quite clear that Cooper will eventually manage to reach Amelia and helps her to ready the colony.

Note: It is unknown whether the wormhole at Saturn still exists or not, after the bulk beings closed the Tesseract. It's unsure whether the construction of the Tesseract affects the creation of the wormhole or not. Let's just hope for Cooper's sake, it's still exists.


19. What does the poem mentioned by Professor Brand means?

"Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the dying of the light." 
It was taken from the poem, Do Not Go Gentle Into That Good Night, written by Dylan Thomas. It means that do not give up, do not surrender, do not let go without a fight, live and fight for survival, against the coming change, even in the midst of dire circumstances.


 

Infographic taken from

INTERSTELLAR TIMELINE

Such an ambitious and risky movie will inevitable create a lot of questions, these answers aren't definite and will progress as the community comes up with more interpretations and a better understand.

Q. When does the soundtrack come out?
A. 18th of November, Hans Zimmer wanted the audience to experience the score for the first time, during the movie. Movie scores are usually released 2 weeks prior.
The two only released tracks at the moment is the Main theme from the teaser trailer, and a bonus track called Day One Dark (this one is slightly different from the docking scene, a bit less epic). All other tracks on youtube are trailer songs or fakes.


Q. What was that Cylinder world at the end, where the baseball hits the ceiling?
It's called an O'Neill cylinder, it's a space settlement design proposed by American physicist Gerard K. O'Neill. It would rotate so as to provide artificial gravity via centrifugal force on their inner surfaces.

Q. Who are 'They'?
A. Cooper assumes “They” are future humans who have mastered the laws of our universe - allowing them to manipulate time and space. Brand thinks “They” have laid out a series of rudimentary breadcrumbs (binary messages) and advanced technology (the wormhole) for humans to follow – in order to save ourselves from annihilation.

Q.What is the Event Horizon?
A. The point at which the gravitational pull becomes so great as to make escape impossible, aka The point of no return.

What is Singularity?
A. term used to describe the center of a black hole where the gravity is thought to be infinite. What happens inside black holes is still not completely known or understood. This gives filmmakers some leeway.

Q.How did Cooper not die when going into Event Horizon?

A. When he flew into the black hole and reached the Singularity, he was transported by "They" into a 5 dimensional world ("tesseract") where, after, with the help of TARS, sends a message to his daughter in the past, afterwards he ends up going back through the wormhole located near the orbit of Saturn. Where he is found.

Q. Did Love save Humanity?
A. No, It is explained that the Tesseract is simply a creation of 5D beings who are using the faith and motivation that Coop has, fueled by love, to complete this time loop. The bookcase is important because it is his most vivid and strong connection he has to his daughter, and she is the key to solving everything. From there, the idea that gravity is the only thing that can transcend time and space become a key point, a concept that is very much rooted in current physical theories and understanding. Love, an evolutionary drive, was the motivation for Cooper to keep desperately trying to find a way to save Humanity and his daughter Murph.

What is a Tesseract?
A. It's a four-dimensional cube, 'They' custom build the Tesseract that Cooper falls into so that he can communicate with his Daughter, time is non-linear in 5 dimensions, this allows Cooper to visit his daughter through the bookcase at any point in time.

Q. Could Cooper have just died when detached near the black hole, and dreamt up the Tesseract scene?
A. Some claim this, Dr. Mann says that Cooper will see his Kids when dying.

Q. What was the key equation that allowed Humans to survive in the end?
A. It was an advanced equation, that if solved, will allow humans to harness fifth-dimensional physics – specifically gravity. Should Brand succeed, NASA will be able to defy our traditional understanding of physics and launch an enormous space station (carrying the remainder of Earth’s surviving population) into space. The very facility that Cooper and Murph stumble upon at the beginning of the film isn’t just a NASA research station – it’s a construction site for humankind’s space-traveling ark.

What's the message of the movie?

