Saturday, 8 November 2014

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

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.

The following explanations are provided based on my understanding of the film after watching it the first time on November 5, 2014 and what I know about the basics of quantum mechanics and Einstein’s Theory of Relativity. Note that these are highly complex theories with lots of mathematical calculations and formula. I've tried my best to make them as short and concise as possible for easier understanding without the maths.

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

For my review of the film, please visit this link:


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 (right click, open image in new tab to enlarge): 

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 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.

A new model of a spinning black hole for the movie Interstellar, with an accretion disk comprising detritus, is based on new discoveries by theoretical physicist Kip Thorne. At the center of every black hole is an extremely dense, massive, compact star called a neutron star. Astronomers have known for decades that certain neutron stars spin — some at a rate of thousands of times per second.
The stunning rendition is the most scientifically accurate image of a spinning black hole ever created.
"This is the first time the depiction began with Einstein’s general relativity equations," - Kip Thorne

Note: Kip Thorne, had never known black hole in more realistic terms than the theoretically conceived one (through mathematical equations). It is said that no scientist really knows what a real black hole actually looks like.

A black hole warps the surrounding space-time fabric so severely that anything comes within its event horizon, can’t escape from its gravitational grip. No one knows exactly what happens at the deepest interior point of a black hole (Brian Greene)

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity, once they cross the event horizon. When they reach the singularity, they are crushed to infinite density and their mass is added to the total of the black hole. Before that happens, they will have been torn apart by the growing tidal forces.

In the case of a charged (Reissner–Nordström) or spinning (Kerr) black hole, it is possible to avoid the singularity. Extending these solutions as far as possible reveals the hypothetical possibility of exiting the black hole into a different space-time with the black hole acting as a wormhole. The possibility of traveling to another universe is however only theoretical, since any perturbation will destroy this possibility. It also appears to be possible to follow closed timelike curves (going back to one's own past) around the Kerr singularity, which lead to problems with causality like the grandfather paradox. It is expected that none of these peculiar effects would survive in a proper quantum treatment of spinning and charged black holes.

The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory of relativity. This breakdown, however, is expected; it occurs in a situation where quantum effects should describe these actions, due to the extremely high density and therefore particle interactions. To date, it has not been possible to combine quantum and gravitational effects into a single theory, although there exist attempts to formulate such a theory of quantum gravity. It is generally expected that such a theory will not feature any singularities.



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