The spin is the intrinsic angular momentum of particles. For the fundamental particles, it is a quantized, internal particle property like the mass. It is a half or integer multiple of the reduced Planck quantum ℏ. Apart from the fact that, according to the current state, it is not caused by the angular motion of a mass, it has all the properties of a classical mechanical intrinsic angular momentum, in particular with respect to conservation of angular momentum and coordinate transformations. That the angular momentum is nevertheless caused by a rotational motion of nucleons or that an energy or a velocity can be assigned to the angular momentum of nucleons or the rotational wave, could recently be shown impressively by PD Dr. Blau from the University of Tübingen in a publication in Science Advance.

Rotational waves of protons

The rotation wave in protons as the cause of angular momentum is comparable to matter waves with a De Broglie wavelength of λ=c/f. The angular momentum of particles is the result of rotation waves of mass points, which are assumed not to rotate in the classical sense. However, if the rotational velocity were also quantized (i.e., oversized) due to the quantized angular momentum, the rotational energy would not be proportional to the mass of a particle, but inversely proportional to it, which is not possible. Therefore, the rotational wave of protons very likely has a different velocity value than the one calculated from the spin. Thereby the velocity value of the circling wave could be increased e.g. by magnetic fields.

According to Heisenberg, the position and velocity of a circling particle cannot be accurately measured at the same time, but this is true only for pr < h/4π, which is not true for protons, and only during spin interactions or measurements. The electrons on their orbits form a standing wave because the particle wave always orbits around the same particle radius. This means that the electron only has a certain probability of being in one place in the orbital. Scientists at the University of Virginia in Charlottesville have now succeeded in getting electrons to orbit around the nucleus in the classical sense by applying high excitation. At these high energies, electrons lose their wave properties in favor of particle properties. In the case of nucleons, the rotational velocity truncates out of the spin formula, so that only the radius is quantized in this process. Therefore, the mass points in the proton do not form a standing wave because they effectively rotate around the much larger quantized radius, so they have a comparatively very large wavelength. Accordingly, nucleons can very well be assigned a defined rotational frequency and a rotational motion. 

A spike in the polarizability curve that should not be there

A fundamental property of the proton represents the response of the system to an external electromagnetic (EM) field. It is characterized by the EM polarizabilities, which show how the charge and magnetization distributions within the system are distorted by the EM field. In addition, the generalized polarizabilities outline the deformation of the densities in a proton subjected to an EM field. They reveal essential information about the system dynamics and provide a key to deciphering the proton structure and the strong interaction with its elementary quark and gluon constituents. Of particular interest is a puzzle in the electrical generalized polarizability of the proton that has remained unsolved for two decades. R. Li et al. currently reported measurements of the generalized EM polarizability of the proton at low square of the four-momentum transfer. They show an anomaly of the behavior of the electric generalized polarizability of the proton with a spike in the curve that contradicts the predictions of nuclear theory. The reported measurements suggest the presence of a novel mechanism in the proton that could be associated with the presence of a rotational wave in the proton that behaves like an ordinary particle wave.

Due to the same wave energy hf of the electron and proton, the two waves superimpose on each other during scattering, leading to the spike in the polarizability curve in the experiments. The maximum of the spike is about twice the value expected by extrapolation for Q2 = 0.33 GeV2, which is caused by the interference of two waves of the same size. Therefore, especially since other explanations are lacking, the observed spike is most likely due to the rotating wave energy of the proton. Also, the form factor of the protons and neutrons shows an oscillating pattern instead of a straight line, which can also be reconciled with the rotation waves of the nucleons. 

Direct observation of nucleon rotation

Dietrich Leibfried from NIST, Colorado was even able to directly observe nucleon rotation in a confined 9Be+ ion and measure the oscillation frequency of the ion. The measured oscillation frequency of f(r) = 7.2 MHz in the ground state corresponds quite exactly to the rotation frequency of the nucleons (2072.18 Hz) determined by transforming the gravitational equation. For a beryllium ion, the quantized radius is 7.374∙10^-7 m (r=h/4πmv=h/8π^2m(Be)f(r)r(Be)). Transferred to the oscillating atomic diameter of the confined beryllium ion (105 pm), this is 7022.904 times smaller, corresponding to a 7022.904 times larger oscillation frequency of the confined beryllium ion compared to the rotation frequency of a nucleon (spin 1/ 2) of the ion. The unaffected rotational frequency of a nucleon is then calculated to be 7.2 MHz divided by 7022.904 times 2 (the ion oscillates about the atomic diameter, not the radius) = 2050.4338 Hz (deviation 1% due to Slater's inaccurate, empirically determined atomic radius of r(Be) = 105 pm).

Gravity arises from the rotation of the nucleons

According to the present state of knowledge, the mass of hadrons is composed predominantly of the kinetic energy of the quarks as well as of the energy of the gluons. Through the proton magnetic field, the fast motion of the charged quarks, which ideally move in a circular or elliptical orbit, induces a Lorentz force, which results in a rotation of the proton perpendicular to the major axis of the quarks. This rotational motion of protons and neutrons attracts mass not only within a nucleon, but also mass outside, up to the quantized radius 19 powers of ten larger than the actual proton radius to satisfy the Heisenberg inequality mvr>h/4π (r>h/4πmv, which is very much larger than a nucleon). Thus, the fast quark motion within the nucleons is responsible for the formation of the gravitational force, while the small proton gravitational fields add up to the gravitational field of large masses plus their mass defect. This gravitational mechanism has a range of c/16πf, i.e. 10^23 m for galaxies and is even larger for rotating galaxy clusters. From this origin mechanism of gravitation from quark motion, the rotational velocity of protons can be determined as equivalent to the gravitational force from the rotational frequency of quarks and thus from the nuclear force, which is a unification of both forces that has never been achieved before. This gravitational mechanism could be confirmed by exact measurements of the magnetic flux density of protons and neutrons. 

Source: Science Advance.