A. There are many, but here's what the script Writer Jonah Nolan wrote in an interview with IGN:

Question: What are some things that you'd like audiences to take away from the film?
Jonah Nolan Answer: "The paradoxical aspect of human beings. We love with such an intensity: our children, our parents, our families -- and yet all of us, to different degrees, make choices that take us away from those people, because of our curiosity or our ambition; all these warring, paradoxical desires. I don't have an answer for that. I don't think anyone has an answer for that. What's more important: your career, your kids -- we all struggle with that every day, and that paradox is at the center of this film. Human organisms are forged by natural selection to want to continue to explore, even in the most unlikely ways -- standing on the shores of a tiny island and imagining that there might be another island a thousand miles hence over the ocean, and then going and looking for it. Human beings are incredible survivors on that level, but we're also very connected to our children and our loved ones. Those things are so often in conflict with each other"


Q. Isn't there a time travel paradox? How did future humans first survive to make a Tesseract – given that there would have been no Tesseract to save them?
A. Here is a possible explanation apart from the common 'What comes first? The chicken or the egg' explanation.

'At the end of the movie we see that the third planet, on which Brand lands on, is habitable. She puts Plan B into action; the fertilized human embryos. It's possible that Brand and the human embryos are “They” (future race of humans who created the wormhole and placed the tesseract inside the black hole for Cooper). Only human to know that Cooper had went into the black hole would be Brand. Meanwhile they found a planet habitable like Earth.That is where Nolan’s non-linear style comes into play because the very end of the movie (last shot of Brand) is actually the beginning for it all. “Murphy’s law means whatever can happen, will happen” So not only did they find a habitable planet but they were also able to travel back in time to ensure that present human race’s survival.' (Credits: Rashonxxx from Screenrant)

This can be explained by this flow:

Artists are often asked to produce images of things never seen before, and often times asked to make them look real when no one is quite sure how they would actually exist. In Christopher Nolan’s Interstellar, visual effects supervisor Paul Franklin and the team at Double Negative were asked to produce images of things that aren’t even in our dimension, and furthermore have them accurate to not only quantum physics and relativistic laws but also our best understanding (guess) of quantum gravity.

Luckily, amongst the key team at Dneg was chief scientist Oliver James. James has a first from Oxford in optics and atomic physics and a personal understanding of Einstein’s relativity laws. He worked, as did Franklin with the film’s executive producer and scientific advisor Kip Thorne. Thorne would work out complex equations in Mathematica and send them James to recode into IMAX quality renderings. To meet the needs of the film and to solve the visual problems involved, James had to not only visualize equations describing the arcing and bending trajectory of light but also equations that ended up describing how a cross section of a beam of light changes its size and shape during its journey past the black hole.

Even then James’ code was only part of the solution – he worked hand in hand with the artistic team lead by CG supervisor Eugenie von Tunzelmann which would add say an accretion disc and create the background galaxy and all its stars and nebulae, that get warped as their light rays are bent past a black hole. But as complex as it is to for the first time show a black hole scientifically correctly in a film, the team also had to show someone entering a four-dimensional tesseract, which also extrudes or shadows into the three dimensions of a little girl’s bedroom – all in a way an audience could follow.

In this article we describe some of the key sequences created by Double Negative, and the scientific research behind them.

Building a black hole

Perhaps the single most stunning results of Nolan’s quest for realism in the film is the depiction of the black hole Gargantua. After input from Thorne, the filmmakers strove to properly show the behavior of a black hole and a wormhole, right down to the lighting or lack of it. For Double Negative, this even necessitated the writing of a whole new vastly physically complex renderer.

Above: view from a camera in a circular, equatorial orbit around a black hole that spins at 0.999 of its maximum possible rate. The camera is at radius r=6.03 GM/c^2 , where M is the black hole’s mass, and G and c are Newton’s gravitational constant and the speed of light. The black hole’s event horizon is at radius r=1.045 GM/c^2.

“Kip was explaining to me the relativistic warping in space around a black hole,” recalls Paul Franklin. “The gravity being bent in space/time deviated the light around it producing this thing called the Einstein lens which is this gravitational lens all around the black hole. I was thinking about how we might go about creating that image and I was thinking about ways or references we could look at and see if there was an existing VFX process.”

“I saw some very basic simulations that had been done by the scientific community,” adds Franklin, “and I thought, well, the movement of this thing is so complex, maybe there’s something we can do ourselves and implement our own version of this. Kip then worked very closely with the R&D at Double Negative, particularly with Oliver James, our chief scientist, to take Kip’s equations that he’d worked out to calculate all of the light paths, the ray tracing paths around the black hole and then Oliver worked out how to implement that in a new renderer we called DnGR which stands for Double Negative General Relativity.”

