DoT: The Duality of Time Postulate

  If we want to consider mass to be variable with speed as in early Special Relativity, and distinguish between rest mass:  and relativistic mass: , according to the standard equation that uses Lorenz factor: , then we can arrive to the equation  by calculating the derivative  which in this case will not be equal to zero as we required in equation 9 above. However, the above relativistic equation of mass () is only obtained based on the same mass-energy equivalence relation that we are trying to prove here, so in this case it will be a circular argument. Therefore, the two equations:  and  are equivalent, and deriving one of them will lead to the other. See also 9 for how to derive the  from .