9. Appendix: Deducing from :
Starting from equation 8 above:
(26)
and we can find
by differentiating
, with respect to
:
(27)
From this equation we find:
, and by replacing in equation 26 we get:
(28)
This method, however, can not be considered a mathematical validation of the mass-energy equivalence relation
, because the starting equation
is not derived by any other fundamental method from current Relativity, other than being analogous to the equations of time dilation and length contraction:
,
.
Using the same equation
with
; thus:
, we can also derive the relativistic energy-momentum relation, by squaring and applying some modifications:
(29)
From this equation we get:
, thus
, or:
(30)
Again, since this derivation relies originally on the equation:
, it can not be considered a mathematical validation of the mass-energy equivalence relation.


