Recent Insight into Relativity

In 1905 Einstein's paper on relativity described the magnet/conductor problem.

It is known that Maxwell's electrodynamics – as usually understood at the present time – when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena. 

This observation of Einstein's was mirrored by experimental asymmetries in Maxwell’s electrodynamics.

He quotes our most primitive observation of relativity that where we have two objects moving past each other, we expect a symmetry between either one object moving or the other. Either way, the two phenomena should be equivalent.  This was explained as an exercise in how magnetic fields are observed in different frames of reference, Galilean and Lorentzian. Can SFT tell us more about this situation?

Historical Electrodynamics

We begin by giving the example of how the classical Coulomb's Law of electrostatics and the Biot-Savart Law of magnetostatics are modified within SFT by the inclusion of fields that are taken to be measured between centres of rotation rather than directly between charges. In this case both the electron and proton will  each move in two rotations that should each have their own unique centres of rotation.

In the SFT formulation for the hydrogen atom the result of this change in metric is that the fields are spinorial, they spin. The fields are

 SFT version of Coulomb's Law

SFT emagnetostatics eqn     SFT version of Biot-Savart Law

where the form is both relativistic and coupled electromagnetically rather than the uncoupled electrostatic form of Coulomb’s electrostatic equation and the Biot-Savart equation for magnetostatics. The SFT forms are compatible with the classical electrostatic and magnetostatic forms where the orbital and cyclotron frequencies of a particle are assumed to be ω≈0 and ωc≈0 at macroscopic levels. Note however that in the atomic case a finite circulating current is required at  ro≠0 and rc≠0 as found inside atoms.  Since SFT is not a computational method, rather it is an analytic method we can simply note any degenerate solutions.  Both field forms, the classical and the SFT forms, are identical when a time average is taken for the complex exponential term  indicating the close relationship between these two forms, the classical and the SFT.

The electric and magnetic currents, or the orbital and the cyclotron motions, are analogous to gravitational motions. It is the (di-) magnetic or cyclotron part of the planet's motion that accounts for the procession of Mercury in the case of gravitation. For such gravitational effects we must differentiate the EM effect between two atoms; this now becomes di-electromagnetic where there are again two coupled motions; in the gravitostatic approximation the coupled solution becomes uncoupled into two separate motions, one dielectric and the other dimagnetic. In the case of light bending relativistically this too is due to the differentiated mix of both electric and magnetic spinors; this indicates that light, the photon, is also dielectromagnetic or dipolar. Returning to the EM case at hand in terms of the relativistic electrodynamic motions within the atom, the complete electric and magnetic solution gives us both relativistic parts of the electron and proton motions. Crucially we must obtain the magnetic currents.

The difference in the classical and SFT formulations is first how the distances are being measured. In SFT distances are not measured between charges but between centres of rotation. Further the SFT formulation is a mutual effect between particles and not simply a particle and a field in which the particle is embedded.  We need to be careful about what we are seeing at the macroscopic level and below.  Our measuring devices including our eyes are not able to discern clearly the atomic jiggling that is going on; until we have good nanoscopic methods of detecting such jiggling we are not able to detect the SFT solution other than in theory, nor the quantum solutions for that matter. We need to carefully examine the spinorial equations given above which are revisions of the macroscopic equations known as Coulomb's Law of electrostatics and the Biot-Savart Law of magnetostatics.

After Einstein's paper in 1905 many scientists felt that something was wrong with Maxwell's well-known equations.  Historically it was at this precise point in scientific history, after Einstein discussed the asymmetry in Maxwell's equations, that all of science began looking for an alternative way to calculate the various problems besetting science other than Maxwell's equations. This was the motivation and origin of quantum theory.

As we noted in all cases SFT requires a finite circulating current at  ro≠0 and rc≠0. Rather than one moving and one stationary particle a true EM effect requires two moving  particles . In having the magnetic field stationary the second equation (the Biot Savart-like equation) becomes singular and degenerate if rc=0.

The magnetic effect in EM has been widely misunderstood by quantum theory. The solution for the fine structure in hydrogen atom's spectrum due to an external magnetic field was achieved by modifying the Hamiltonian for the non-relativistic case via computations and not directly via Maxwell's theory. We might call this a 'manufactured' way of treating magnetic fields without having to use motions. In hindsight this was done to avoid using Maxwell's equations; but it did not avoid carrying over the problems inherent in classical electromagnetics.

Hamilt_spin

At its core quantum mechanics is a numerical model; it uses approximation techniques. To enable a matrix solution the Hamiltonian is assumed quadratic (Hermitian) in form. For example L is taken to be the angular momentum operator of the electron, while the momentum and potential are similarly quadratic. This recourse to a Hamiltonian (or more generally a Lagrangian) with its spin action term obviated the need for detailed equations of motion and concentrated on the energy within the whole system. But this was done at the expense of having to solve a differential equation of second order via computational methods at a time when computers did not exist. Even Dirac's first order equation was derived from the second order wave equation; hence it too had truncation errors of second order. On the overwhelming up side quantum theory did result in the development of computer technology and numerical methods to solve a wide range of physical problems over the coming decades.

In contrast SFT obtains an analytic solution  for the magnetic field of the electron without recourse to computational methods by using the mutual set of first order differential equations that relate the electron's motion to that of the proton, both the electric and magnetic components of motion, and using the correct method of measuring distances, not between charge points, but between the centres of rotation of the electron and proton.

POSTSCRIPT:  At Hydrogen Atom - Origins of Quantum Theory we see historically there were two problems within applications of classical electromagnetics that were carried over into quantum theory. In hindsight knowing how SFT handled the hydrogen atom in 2005 we see there were two problems: (1) the fields were being measured incorrectly (2)  the magnetic currents of particles were omitted in the formulations. Overall we see SFT completely solves the problems inherent within the classical formulation, while quantum theory was a confection that didn't fix the inherent problems in classical electrodynamics.