That approach allowed Double Negative to set all the necessary parameters for their digital black hole. “We could set its rate of spin, its mass and its diameter,” explains Franklin. “Really, those are the only three parameters you have to play with with a black hole – that’s all we can have to measure with black holes. They spent a lot of time working out how to calculate the paths of ray bundles around the black hole. It was pretty intense – it was a good six months of work – those guys putting the software together. We had an early version of it running by the time we finished pre-production on the movie.”

Above: The black hole, initially non-spinning, gets spun up to 0.999 of the maximum; then the camera zooms in from radius 10 GM/c^2 to near the black hole, r=2.60 GM/c^2, and then moves along a circular equatorial orbit. The hole’s enormous shadow is distorted into a boxy shape due to mapping the camera’s spherical sky onto a flat display.

That early imagery was in fact used on set as projections outside the windows of the spacecraft onto giant screens, providing actors with something to look at while filming. No greenscreen was used during production on Interstellar. Later, Double Negative would replace selected views and also fix up some star fields. “Quite a lot of the stuff you see in the finished film where you’re looking over the shoulder of an astronaut and looking out the window,” notes Franklin, “quite a lot of that is straight in-camera. We had a whole bunch of shots which don’t get into the VFX shot count but there’s a whole bunch of stuff which is in-camera visual effects done in this way.”

Those in-camera shots were made possible via a collaboration between Dneg, DOP Hoyte Van Hoytema and LA-based Background Images, which employed new 40,000 lumen projectors on set. “We had two of them converged onto the space,” says Franklin, “so we were overlaying the images one on top of the other to boost the exposure just a stop. We found that we had to be really careful not to make the images too large otherwise we lost exposure.”

Above: Close up of this same simulation, showing the complex fingerprint-like structure of gravitationally lensed starlight near the left edge of the black hole’s shadow, the edge at which the hole’s horizon is moving toward us at near light speed due to its spin.

“We had to re-position and re-converge the projectors from setup to setup,” continues Franklin. “Normally the guys like to have a good week to get a projector in place, converge it properly, get it all finely tuned. But we got that process down to in some cases 15 minutes. They were working so hard. The projectors are big hunky objects – each one weighs 600 pounds. We had two in a specially built cage mounted on a big heavy duty reach lift, with a special pan and tilt head so we could basically use this thing to position the projectors. I’d be on the radio directing content, getting playback working, talking to the projector guys to calibrate the projectors, and also talking to the teamster who was driving our forklift to dance this thing around an extremely crowded stage.”

Making waves

In the film, Cooper (Matthew McConaughey), Amelia (Anne Hathaway), Doyle (Wes Bentley) and the AI robot CASE visit a water-covered planet that also experiences enormous tidal waves, given its close proximity to the gravitationally dense Gargantua. Audiences are perhaps used to seeing waves that can get to be a few hundred feet in films, but due to the story, that wasn’t even close to what was required, the waves needed to be 4,000 feet tall. To help sell the scale of the waves, Double Negative had to re-think the usual approach to making water. “When you take something that large,” explains Franklin, “all of the characteristics you associate with a wave like breakers and a big curl at the top, they just go away because they’re tiny in relation to the mass of water, because it’s more like a moving mountain of water. So we spent a lot of time in previs working out how we can use the one scaled reference we did have which is the Ranger spacecraft, the white shuttle that gets swept up. The key moment of that sequence is when the wave hits the Ranger and sweeps it up the face of the wave. And you see it travel up and become lost and it becomes a tiny little speck and disappears in the face of the wave. That was a key moment for the scale.”

                                                                             Anne Hathaway as Amelia on the water planet.

Double Negative artists controlled the waves with animation deformers, sculpting them effectively with keyframes. “That gave us the basic shape of the wave,” says Franklin, “but then obviously to sell it as real you’ve got to create the surface foam, interactive spray, wavelets and tiny breakers on the surface. For that we used an in-house tool called Squirt Ocean. It’s been in development for quite a while, and then there was a lot of additional Houdini work over the top of that.”

