The Duality of Time Theory

To derive the relation of the effective relativistic mass, we can start from equation 5.6 above:

(5.16)

Now we can findby differentiating:

(5.17)

From this equation we find:

(5.18)

Replacing in equation 5.16 we get:

(5.19)

This method, however, can not be considered a mathematical validation of the mass-energy equivalence relation, because the starting equationis not derived by any other fundamental method from Relativity, other than being similar to the time dilation and length contraction:,.

Using the same equationwith; thus:, we can also derive the relativistic energy-momentum relation, by squaring and doing some modifications:

(5.20)

From this equation we get:

(5.21)

Thus:

(5.22)

Or:

(5.23)

Again, since this derivation relies originally on the equation:, it can not be considered a mathematical validation of the mass-energy equivalence relation.