Is there a relationship between electromagnetic energy and inertia?
The following is based on current understanding. There has been an effort to pull together all the interactions we know of into a single theory – a so-called Grand Unified Theory (GUT) of everything. However, although Einstein spent his last 4 decades trying to come up with one, and many others have spent years and decades on it since, we still do not have a convincing model for this that has been supported by experimental evidence. Lacking a quantum gravity theory, which would be unified with the electro-weak and quantum chromo-dynamic (QCD) interactions, we do not know of a relationship between EM energy and inertia. What we do think we know is that photons, which have no mass (and thus no inertia) do have EM energy. They also have momentum, which for particles with mass would be the product of the mass with the velocity vector, but for the massless photons is calculated from the wavelength or energy of the photon. The quantum mechanical explanation for inertia is similar to the clas