"What is mass?" Good question.
I visited your site "The Photon Theory" from which I extracted the following 3 statements:
(1) All forces in nature are transferred through the interaction of (electromagnetic) force fields. (you added the word electromagnetic before force fields in a later statement.)
(2) The Photon Theory is a theory that explains mass and gravity in terms of electromagnetic waves.
(3) If the above described photon is curled into an orbit, in which its wavelength exactly matches the circumference of the orbit ( 2*r = 2.43053*10-12 m = * ); the orbit is stable and the photon remains trapped in the orbit. ... The photon is then observed as an electron or positron depending upon the charge (positive or negative) on the outside of the bend.
Statement 1: Makes sense. Will revisit this below.
Statement 2: This implies that photons are electromagnetic in nature and/or behavior.
Statement 3: This implies that electrons in atomic orbits are due to photons that met certain constraints and became trapped in those atomic orbits.
I've seen lots of experimental proof that electrons are influenced by electric and magnetic fields (vectors, force fields...), but I've not seen any experimental proof that photons (any wavelength: gamma to radio) are influenced/deflection by electric or magnetic fields. I've read about photon entanglement, but that is not proof.
My problem with "The Photon Theory" is that photons of all wavelengths (energies) are not influenced/deflected by magnetic or electric fields when those fields are inside a ultra-high vacuum container, but electrons when freed from an atom in UHV are easily influenced by electric and magnetic fields. This seems to be proof that photons do not become electrons in orbits and vice versa.
Returning to statement (1), and the original question: "What is mass?"
My current definition of mass is that: The mass of a collection of particles is equal to the sum total interaction of all electric and magnetic force fields contained within a collection of particles.
Putting this into perspective: Gravity is equal to the sum of all electric and magnetic interactions of one or more collections of particles acting on another collection of particles. Inertia and friction are variations of gravity. All of these forces/force fields operate on a relative basis since everything is constantly moving.
The question that then arises is: "What is a particle?"
My answer is: a particle is a collection of electric and magnetic force fields with no real mechanical mass. To accommodate the existence of protons, neutrons and other particles, there are various types and numbers of these force fields within any given particle.
Why do I suggest that a particle has only force fields and no mechanical mass?
Well, let's look at hydrogen, since hydrogen accounts for 90% of the known particles within our universe, and since a single hydrogen atom has only one electron which by itself accounts for 45% of all known particles in the universe.
I highlight the electron because, despite popular belief, we still have very little classical type knowledge about the makeup of an electron. For example: Does it have a real mechanical mass? What is the radius of the mechanical mass if it exists? What is the shape of the electric entity inside the electron? How does the electron produce +/- 1/2 spins? and so on
Our best scattering experiments on the electron suggests that, if there is indeed a true mechanical mass at the center of the electron, then its' radius must be smaller than 10(-18)cm. On the contrary, classical experiments and quantum mechanical calculations have clearly revealed an "entity" that has a radius between 10(-11) and 10(-13) cm that we define as being an electrically charged entity. (The magnetic radius of the electron should also be in that range.)
Since we have detected an electrical entity within the electron, and have a rough measure of its size, we know we have something that occupies space. We don't know its' shape, but we know it exists. Mechanical mass on the other hand, can be said not to exist because we can not detect its' presence by any known means. Therefore, if we choose to eliminate the idea that the electron has a real mechanical mass, then we can start to make progress on many fronts.
In closing: It is my perception that the electric and magnetic force fields of any particle are permanent, not transient, and that they are inherently connected to each other. And since all particles are in relative motion at all times, we can safely speculate that all particles "at-rest" also have permanent electric and magnetic force fields.
So I'll make an assertion that should get some feathers up.
Somethimes that is necessary.