The shots were being completed in high enough resolution to work for IMAX, a requirement that limited the amount of time Double Negative had to do iterations. “I would see the layout of the wave sequence and say great let’s get the wavelets onto it and everything else,” says Franklin, “and I’d have to wait about a month and a half to actually see this stuff come back – it was that long a process since we were doing all this IMAX resolution. So we didn’t have that many goes at it. Normally you would expect to have multiple iterations but we really only had three goes at it.”

CASE ultimately rescues Amelia from the tidal wave. CASE and its counterpart TARS were actually 200 pound metal rob puppets operated on set in Iceland by actor Bill Irwin, again the result of Nolan’s push to have as many practical elements as possible. Double Negative carried out performer and rod removal for many shots. “The early shots in that sequence consist of the CASE robot walking through the water,” explains Franklin. “That’s the physical puppet and we just removed the performer from behind it.”

When CASE reconfigures himself into the water wheel and spins his way through the water and picks up Amelia and runs off with her, the shot was completed with a practical and digital solution. “What special effects gave us was,” says Franklin, “they built a little water rig attached to a quad bike we could drive through the water and derive interactive splashing. We had another rig again built off a quad bike which essentially had a forklift on the front of it, so that carried our stunt performer. We had the arms of the robot holding the stunt double for Anne Hathaway. The thing would churn up the water and then we got rid of the quad bike and then replaced it with the digital robot.”

Double Negative limited digital robot moments to those of TARS or CASE doing ‘extraordinary things’, such as running through the water, climbing up into the spaceship at the end of the water sequence, running across the ice and some zero gravity freefall shots. “What we’ve always found with these things is that you can really make that digital moment work if you bookend with reality,” suggests Franklin. “So that sequence he runs up to the spacecraft and climbs inside it, as he comes up through the hatchway inside the spacecraft, that’s the practical robot – the physical prop. It finishes it off with a moment of reality and it helps sell all the digital parts of the sequence.”

Inside the tesseract

In the film ‘they’ turn out to be us, advanced enough to help Cooper communicate with his daughter on Earth, years earlier in her life. As time travel is impossible in an Einsteinium universe of quantum and relativistic laws, the story solved this by having Cooper leave our dimensions and move into the ‘bulk’ or hyperspace of higher dimensions. If our universe was depicted as a 2D disc or membrane then the bulk or hyperspace would be the box surrounding it in three dimensions. A way to think of this is every dimension is dropped one level to image it. Thus 3D space is drawn as a 2D disc (albeit sagging around the black hole) and the 3D environment around this disc or the brane (physicists use brane not membrane) is the higher dimension or the bulk.

An image, taken from Kip Thorne’s black board imagery, showing the brane and bulk. Source: http://interstellar.withgoogle.com

In the film Michael Caine’s character Professor Brand is trying to understand gravitational anomalies. The black boards in the film clearly show him trying to solve gravity in four and five dimensions with diagrams of our brane in the bulk. The film says that if Brand can understand these anomalies then they could be used to change gravity on Earth and lift huge mankind-saving craft into space.

While leaving our three dimensions and entering the fourth does not solve the time travel issue, in the film it does allow for Cooper to send gravity waves back in time. He can see all of time, but he can only cause ripples in those threads of time – gravity ripples that Cooper’s daughter, Murphy, comes to understand as vital information.

The job of Dneg’s team was to visually show a fourth dimensional tesseract, that some future ‘us’ provides for Cooper to cause these gravity waves. It would have been possible for this to be done symbolically or in some white dream sequence but instead Dneg set to trying to actually visualize the four dimensional tesseract in some meaningful way, noting of course, that such concepts are just educated speculation. Here’s where Thorne was again involved. For him, such speculations “will spring from real science, from ideas that at least some ‘respectable’ scientists regard as possible,” to quote from his new book The Science of Interstellar.

