Einstein's:Mass increase resulting from Acceleration increase

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robphy said:
If you are implying that "apparent energy measured by this observer" is redundant, yes, I agree... that is why I did not use such a phrase.
If one is speaking of flat spacetime an inertial frames then it depends on usage. If there is no field present then its bet to refer to the sum of mass-energy and rest energy as "inertial energy." If there is a field present then the potential energy must be added and then one refers to the sum as the "energy" or "total energy." The time component of the 4-momentum will be the inertial energy. The time component of the canonical 4-momentum will be the the total energy.

Pete