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 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.
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.
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.
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.
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.
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:
PREVIOUS < PART 3
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.
Note: The existence of more than four dimensions would only make a difference at subatomic (quantum) level.
The theory attempts to reconcile quantum mechanics and Einstein’s general relativity.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
PREVIOUS < PART 3
No comments:
Post a Comment