A further black board image depicting Kip Thorne’s explanation of gravity in four and five dimensions. Note that ‘our brane’ is sandwiched between two alternative realities or other branes. Source: http://interstellar.withgoogle.com

To understand the Dneg solution one has to understand the nature of higher dimensions. If an object is at rest – say a ball – to a flat table it is a dot. If the ball could move through the table – much like an apple being sliced thinly – the ball would appear as ever increasing bigger circles and then ever reducing circles until it passed all the way through the table. From the flat surface point of view the circle makes sense…and a circle is not a bad approximation to a ball when drawn on paper. This example moves from 3D to 2D. But how do we move to 4D and beyond? One theory that is common even in every day CGI is to think of the fourth dimension as time. Thus that same ball bouncing is only seen at one instant as a ball – but over time its path defines a tube. From a 4D view the ball is a tube and the sphere we know is just a 3D slice of that 4D world. Now there is some question over time as the fourth dimension, but if we assume it is, then the 5th dimension is the stuff in the bulk, the stuff outside our universe.

If a 4D/5D tesseract was made vastly in the future it would represent a box that grows to be a bigger box, and can animate and change ‘form’, as seen in this short video below.

In this is a box, over time having its timeline varied. If you entered the tesseract by the film’s logic – as this tesseract touched 3D space, you would see all the timelines (4D extrusions of objects) and all the paths forward and backward in time. Furthermore, as the physics of today predicts that there are a vast number of separate realities (sandwiching our flat brane) you would see these lines shooting off in multiple directions. It is in this conceptual space that one can start to see the graphical solution that DNeg came up with, based on the direction of Nolan. The ’threads’ of time that Cooper seems to influence are like strings and his attempts at hitting them causes vibrations that ripple back up the timeline and thus communicate with his daughter Murphy. It really is a brilliant piece of artistic scientific visualization.

But how to film it?

Nolan’s determination to give the actors something physical to interact with applied also to the tesseract sequence. Cooper enters a black hole and emerges inside a multi-dimensional space in which he can see objects and their timelines, including the childhood bedroom of Murphy. “Chris said,” relates Franklin, “‘It was a very abstract concept, but I’d really love if we could build something that we could film. I want to see Matthew interacting physically with these timelines. I want to see him in that space, I don’t want to see him hanging against a greenscreen – that feels like a cop-out compared to everything else we were planning to do in-camera.’”

This led Franklin to consider how the tesseract should look. “I spent a bunch of time thinking about how to make time visible as a physical dimension,” he says, “how to show timelines of all the objects in the room in a physical way that would be comprehensible. Because the danger was it would get so cluttered that all you would see is these timelines and you would have to work out what they came from. Also, it was important from a story point of view that Cooper see the timelines and see the way it’s affecting the objects back in the room and would be interacting with what is going on inside the room.”

The final ‘open lattice’ look was, notes Franklin, inspired by the concept of a tesseract itself. “A tesseract is a three-dimensional shadow of a four-dimensional hyper cube. It has this beautiful lattice-like structure, so that partially informed what we were doing there with that. I also spent a lot of time looking at slit-scan photography and the way that slit-scan allows you to record a single point in space across a whole range of moments in time. So the photograph itself turns time into an axis in the final image. A combination of those two things together gave us these physically extruded three-dimensional timelines, streaming off from the object. The rooms are snapshots, moments in time, embedded in this lattice of timelines that Cooper can then navigate backwards and forwards along the timelines to find specific moments in space.”

Since Nolan wanted some kind of physical presence for the tesseract to shoot with, the visual effects and art departments would exchange information in terms of models and lighting designs and studies. “We ended up building one section of that as a physical set with four rooms around it,” states Franklin. “Then digitally we extended that off into infinity so everywhere you look it’s going off forever. We also used a lot of in-camera projection on set. We overlaid the active timelines onto the physical set using the projectors. That gave us a sense of trembling, febrile energy – all the information streaming along the timelines in and out of the rooms. But every single image of the final sequence has huge amounts of digital work overlaid onto it. A very fine lattice of threads that Cooper encounters when he is actually trying to push up against it – he can’t penetrate the rooms. Every object in the room had to be connected with its own faint moving timeline threads that went in and out of the objects.”

Still, certain moments required fully digital Double Negative backgrounds such as when Cooper moves through the ‘tunnels’ of the tesseract. “We didn’t have enough sets to do that travel,” says Franklin, “so we shot Matthew against a projection screen and we projected the previs of those sequences onto the screens around him, so he had something to ground himself against. The actors all loved that because they had something to look at rather than just having greenscreens and working it out later on. We then replaced that material with the more developed version of the tesseract. There are a couple of moments where we kept the previs because the depth of field was so shallow that the background was out of focus.”

