Angular Momentum Field

In this paper, I describe three fields by 4*4 matrices: the electromagnetic field, the kinetic field, and the angular momentum field. These three fields are put into standardized forms related to Maxwell's equations by a unique hypothesis. Although, the implications of this hypothesis may not be clear at first sight, we can derive well-known equations that offer insight into the meaning of Lagrangian density. The results point toward the conclusion that the laws of the universe are based on the minimum action principle.

I examine two fundamental forces via the math of line integrals using my candidate proportionality ratio (α) which: • Restates electrostatic force based upon Planck (ħc) and that ratio of field strength at the square root of particle radius distance (re) versus the Bohr radius (a0) equilibrium distance, root(a0/re), the fine structure constant (α), as a line integral relative to that field, not as a point force or quantum e f potential. So, electrostatic has a line integral format more useful for examining certain subatomic events. • Generates a revised equation for strong nuclear force via elimination of and integral and e f part as now =1 by that proportionality. That causes strong with my root(a0/re) change versus electrostatic which is the 1/r of Bohr's angular momentum properly scaled. • Generates force vector equations of 1/distance-squared restated electrostatic force vector versus redefined strong now as direct, isotropic 1/distance-cubed force. Electrostatic primary outside Bohr, strong as primary inside Bohr, and both in conflict and in equilibrium near Bohr, meaning that strong nuclear force keeps electrons in fields, not angular momentum. • Has both static equations constants with physical meaning as reduced Planck basic unit of energy, radiating via a line integral over the equilibrium, at the speed of light, the field propagation rate in time, via proportionality with the Bohr radius, a distance. No movement is necessary. • Also implies that the strong nuclear force should use mass units, rather than charge units. • Implies that 'charge' and 'mass' get determined by those line integrals for future papers.

The electron-proton scattering experiment by the PRad (proton radius) team at Jefferson Lab measured the root mean square (rms) charge radius of the proton as rp = 0.831 ± 0.007(stat) ± 0.012(syst) fm.

Assuming all of the electric charge in the proton is packed into a single pointlike (elementary) charge and applying the ring current model to a proton, one gets a radius for the circular current that is equal to a = 2μ/qc = 0.58736 fm. Using CODATA values for all variables and constants in this equation, and applying a SQRT(2) form factor to, somehow, account for the envelope of the magnetic field around the ring current, yields an electric charge radius of 0.8065 fm. The difference between the PRad point estimate and this theoretical value is 0.00035 fm, which represents 5% of the standard error (0.007 fm) of PRad’s point estimate. It is, therefore, hard to argue this is a mere coincidence.

We can also calculate a proton radius based on the idea of a strong charge. This radius corresponds to the range parameter in Yukawa’s equation and is equal to a = ħ/mpc = 0.2103, which is about 1/4 of the PRad point estimate. This 1/4 factor is, obviously, far more mysterious, and the difference between 0.831 and this strong charge radius multiplied by 4 is 0.01 fm, which is about 50% of the combined statistical and systematic error (0.007 + 0.012 = 0.019). We, therefore, think that, while being somewhat less precise, the 1/4 factor cannot be a coincidence.

We, therefore, feel the new measurement of the proton radius by JLAB’s PRad team may lend credibility to attempts to extend the Zitterbewegung hypothesis from electrons to also include protons and other elementary particles. In contrast, the measurement is hard to fit into a model of oscillating quarks that have partial charge only.

We analytically calculate the time series for the perturbations induced by a general disturbing acceleration on the mutual range and range-rate of two test particles orbiting the same spinning body. We apply it to the general relativistic Lense-Thirring effect, due to the primary's spin, and the classical perturbation arising from its quadrupole mass moment for arbitrary orbital geometries and orientation of the source's symmetry axis. The Earth-Mercury range and range-rate are nominally affected by the Sun's gravitomagnetic field to the 10 m, 10^-3 cm s^-1 level, respectively, during the extended phase (2026-2028) of the forthcoming BepiColombo mission to Mercury whose expected tracking accuracy is of the order of 0.1 m, 2 X 10^-4 cm s^-1. The competing signatures due to the solar quadrupole, if modelled at the $10^-9 level of the latest planetary ephemerides INPOP17a, are nearly 10 times smaller than the relativistic gravitomagnetic effects.