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5.3.3.4 Note on Relativistic Mass
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 5.7 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 section 3.3.8 for how to derive the
from
.