Franklin also notes that layers of digital work, and significant amounts of roto and rig removal was required to complete the scenes. There were some challenging CG requirements too, including when the tesseract closes and begins to break down. “We actually took the CG geometry of the tesseract and put it through a hypercube rotation. The guys worked out how to implement the transforms for the hypercube rotation and apply it directly to the geometry of tesseract set that we’d actually created. That’s a particularly special moment for me. When I saw what the guys had done I thought that’s just perfect, that’s exactly what I want.”

Another challenging section, says Franklin, involved the moment when Cooper interacts with the dust and draws out a binary pattern in the floor during the dust storm. “We had to work out the moves that Matthew was miming on set and make that work with something that could actually drive those shapes appearing on the floor of the room below him.”

'Interstellar' Black Hole is Best Black Hole in Sci-Fi

The black hole as seen in the movie 'Interstellar' -- the most scientifically accurate black hole envisaged on film.
Christopher Nolan’s movie ‘Interstellar’ will be an epic space adventure encapsulating humanity’s need to explore the Universe, but it’s the visual effects for the movie that are garnering early attention.

By combining the help of one of the world’s leading black hole physicists with a cutting-edge visual effects (VFX) team, ‘Interstellar’ will depict the most scientifically accurate black hole in science fiction history. And, during production, some new discoveries were made as to how a black hole would appear if we could view it up close.
ANALYSIS: ‘Interstellar’ Feeds off our Exoplanet and Wormhole Dreams

“Neither wormholes or black holes have been depicted in any Hollywood movie in the way they actually would appear,” said Caltech physicist Kip Thorne in a behind-the-scenes video released by Paramount Pictures (featured below). “This is the first time that the depiction (of a black hole) began with Einstein’s general relativity equations.”

General relativity describes the nature of gravity. How a black hole, being the most gravitationally dominant object in the known Cosmos, would look to an observer can therefore be described by Einstein’s equations — except for when tangling with the Black Hole Information Paradox, then you’ll need some quantum equations to boot.

Thorne is a lifelong friend of fellow black hole guru Stephen Hawking and between both of the theoretical physicists, our modern understanding of how these singularities work has flourished. So with the help of Thorne, Nolan has done something very smart; he’s been able to provide the movie-viewing public with a rare sci-fi look into the actual science of a black hole while maintaining an artistic representation that we can easily comprehend.
OPINION: Interstellar Earth: The Future We See In Our Stars
 

“The visual effects department under Paul Franklin and everybody at Double Negative took Kip’s mathematical data and they created real visual representations of what a black hole is meant to look like,” said ‘Interstellar’ producer Emma Thomas.

Warped Spacetime

While crunching the mathematics and arriving at graphical representations of Einstein’s famous equations, Thorne and the movie’s VFX team realized that if a star is positioned behind the black hole, the starlight may become trapped in the warped spacetime close to the black hole’s event horizon. Known as gravitational lensing, this spacetime effect can be used by astronomers to detect exoplanets, for example. But during the production of ‘Interstellar,’ the team realized a spacetime subtlety.

 

 

Theoretical physicist Kip Thorne runs through some equations on a blackboard with 'Interstellar' actress Jessica Chastain.

Paramount

Intuitively, light from a star behind a black hole may circle the event horizon several times before being released in the direction of the observer (in this case the ‘observer’ is the camera). Visually, the edge of the black hole will be stunning — several different images of the same star will be created at the event horizon’s edge.

This produces “a strange sort of funnel in the sky,” with a black disk surrounded by gravitationally warped starlight, said VFX supervisor Paul Franklin.

The Matter of an Accretion Disk

Of course, no black hole would be complete without the addition of a radiating accretion disk. But how would that appear on film?

As matter falls toward the spinning black hole’s event horizon, the gas collects into a hot accretion disk, shining brilliantly. By adding the disk, “we found that if you then render this whole thing and you visualize it all through this extraordinary gravitational lens, the gravity twists this glowing disk of gas into weird shapes and you get this extraordinary ‘rainbow of fire’ across the top of the black hole,” said Franklin.

ANALYSIS: Alpha Centauri Bb: An Interstellar Target?

