String Theory- A Primer

A grand contender for a final theory of everything. One where the macrocosm and the microcosm unite in synchrony, humming to the tune of vibrating yet infinitesimal filaments of energy. Since the ancient Pythagoreans and their love affair with the octaves, thirds and fifths of the lyre; to the contemporary developments of modern physics, string theory has emerged as an controversial contender for the unification of the forces of nature. It is a presumptuous idea, that all phenomena, matter and energy are bound by the dynamic fluxes of vibrating strings in hyperspace.Such strings behave much like the strings of a cello or violin, except producing particles as opposed to musical notes; therefore quarks can be envisaged as strings vibrating in a single pattern such as an A-flat or even neutrinos as filaments oscillating in a C-sharp. Now down to the details. In 1968, Veneziano 'accidentally' discovered that the beta function of Euler mirrored some aspects of the strong force that acted upon hadrons. This lead to its physical interpretation involving vibrating one dimensional strings that modelled point-like particles. Unlike quantum field theory which experiences infinities as a result of viewing particles as dimensionless points and by consequence bringing those points close together to create infinitely strong forces, strings can avoid this anomaly. A string my be open with its ends fluttering or closed into a loop; originally, open strings were found to masquerade as a spin-1 bosons. But a string is not an object in space, it is literally a piece of space and unlike a violin, whose oscillation is deadened as it transfers it energy to the outer environment, a piece of string is isolated with its energy contained, thus its oscillation isn't deadened. And since there is an infinite degree of harmonics or resonant modes, such strings can imitate an infinite number of types of particles, endowing each with specific energy.

Moreover, because patterns of string vibration arise in pairs, varying by around half a unit of spin, it creates an internal supersymmetry (SUSY). SUSY allows one to merge bosons and fermions given that they return to their original states after 360 and 720 degree rotations respectively, if one can define such transformations as manifestations of a greater multidimensional geometry, each of the known particles can be related by heavier superpartners. The additional dimensions are for mathematical consistency and Kaluza was the first to realise that adding a fifth dimension to spacetime mirrored Maxwell's equations, the extra dimensions curled up like a cartesian plane passing via each point in space. But among the hallmarks of string theory included the ability to mimic spin-2 gravitons with closed strings, allowing the possilibity of describing gravity quantum mechanically but without invoking fields directly. The only free parameter in question is the tension of the string, which can be calibrated more precisely using the graviton to meet the strength of the strong force. As a result, the minimum energy of a string, the planck energy, can be multiplied many times over by the amount of wavelengths in each mode or oscillation to give a large resultant, such may be cancelled out by quantum fluctuations leading to a massless string. As for other particle properties, spin simply becomes the aspect of how a string vibrates, as these vibrations can extend over curled up dimensions it becomes relatively simply to imagine a fermion moving in a gyrating fashion in another dimension, thus gaining a 720 degree rotation in the 3D space to resume its original position. So if mass and spin can emerge from a multi-dimensional geometry, what about the other forces?

 By the 80's, the 5 string theories which all paired their bosons and fermions differently were united by Witten into M-theory into a context of an 11 dimensional Calabi-Yau space-time (10+1). It incorporates one dimensional strings in conjuction with branes (membranes), allowing gravity and the non-gravitational forces to unite at a single energy. This wasn't previously possible, given that the gravitational coupling constant refused to match the quantum forces except until an energy density that exceeded the unification energy; in M-theory it matched neatly. But we are talking ridulous scales on the order of 10^-35m, around 10^-20 the diameter of a proton; at such tiny scales gravity competes with the other forces so we need to unite quantum field theory with general relativity. Such a stark incompatility between the two arises because of the Uncertainty principle; in general relativity, perfectly flat space arises in the absence of a significant mass (such as the quantum vacuum) and thus the value of the gravitational field should be exactly zero. However, the Uncertainty principle needs only a mean value of zero and so the value of the gravitational field can fluctuate in a random 'foam'; therefore we get infinities (or ultraviolet divergences). These infinites come about because in quantum field theory, you deal with points that act as sources of fields, but with one dimensional strings infinities never occur because the energy of a vibrating string is dependant on its frequency as well as the amplitude at which it oscillates (closed strings and loops rely on circumference) and more frenzied modes of vibration produce more energy than placid ones. Much like a Feynman diagram, which capture the history of a particle, a 'worldsheet' capture snippets of a bunch of strings and recording their history as a static network of connecting tubes in spacetime; when the loops interact, two loops may merge and split into a different figuration. Such allows gauge bosons to be expressed as aspects of vibrating strings rather than the conventional view of seperate fields for each charge and particles as point-like bundles of energy osillating in those fields.