Testing the Ampère–Maxwell law on the photon mass and Lorentz symmetry violation with MMS multi-spacecraft data

We investigate possible evidence from Extended Theories of Electro-Magnetism (ETEM) by looking for deviations from the Ampère–Maxwell law. The photon, main messenger for interpreting the universe, is the only free massless particle in the Standard Model (SM). Indeed, the deviations may be due to a photon mass for the de Broglie–Proca (dBP) theory or the Lorentz Symmetry Violation (LSV) in the SM extension (SME), but also to non-linearities from theories as of Born–Infeld and Heisenberg–Euler. With this aim, we have analysed 6 years of data of the Magnetospheric Multi-Scale (MMS) mission, which is a four-satellite constellation, crossing mostly turbulent regions of magnetic reconnection and collecting about 95% of the downloaded data, outside the solar wind. We examined 3.8 million data points from the solar wind, magnetosheath, and magnetosphere regions. In a minority of cases, for the highest time resolution burst data and optimal tetrahedron configurations drawn by the four spacecraft, deviations have been found ( 2.2 % in modulus and 4.8 % in Cartesian components for all regions, but raising up in the solar wind alone to 20.8 % in modulus and 29.7 % in Cartesian components and up to 45.2% in the extreme low-mass range). The deviations might be due to unaccounted experimental errors or, less likely, to non-Maxwellian contributions, for which we have inferred the related parameters for the dBP and SME cases. Possibly, we are at the boundaries of measurability for non-dedicated missions. We discuss our experimental results (upper limit of photon mass of 2.1 × 10 - 51 kg, and of the LSV parameter | k → AF | of 6 × 10 - 9 m - 1 ), and the deviations in the solar wind, versus more stringent but model-dependent limits.