Einstein’s energy and space isotropy

Abstract In this note, we derive an extension of the conventional Einstein variation mass formula with a specific expression arising from Lorentz invariant equation for energy rate $$\hbox {d}e/\hbox {d}p$$ d e / p where $$e = mc^2$$ = m c 2 is particle energy, $$p mu$$ u momentum and u velocity. This simplest one-parameter Lorentz-invariant mass–energy relation. Implicit in new space–time anisotropy such that has different rest masses positive negative x directions. While numerous experiments have been undertaken aimed at testing hypothesis, all indicate veracity assumption space isotropic, nevertheless since it generally believed black-holes exist centres galaxies, must be intrinsically anisotropic some sense. Finally, note very curious connection both energy–mass e_0/ (1 - (u/c)^2)^{1/2}$$ 0 ( 1 - ) derived here certain singular integral equations usually associated aero-foil problems, fluid mechanics punch problems elasticity, not vague intangible relationship, but involves exact correspondence.