String Theory Part I: A Cosmic Symphony

Tom Ruane

Everything is made of tiny vibrating strings. According to string theory, at least. By attempting to explain the origin of both matter and forces, string theory is a theory of everything which stitches together the clumsy patchwork of the standard model and resolves the disastrous clash between the two pillars of modern physics: quantum physics (that of the very small) and general relativity (that of the very large). The first part of this article series will look at what string theory is and where it came from. The latter two parts in later OS-TEC publications will investigate why we need it and question whether a potentially untestable string theory is undermining the scientific method.

Why Strings?

In 1968, a young Italian physicist at CERN was struggling to make sense of recently collected data on particle interactions involving the strong nuclear force. For those less familiar with the physics section of science magazines, CERN is an intergovernmental organisation which examines the characteristics and contents of particles by smashing them together using particle accelerators, such as the 27km Large Hadron Collider. To give another lose definition, the strong nuclear force (SNF) is one of the four fundamental forces (the others being gravity, the electromagnetic force and the weak force), which is responsible for binding together the protons and neutrons in atomic nuclei, countering the repulsive force between the positively charged protons.

Euler and his beta function

Working on the problem, Gabrielle Veneziano remarkably noticed that the behaviour of the particles under investigation could be mathematically described using an obscure equation called the ‘beta function’ set out by an 18th century Swiss mathematician – Leonhard Euler. The more physics you encounter, the more you realise that there is very little that hasn’t been somehow influenced by Euler’s genius.

Veneziano’s coincidence caused a significant stir, however physicists were left feeling like schoolchildren who had been told to use an equation, but didn’t know what it meant or why they were using it. Unlike mathematicians, physicists crave an explainable link between their axioms and the physical world. To remedy this, the beta function was generalised to encompass not just Veneziano’s 4 particles, but any number of particles (‘n’ particles). Though it may seem like a leap for both the reader and myself, to a trained physicist, this generalisation had a perfect resemblance to ‘n’ harmonic oscillators. Strings. Strings that vibrate at harmonic (resonant) frequencies and are subject to a tension. Note that the term ‘resonant’ means that a whole number of wave-like peaks and troughs fit along a string’s spatial extent. Through this haphazard and abstract series of events, string theory was born.

Various resonant vibrational patterns of both open and closed strings.

Implications of String "Tension"

As mentioned, strings have an intrinsic tension - in fact, they have one that is incredibly high. Take the graviton (the string/particle associated with gravity), which has a tension of 1039 billion tonnes. This has four major consequences:

1) Strings are about 10-35m long, on a scale called the Planck length.

2) No ‘frame’ is required to hold a vibrating string in place, unlike for a musical instrument.

3) If energy and mass are considered to be two sides of the same coin (think E=mc2), strings that have this high tension will vibrate with high energy and so should represent particles with masses that are far greater than what we observe in the real world.*

4) Strings can execute an infinite number of vibrational patterns, thus an infinite number of different particles should exist. There are two main explanations as to the whereabouts of these missing particles: either they are too heavy for us to create and examine with our current technology, or, with heavier particles being more unstable, they decayed into showers of smaller particles soon after the big bang.

* To get around this quantum mechanics must be considered. Heisenberg’s uncertainty principle states that a string’s position and motion can never be known with absolute precision. (Importantly, this is not just true for an observer, such as a human or a measuring device, but for nature itself.) Thus, the string’s position and motion varies uncontrollably, causing quantum ‘jitters’ which cancel out a proportion of its vibration, reducing its energy and so yielding masses of an agreeable magnitude.

Extra Dimensions

Often extra dimensions are directly credited to string theory, however the German theoretical physicist Theodor Kaluza (1885-1954) first pondered this seemingly outrageous suggestion. Einstein’s general relativity showed that gravity could be described geometrically by considering the warping of spacetime, requiring a universe with 3 spatial dimensions and 1 ‘time’ dimension, giving 4 in total. Kaluza, so obsessed with theory that he, a non-swimmer, hurled himself into a lake having only read a textbook on the sport, wasn’t afraid to ask what would happen if one considered the universe to have 5 dimensions: 4 of space and one of time. From this assumption, out popped not only the equations of general relativity, but also Maxwell’s equations. Those of the electromagnetic force. How elegant is that? Could it be possible that the other fundamental forces can also be described geometrically by considering extra dimensions? String Theory does just this, however not by will, but by requirement: Probabilities, by definition, range from 0 to 1, but the mathematics of string theory yields some nasty ‘negative’ probabilities… unless the universe is considered to have 11 dimensions. Consequently, it is possible that we live in a super-dimensional universe in which we can only experience three dimensions, but it is more likely that these extra dimensions are curled up into tiny structures, called Calabi-Yau manifolds, that exist at every single point in space. Crucially, Calabi-Yau manifolds are around the size of the Planck length (very, very tiny), explaining why humans can’t interact with them, but meaning that strings can. Here, we finally get to the point: the shape of these Calabi-Yau manifolds determines the way in which strings vibrate inside them. The way that strings vibrate determines their properties. Their properties are represented by the particles which make up all of the forces and all of matter. Nature. Therefore, if you follow, the shape of these extra dimensions describes the reality we experience.

A visualisation of Calabi-Yau manifolds. Note that, contrary to the visualisation, they exist at every point in 3D space and represent new directions of movement which we cannot visualise.

Alongside many other things to come in Part I and II, string theory offers us a geometrical explanation for our world in which forces and matter are merely an illusion cast by extra dimensions that are too small for us to see.

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