Published on Nov 24, 2012

Professors Lawrence Krauss and Brian Greene discuss Brian Greene’s introduction into the field of String Theory and the educational reasons to how he came to study and popularise the subject with physics in general.

Theoretical Physics requires tailor made mathematics to describe the mechanism of reality as probed and observed by Experimental and Observational Physicists.

Modern physicists stand on the shoulders of previous giants in science who, through the marriage of theory and experiment, discovered how nature works and how nature can be used in technology.

Gravity was discovered and explained by Isaac Newton through his invention of classical mechanics and fundamental calculus.

James Clerk Maxwell formulated Faraday’s, Gauss’ and Ampere’s Laws into his theory of Electromagnetism.

Einstein used the evidence from the Michelson-Morley Experiment and his own thought experiments on simultaneity as his central axioms in Special Relativity.

Einstein then developed the famous mass-energy equivalence and concept of space-time, essential concepts for high energy physics.

Einstein extended Relativity to General Relativity, describing accelerating bodies and used the relationship between energy and space-time to describe curvature in the form of his field equations, discovering the true nature of the gravitational field which had troubled Newton and his predecessors for centuries.

Theodore Kaluza extended General Relativity with the concept of Maxwell’s Theory of electromagnetism and, along with Oscar Klein, developed the Kaluza-Klein Theory, a theory which describes electromagnetism as a gauge theory where the gauge symmetry is the symmetry of circular compact dimensions.

This all lead to the development of modern string theory, which views the Standard Model, the guidebook of elementary physics, as gauge groups existing on a flat spacetime; with the elementary particles as strings on a flat world sheet, vibrating with different couplings and flavours forming the different particles.

The higher dimensions are in a curved spacetime in this theory, containing particles beyond the Standard Model as being higher resonances of the strings, contained on a different world sheet, or brane.

The Standard Model is an extended patchwork of mathematics that describes 3 of the 4 fundamental forces.

The work of Richard Feynman, who developed the path integral formalism for quantum mechanics used this to develop Quantum Electrodynamics, QED.

QED was the first theory to describe relativistic quantum mechanics and the beginning of the Standard Model’s framework.

Soon, the Weak Interaction was developed using quantum field theory, however the theory was too chaotic to make predictions as the coupling constants were impossible to determine at low energies; unlike QED the Weak Interaction is Non-Abelian and uses vector Bosons to commute. Predictions can be made from the dynamics only if you combine the theory with QED itself, which leads to symmetry breaking which is mediated by massless bosons. The mass for these bosons has to come from an outside field, the famous Higgs field which operates via The Higgs Boson.

The work of Murray Gell-Mann produced Quantum Chromodynamics, QCD a theory describing the strong nuclear force that holds protons and neutrons (nucleons) together and describes how the fundamental particles inside them, the quarks and gluons, interact with each other in high energy interactions.

Feynman’s path integral method can also be used to extend Kaluza-Kelin theory to Yang-Mills theory to describe how Quantum Chromodynamics, QCD, works in the low energy regime, as running of the coupling constants for this theory becomes chaotic, like the weak interaction, at even low energies.

The question that remains: is there symmetry breaking of these gauge theories at a universal level, where all coupling constants are the same and if so why do they trend towards infinity? Is their some mass gap that must be included to achieve this? Where does gravity fit into the Standard Model? How can we renormalise the Standard Model itself? And with what?

A lot of these questions have to be answered by the extensions of the Kaluza Klein model into the different interpretations of String Theory, which are all equivalent to M-Theory, which attempts to unify a lot of the different string theories to from a Unified Field Theory.