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# String Theory

String theory is the leading theory that explains the mystery of the Planck length, the incredibly tiny distance at which the force of gravity interacts with the quantum world.

Although it has never been experimentally proven, its predictions are astonishing.

The universe appears to have four fundamental forces that determine the interactions of everything within it. Three of them have been well explained by the Standard model of quantum mechanics.

But the fourth force, gravity, remains an outlier. Compared to the other forces it is exceptionally weak, which has made it impossible to detect in a particle collider, the main instrument used to examine the world of quantum mechanics.

But unlike the other forces, it has a long range, meaning that it becomes by far the dominant force on the large scales of moons, planets, stars, and galaxies.

So far we have been able to split our models of the universe in two: The Standard Model explains the small, and Einstein’s general relativity explains the large. Both models are exceptionally accurate.

General relativity has been the theoretical base with which we have landed men on the moon, put robots on Mars, Jupiter, Venus, and Titan, and flown probes past Pluto and into interstellar space.

Physicist Richard Feynman compared the accuracy of the predictions from quantum mechanics as akin to specifying the width of North America to within one hair’s breadth of accuracy.

But the two theories are mathematically incompatible. In areas where the two overlap, such as in black holes or in the early seconds of the universe following the big bang, applying the two theories at once produce illegible and mathematically impossible outcomes. Part of the reason for this is that, at the Planck length, general relativity assumes that the universe is smooth and uniform, while quantum mechanics assumes it to be chaotic and warped. Using the two together produces strange results like lengths that somehow have less than one dimension.

This means that the world of the Planck length and the secret that lies there is a new frontier of science. String Theory is the leading theory that attempts to unify all four fundamental forces of the universe into a single framework. A theory of everything that explains the basis of all known phenomena in the universe.

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What is String Theory?

Instead of a smooth or warped surface at the planck length, string theory speculates that every particle contains planck length-sized string-like structures that vibrate in different ways. The vibrations of these strings create the particles described in the Standard Model, like plucking a guitar string can create the musical notes G, A, B, C, etc.

It is through these different vibrations that properties like mass, and force charge is created. So an up quark is created by one set of vibrations, an electron is created by another, and the explanation for how gravity comes about at the quantum level is that there is another set of vibrations that create a particle called a graviton.

These strings are really weird. They don’t just move in four dimensions (three for space, one for time) like a tiny piece of regular string, they move in up to eleven dimensions. This concept is absolutely wild.

An artist’s conception of a vibrating string. The diameter of the string is equal to the Planck Length.