“When I saw this disk wrap up over the black hole and under the black hole, I’d known it intellectually, but knowing it intellectually is completely different from seeing it,” said Thorne.

It’s all very well having a scientifically accurate black hole, but if the visual interpretation of a black hole’s mathematics makes no sense, Nolan was under no illusions that he may have had to take some artistic liberties to make the black hole appear more familiar to the viewing public.

“But what we found was as long as we didn’t change the point of view too much … we could get some very understandable, tactile imagery from those equations. They were constantly surprising,” said Nolan.

Now Thorne and the VFX team are preparing some technical papers about their findings for the astrophysical and computer graphics communities. The publications will say: “Here are some things that we’ve discovered about gravitational lensing by rapidly spinning black holes that we never knew before,” added Thorne.

ANALYSIS: What Would an Interstellar Spaceship Look Like?

Science fiction movies are produced to entertain, first and foremost. But as computer graphics become more sophisticated and the science fiction-viewing public becomes more savvy, there is a growing motivation by filmmakers to make space phenomena as ‘real’ as possible. And often that will mean employing the help of scientists to make our most extreme space fantasies as scientifically accurate as possible to maintain a credible storyline.

‘Interstellar’ is shaping up to be one of those rare movies that will combine science and fiction, exciting the viewing public, potentially engaging us with astrophysics in a way we’ve never experienced before.

The Science Of Interstellar

by Kip Thorne

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Science, and Interstellar
November 20, 2014


I have tried hard the past week to keep myself from writing about Interstellar, but it’s come to the point where I give up, and will indulge myself. I consider it indulging myself since I have never actually written a blog entry about a single sample movie, using just one case as a subject. The only time I have come close is a spectacularly ill-received rant two years ago where I related Christopher Nolan’s depiction of Batman to the role of the United Nations in international relations (if you didn’t like that, you sure as hell won’t like this!). Interstellar is another Nolan movie, and that is no coincidence.

Rather surprisingly, his big-budget movies resonate long after the credits roll, and the fact that they are blockbusters makes it all the more powerful, since you don’t really expect to see any meaningful ideas put forward in this type of loud, effects-heavy movie. Interstellar indeed had some idea that linger in the brain and that I have ended up liking rather a lot. By saying that I like these ideas of course really means that I agree with the line of thinking, and consider it close to my own ideas and opinions, and naturally I am a big fan of those (they are my favourite). Just to clarify, this blog is about the ideas put forward in Interstellar, rather than actually the quality of the movie, which has proved quite divisive: some people love it, some people hate it. I am not discussing here whether it was a good movie or a bad movie, nor am I ranting about the scientific legitimacy of the theoretical physics writ large that dominate the movies’ dramatic beats. This isn’t about the science of Interstellar, it is about Interstellar and Science. That’s because Interstellar is all about the idea that science, specifically the pursuit and accumulation of knowledge, makes us immortal.
 

                    

The importance of science dominates the early earthbound portion of Interstellar, where Matthew McConnaughey struggles to give his children a scientific education in the face of opposition from their school teachers, who don’t see the value in overeducating people in this different, desperate post-World War III world of theirs. Similarly, NASA has had to go into hiding in order to continue working, as the US government fears public revolt if tax money that could be spent on food production is wasted on far-flung theoretical research. As the plot moves into the second phase and the astronaut crew leaves earth, this theme is subtly reinforced by the constant stream of technological and theoretical achievements that enable the mission to travel between galaxies. The power of science is so great that in all the worlds visited, the protagonists never encounter anything that truly surprises them: all has been predicted using generations of cumulated knowledge. The team failed to predict Matt Damon’s demons, which is something we can all understand, as it is human nature to be unpredictable and selfish. The only other event that catches them off guard are giant, crushing waves caused by an immensely strong gravitational pull. This is explained by a simple calculation error in applying Einstein’s Theory of General Relativity to an actual physical world: bad science. Even the mind-bending events of the movies third act are predicted and explained by Anne Hathaway (who explains the idea of a plane of existence where time can be transcended) and the giant Swiss army knife that is the TARS robot, who, using his computer brain filled with the entirety of human knowledge, can predict possible outcomes of travelling too close to a black hole.

