Some problem with the Lorentz transformations of energy and momentum of the electromagnetic field

Abstract

In this work, it is shown that the energy and momentum of electromagnetic fields created by a classical charge, whose velocity varies with time, do not form four-vector. A possible explanation for this result is that the calculation of energy and momentum is performed as an integration of the densities of these quantities, {\it i.e.} the squares of the electromagnetic field $E^2$ and $H^2$ in the whole space at the hyperplane $t=const$. But $E^2$ and $H^2$, which are calculated at a fixed point in time, $t$, are all created at previous (retarded) instants of time. In other words, all densities $E^2$ and $H^2$ are independent of each other. Meanwhile, Lorentz transformations are defined as transformations between physically connected quantities.