# Working notes

• Draft outtakes:
• What makes things kind of difficult is that it is a really elegant theory, and there are hardly any competing theories that come close. But right at the outset, there is no evidence that it is true.
• in the tiny world of the Planck length. The Planck length is a truly ridiculous order of magnitude away from anything that we’re working with experimentally at the moment.
• They work by stripping the electrons away from small atoms like hydrogen or helium until you're left with just a proton or a neutron. The particles are then fed into an enormous loop, and magnets running the length of the loop accelerate the particles to incredible speeds, before colliding them with each other. The resulting explosion is studied to see the components of the particles.
• It has given us a wealth of data from the quantum world of quarks and gluons, and has led the refinement of our models of this scale. But quarks and gluons are almost 10 orders of magnitude larger than the Planck length, approximately equivalent to the size distance between the Earth and the entire solar system.
• Smaller particles need larger colliders to see them, and a collider of the scale required to experimentally test string theory appears, with current technology, to be well out of reach.
• String theory is the leading theory of what happens at the Planck length.
• So far, quantum theories have been developed for three of the four major forces.
• We do not have a way of explaining how gravity emerges from the quantum level, and it has to be there somewhere. This is the basis of creating a 'theory of everything', a theory that explains all of the four basic forces in one conclusive explanation. String theory is one popular attempt, but it remains a long way from being proven.
• Wikipedia, Quantum mechanics
• Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work.
• Gravity, the fourth force, has remained elusive.
• Wikipedia, Quantum mechanics
• It has proven difficult to construct quantum models of gravity, the remaining fundamental force. Semi-classical approximations are workable, and have led to predictions such as Hawking radiation. However, the formulation of a complete theory of quantum gravity is hindered by apparent incompatibilities between general relativity (the most accurate theory of gravity currently known) and some of the fundamental assumptions of quantum theory. The resolution of these incompatibilities is an area of active research, and theories such as string theory are among the possible candidates for a future theory of quantum gravity.
• Part of the problem is that gravity is very, very weak compared to these other forces. The weak nuclear force, for instance, is 10^24 times as strong as gravity. We have a separate theory for gravity, called General Relativity, but it does not 'fit' with any of our quantum theories.
• Wikipedia, Theory of Everything
• Through years of research, physicists have experimentally confirmed with tremendous accuracy virtually every prediction made by these two theories when in their appropriate domains of applicability. In accordance with their findings, scientists also learned that GR (general relativity) and QFT (quantum field theory), as they are currently formulated, are mutually incompatible – they cannot both be right. Since the usual domains of applicability of GR and QFT are so different, most situations require that only one of the two theories be used. As it turns out, this incompatibility between GR and QFT is apparently only an issue in regions of extremely small-scale and high-mass, such as those that exist within a black hole or during the beginning stages of the universe (i.e., the moment immediately following the Big Bang). To resolve this conflict, a theoretical framework revealing a deeper underlying reality, unifying gravity with the other three interactions, must be discovered to harmoniously integrate the realms of GR and QFT into a seamless whole: a single theory that, in principle, is capable of describing all phenomena. In pursuit of this goal, quantum gravity has become an area of active research.
• One theory of 'everything' or all of the fundamental forces is String theory. It explains that neither QFT or GR provide an accurate picture of what goes on at the Planck length - a very small scale. Instead, it supposes that the Planck length is the realm of something called 'strings'.
• Wikipedia, Superstring theory
• General relativity typically deals with situations involving large mass objects in fairly large regions of spacetime whereas quantum mechanics is generally reserved for scenarios at the atomic scale (small spacetime regions). The two are very rarely used together, and the most common case that combines them is in the study of black holes. Having peak density, or the maximum amount of matter possible in a space, and very small area, the two must be used in synchrony to predict conditions in such places. Yet, when used together, the equations fall apart, spitting out impossible answers, such as imaginary distances and less than one dimension.
• The major problem with their congruence is that, at Planck scale (a fundamental small unit of length) lengths, general relativity predicts a smooth, flowing surface, while quantum mechanics predicts a random, warped surface, neither of which are anywhere near compatible. Superstring theory resolves this issue, replacing the classical idea of point particles with strings.
• Wikipedia, Theory of Everything
• String theory posits that at the beginning of the universe (up to 10−43 seconds after the Big Bang), the four fundamental forces were once a single fundamental force. According to string theory, every particle in the universe, at its most microscopic level (Planck length), consists of varying combinations of vibrating strings (or strands) with preferred patterns of vibration. String theory further claims that it is through these specific oscillatory patterns of strings that a particle of unique mass and force charge is created (that is to say, the electron is a type of string that vibrates one way, while the up-quark is a type of string vibrating another way, and so forth).
• Wikipedia, Introduction to M-theory
• These "strings" vibrate in multiple dimensions, and depending on how they vibrate, they might be seen in three-dimensional space as matter, light or gravity. It is the vibration of the string which determines whether it appears to be matter or energy, and every form of matter or energy is the result of the vibration of strings.
• Wikipedia, String theory
• In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries gravitational force. Thus string theory is a theory of quantum gravity.
• Wikipedia, Superstring theory
• These strings have an average diameter of the Planck length, with extremely small variances, which completely ignores the quantum mechanical predictions of Planck-scale length dimensional warping. Also, these surfaces can be mapped as branes. These branes can be viewed as objects with a morphism between them. In this case, the morphism will be the state of a string that stretches between brane A and brane B.
• Singularities are avoided because the observed consequences of "Big Crunches" never reach zero size. In fact, should the universe begin a "big crunch" sort of process, string theory dictates that the universe could never be smaller than the size of one string, at which point it would actually begin expanding.
• String theory of popular, but is a long way from being confirmed #[[why string theory isnt confirmed]] and also has a number of incredible implications #[[extra dimensions]] about the nature of reality.
• However many are sceptical that a theory of everything is even mathematically possible (of course).
• Wikipedia, Quantum mechanics
• While Stephen Hawking was initially a believer in the Theory of Everything, after considering Gödel's Incompleteness Theorem, he has concluded that one is not obtainable, and has stated so publicly in his lecture "Gödel and the End of Physics" (2002).
• Gödel's incompleteness theorem states that past a certain point, formal systems of mathematics are incapable of accurately describing a complex system.
• Wikipedia, Introduction to M-theory
• However, Hawking later changed his mind and stated, "M-theory is the only candidate for a complete theory of the universe."