String theory started as a simple way of modelling the
characteristics of elementary particles as the result wave movement on a tiny
circular string so that the various quantum states that produce particles are
the number of standing waves around this string. So more massive particles with more energy had more nodes in the waves thus more waves around the string.
Going back from this, the idea came from an electromagnetic representation of a particle as a photon going in a circle trapped by its own self gravity. So a photon pair when collided can form a little circulating standing wave and the electrical energy so contained makes for a gravitational bending of space so that the photon travels in a circle, when there is only one wavelength round a particle is formed in its ground state and thus lowest mass, higher energy states occur with more waves and thus higher frequency. The relationship of the trapped energy to frequency gives Planck's constant. It is discontinuous because only some combinations of wavelength to circular path and gravitational curvature fit.
I originally discussed this with Jonathan Dostrovski in about 1967-1968, he thought straight strings with mass and tension was easier to calculate, hence "string theory", when we were both working at the Rutherford Laboratory, Oxford.
The original Idea, that I had in about 1961, was based on a unification of Gravity and Electromagnetism and Quantum Mechanics. The theory was much simpler than it sounds. Basically it said that Electromagnetic fields had energy and the energy content warped space time according to General Relativity so if the Electromagnetic field was strong enough the Gravitational effect would make the electromagnetic wave orbit and not travel. This trapped wave then is a particle. You have then to quantize it by saying that the Energy of the wave is related to its frequency by the Planck equation and then that only integer wavelengths are allowed round one of these orbits. These trapped waves form all our particles. They have different frequencies and can form from more than one frequency photons hybridising, so that a very large number of separate particles may come into existence.
The radius of the tron to stop light escaping (the Swartzchild radius) is when the escape velocity equals the velocity of light. I make this:
given by Gm/r^2=c........1 (This is the escape velocity at distance r from m (I think if I remember correctly))
and the energy of the mass m as:
The frequency of light of this energy is given by the Planck equation:
So f=mc^2/h ... This is the frequency of the photon to make up a mass m.
Now for a photon wave to fit the Swartzchild circumference so it goes round an integer wavelength times, then (fL=c) and nL=2.pi.r so nc/f=2.pi.r
Solving these two conditions for m gives:
m=2(c/G)r^2 and m=n(h/2.pi)(1/r) where n is a positive integer.
This gives a series of increasing values of m with each n as m increases then r increases
By eliminating r and taking n=1 we can get an interesting relation between fundamental constants:
h=2.pi.sqr(G(m/c)^3) where m is the mass of the electron. I do not know if this works out.
Here is a more general relation:
If the energy of an element of a electromagnetic wave is E^2/c where E is the local electric field then the equivalent elemental mass is given by the relation dmc^2=E^2/c.
so dm=E^2/c^3. The gravitational force between elemental masses is Gdm1.dm2/(r12)^2
So the gravitational binding energy of the whole wave is:
GSum(dm(n).dm(n)/(r(m,n))^2) over all m,n m<>n.
For a particular element this sum is the energy at that point:
GSum(dm.dm(m)/r(m)^2) goes to GIntegral(dm.dm/r^2)
The differential form is Gdm/r
Using the plank relation hf=energy then f=energy/h
and energy is potential plus kinetic. The potential energy is the gravitational potential and the kinetic energy is poyntings electromagnetic vector as a scalar.
I can't go any further, but it looks like a relation between r, E and f that can be made into a differential equation that will give a similar equation to the Schrödinger equation for an electron orbital, but instead applying to the photon trapped by gravity to form the electron. I think Schrödinger itself could be a case where the proton wave and the electron wave interact to make something new.
When a Proton (very heavy) unites with an electron to form a hydrogen atom it is known that the photons that make them up interact so that the electron occupies more space as Schrödinger said, with the proton photons interacting by interference with the electron photon. The Electron Proton pair having lower energy than either separately and the bonding changing the photon in the electron's behaviour. In fact the electron may end up surrounding the proton with the proton inside the electron so the photons that make them up form an interference pattern that is the atom.
So an electron is therefore a photon that has been trapped, or frozen, by its own mass/energy gravitational field so it cannot propagate. So all particles are like this and are made of photons of various frequencies, and indeed there could be particles containing more than one photon.