ABSTRACT
Themathematical history of electric, magnetic and EM fields reveals
five distinct periods: pre-mathematical ancient knowledge of fields,
electro-and magnetostatic fields, classical EM fields, quantum
theories and SFT. SFT is a new description of electromagnetic
interactions. At its heart are bi-spinorial motions for both the
electromagnetic fields and the interacting particles. Among its
recent successes it has solved a simple model of the hydrogen
atom, obtained an analytic estimate for the mass of the photon and
provided the first glimpse of the structure within the photon. Its
eigenstructure goes beyond that of quantum theory, adding arrays
of molecules of varying photon states that range in flexibility from
solid, liquid crystal, liquid and gas phases. The structure within the
photonmay yield an organisational structure for bosons reminiscent
of the atomic chemical table first noted by Mendeleev in 1860
via a two-dimensional array of elemental properties. The phonon
and gluon are involved in this boson organisation. The self-field
formulation obtains an analytic expression for Planck’s number,
providing a basis for its understanding as a variable of motion
applying equally to the electron, the proton and the photon. The
fields of SFT differ markedly from those of CEM and QFT. The fields
in SFT are discrete streams of photons. The photons are specified
via a bi-spinorial function as spatially and time-varying motions,
including spiral helices between the electron and proton of the
hydrogen atom. In SFT, two rotations are used to model EMmotions,
very different to its forebears. Importantly SFT is fractal, while CEM
and SFT are not; SFT is deterministic, while QFT is probabilistic.