This leads us of course to The Tesseract. McConnaugheys character is pulled into the theoretical realm that transcends space and time. He can here see various stages of his daughters childhood through the shelves of books on her wall, and eventually learns to communicate his experienced knowledge using gravity to manipulate the clock hands of a watch into storing Morse code. Yes, a man, completely outside of any sense of space or time, communicates with the next generation of humanity through a library filled with books and the knowledge contained within. He can travel to any point in time, but can only look out through the library in his daughters room, through the books he has helped her accumulate. To question the theory behind this extra-dimensional encounter completely misses the point. Although this time transcendence tesseract is actually a perfectly viable scientific theory (many astrophysicists argue that it is actually more real than anything we perceive in our everyday existence), its inclusion here serves as the climax and central metaphor in Nolan’s message for Interstellar. It’s a long aul movie, and an hour before The Tesseract, we have Anne Hathaway, in her function as Expositioner General, batting away the idea that time is a constant thing in the universe, and all in existence is subject to its laws. On some dimensional plane, she explains, it may be possible to walk through time just as we can climb a mountain. Again, this idea is theoretically sound: it just does not matter to us because time is just such a powerful force in our plane of existence. In a similar way, I don’t think too much about surface tension in water: our bodily mass makes it quite irrelevant to us, but it sure as hell matters a lot to billions of tiny water-dwelling insects. That world of walking on water is all these insects know of, yet a person could go through their whole lives quite easily without ever knowing that surface tension exists: it’s irrelevant to everyday existence. So don’t think too much about extra dimensions, they probably will never affect you.

              
                                     McConnaughey floating in the inter-dimensional tesserect

But Nolan does go there, and his human version of a time transcendence dimension involves a man shouting at his daughter through the books on her shelf. The protagonists here are important, as from a biological point of view, procreation is simply a mechanism to transfer DNA from one generation to the next, ensuring its survival ad infinitum. Because we experience time so profoundly, we experience our own lives as if they are something very profound and specific, but in the grand scheme of things we are just a link in a long unbroken chain of DNA transfers. We can do what we wish in our lives, but there will always be that urge to shuttle our DNA through to another generation before it dies with us. That’s quite a depressing idea, implying that all existence is meaningless, we are merely passenger vessels for directionless DNA that only cares about surviving. But there is a way that we can transcend our mortal existence, which is by using our short years on this earth to discover and accumulate knowledge, knowledge that is passed down and used by generations to come. Nolan’s tesseract represents the science, art, literature and accumulated knowledge of humanity, and argues that as well as preserving the immortal DNA, we are also transfer vessels of something more profound, we are vessels of humanity. And this humanity, this long, unbroken chain of the existence of humanity can communicate with us from any bookshelf, in any place, at any time. Science therefore, is our tesseract.

Now I can well understand if I have lost a few readers in this past thousand words. As I explained, it was an indulgence, and one that should have been much shorter. After much deliberation, I finally decided to write it because I realised that this interpretation was hidden in a movie that had key elements from the Theory of General Relativity as major plot points, and has inspired public debate in popular culture about the validity of these scientific claims. That’s not bad from a $170m Hollywood Blockbuster. If every big budget Hollywood movie contained half the level of intellectual consideration that Nolan injects into his projects, popular culture would no doubt be in a better place. My last blog entry was concerned with the coming domination of megafranchises within the Hollywood movie studios, and this provides much to contrast with the movies of Christopher Nolan. No $170m Marvel Cinematic Universe movie is concerned with more than expanding the plot to facilitate more and more characters that can later launch their own $170m movie, and there is no reason to believe any of the other megafranchises will be any less derivative.

The megafranchise era also signals the end of one of my favourite eras in the history of Hollywood Blockbusters, that of the existential superhero. The shining example in this era was Christopher Nolans Dark Knight Trilogy, an interpretation of Batman that some eminent scholars argue relates the morose superhero to prominent supra-national organisations.

This era is gone however, and now superheroes are simply employees of some giant corporate-controlled universe, one whose only purpose is to expand. By the looks of Interstellar however, it still seems like there is solid financial backing to the movies of Christopher Nolan, and I hope this continues into the future for probably the most ambitious filmmaker ever to be given over $100m to make a movie.


 

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