From Nikolay Umov <i>E=kmc²</i> via Albert Einstein’s <i>E=&gamma;mc²</i> to the Dark Energy Density of the Cosmos <i>E=(21/22)mc²</i>

Abstract

The paper starts from the remarkable classical equation of the great nineteenth century Russian physicist Nikolay Umov E=kmc 2 where 1/2 &le;k &le;1 , m is the mass, c is the speed of light and E is the equivalent energy of m . After a short but deep discussion of the derivation of Umov we move to Einstein’s formula E= &gamma; mc 2 where &gamma; is the Lorentz factor of special relativity and point out the interesting difference and similarity between Umov’s k and Lorentz-Einstein &gamma; . This is particularly considered in depth for the special case which leads to the famous equation E=mc 2 that is interpreted here to be the maximal cosmic energy density possible. Subsequently we discuss the dissection of E=mc 2 into two components, namely the cosmic dark energy density E(D)=(21/22)MC 2 and the ordinary energy density E(O)=MC 2 /22 where E(D)+E(O)=MC 2 . Finally we move from this to the three-part dissection where we show that E is simply the sum of pure dark energy E(PD) plus dark matter energy E(DM) as well as ordinary energy E(O) .