The proposed relative-velocity-based approach has connections to the work of Wilhelm Weber (in 1864) and Walter Ritz (in 1908), who attempted to develop alternative forms of electromagnetism.
Around 1908, shortly before his early death in 1909 (at the age of 31), Ritz proposed a model in which the speed of light varies with the source velocity (as in classical mechanics) --- this is referred to as Emission Theory. In Ritz's approach, the speed of light would depend on the relative-velocity between the observer and the source of the light. Although astronomical observations that were initially thought to be contradictory (and therefore the rationale to reject Ritz's approach) were later found to be consistent, the approach (i) could not quite explain Fresnel drag and (ii) did not have an accompanying electromagnetic theory, which would require modification of Maxwell's equations --- as discussed in "Ritz, Einstein, and the Emission Hypothesis", Martínez, Alberto A., Physics in Perspective, 6(1), 4-28, 2004.
A suitable modification of Maxwell equations, which enables a source-velocity-dependent propagation of light and matches the Fresnel drag is the main result of the proposed relative-velocity-based model (in article 1 below). Thus, the approach overcomes some of the mathematical modeling challenges for a Ritz-type emission theory.
The following works show that the new relative-velocity-based model captures typical relativistic effects in optics and high-energy particles. Additionally, the model explains experimental discrepancies in two classical experiments in electromagnetism (in Section 3.2 of Article # 1 below). Moreover, the approach can be used to explain anomalies in current cosmological observations.
#1: Nonlinear Models for Relativity Effects in Electromagnetism
This article describes the main theory.
There are two main changes --- (i) the partial time derivative in Maxwell's equations is replaced by the total time derivative; and (ii) the electromagnetic force depends on the relative velocity between particles (which is a modification of Weber's approach.)
The innovation is the association of electromagnetic forces with the relative velocity between a particle and the field (and not the absolute velocity of the particle in the inertial frame under consideration). Under a Galilean velocity addition, the relative-velocity does not change for different inertial frames. Therefore, the force on the particle remains the same in different inertial frames in this approach leading to Galilean invariance.
The proposed approach matches electromagnetism effects from CRT data (in Section 2.2, see Fig. 1), and explains experimental discrepancies in two classical experiments (in Section 3.2).
#2: Response to Comment on Nonlinear Models for Relativity Effects in Electromagnetism
Clarifies that the modified electromagnetism model is invariant with Galilean Transformation; and matches transverse Doppler predictions.
#3: Lorentz Violation in High-Energy Ions
Shows that including the Doppler effect in the emission (which is of the same order as the time dilation effect) in the Special-Relativity (SR) analysis leads to differences between experimental and theoretical SR predictions.
Such experimental studies are important since there are second-order differences in the Longitudinal Doppler Effect between the proposed relative-velocity-based approach and SR.
Current experimental set-ups do not limit the angle of the measured photons (e.g., to be perfectly perpendicular to the ion beams), and the filters used are too broad to verify the frequency of the measured photons. These problems limit the ability to bound Lorentz violations. At present, bounds can only be obtained by assuming that the photons are at "the correct frequency."
If the angle of the measured photon emissions is not constrained and if the observed frequency is not verified (as in current experimental setups), then SR analysis (that includes SR Doppler effects in the emissions) cannot guarantee bounds on Lorentz violation --- as shown in this article. For example, with potential variations in the emission angle, the observations can be explained even with substantial Lorentz violation, and with alternate models, e.g., with the relative-velocity-based approach.
#4: Response to Comment on Lorentz Violation in High-Energy Ions
This response clarifies that, without accounting for the transverse Doppler effect (when using special-relativity analysis), the experimental analysis cannot rule-out (and develop bounds on) the Lorentz violation, especially since the energy of the transition being excited (in the moving high-energy ion, under the experimental conditions) is not measured directly. Therefore, the transverse Doppler effect, in the emissions, should be accounted for when analyzing the results of saturation spectroscopy experiments.
#5: A Relative-velocity-based Cosmology Model
There are several anomalies in cosmological observations, which are challenging to explain using current models. This has led to different alternate cosmology models, some of which do not support the big-bang model. In contrast, the above article is a modified version of the big-bang model --- more like a super super-nova. The relative-velocity-based model is consistent with the Hubble law, with the time dilation seen in cosmological observations, and provides a potential explanation of the farther-dimmer observation in supernovae (SNe).
The article shows that the proposed (relative-velocity-based) model can provide potential explanations to current anomalies in cosmological observations such as: (i) the presence of large number of spectroscopic binaries with short time periods even though nearby visual binaries are not seen with such short time periods; (ii) the apparent lack of time dilation in quasar observations even though time dilation has been observed in supernovae (SNe) light curves; (iii) the possibility that some quasars might be closer than the distance predicted by their large spectroscopic redshifts; and (iv) the difficulty in identifying supernovae progenitors.