Investigations into the Nature of Matter
Stuff is made of molecules, molecules are made of atoms, atoms are made of electrons and nuclei, nuclei are made of protons and neutrons. So far so good.
Protons and electrons are held together by exchange of virtual photons. Protons and neutrons are held together by exchange of virtual pions. Protons and neutrons (and pions) are made of up and down quarks. These quarks are held together by virtual gluons. OK so far?
The theory, called the Standard Model, is awesome and fantastically well verified. But it is incomplete because it leaves out gravitation.
Now we believe that everything is string: electrons, quarks, photons, gluons, .. everything. String Theory appears to be able to incorporate the Standard Model and gravitation.
If so, it is a theory of EVERYTHING, unifying Quantum Field Theory, which already incorporates Special Relativity,
and General Relativity which is Einstein's theory of gravitation and cosmology.
If particles are loops of vibrating string, what gives them their stability? Perhaps the string is knotted and therefore cannot simply shrink to a point. This is the proposal made in my paper, Torus Knots are Rigid String Instantons, published in 1989. Since then, knotted solutions have been found in many
unexpected places, including Maxwell's Equations of electromagnetism.
Strings, Membranes and Lumps
If a stringy model of matter seems to work so well, what about a membrane model, or a lumpy 3-dimensionally extended model (string being a 1-dimensionally extended version of a point particle)?
In my second publication, Self-Dual Lumps and Octonions, a new theory of everything in 8 dimensions is proposed and a new set of quaternionic knotted solutions is sought.
Less ambitious solutions
have been found, but the doubly self-dual, knotted quaternionic lumps in octonionic space-time which were fully described in Self-Duality and Extended Objects and were explained at the University of the West Indies, Jamaica, are tantalizingly close
to an infinite hierarchy of knotted lumps in 8 dimensions by analogy with the infinite hierarchy of torus knots in 4 dimensions discovered earlier.
Our world only has three space and one time dimension you might say. In fact, soon after Einstein proposed his theory of four dimensional curved space-time, Kaluza demonstrated that electromagnetism could be incorporated into a five dimensional version of general relativity where one of the dimensions is curled up very tightly. By this mechanism the extra dimensions required in standard string theory are wrapped up in various ways in the search for a natural way to include all the nuances of the standard model.
Even Love might Succumb to Quantum Physics
One lesson that we have learnt from the standard model is that deep symmetries lead to physical forces. For example, electromagnetic forces are related to symmetries among unit length complex numbers, and strong nuclears
forces are related to symmetries between 3 by 3 matrices of complex numbers which have determinant one and are equal to the complex conjugate of their transpose.
Here is some blue sky thinking for you:
Consider objectively two butterflies fluttering around one another and imagine that this demonstration of 'animal magnetism' is ultimately explicable in terms of some deep symmetry. Of course there is already
an obvious symmetry between the two butterflies. They are the same species, they look the same, talk the same and smell the same, but we are searching for a mathematical account
of their attraction to one another. While it might seem more satisfactory to seek an account of what is happening in terms of the colour and scent experiences of the individual butterflies, perhaps
their behaviour is better understood as a quantum superposition of possible states requiring a completely different mode of explanation. They have the same genetic origins - their gnome is almost identical. There is a deep symmetry here ...
A theory of
everything unifies all ideas into a coherent understanding.