R.L. wrote....

Your advisor is wrong, mass and energy are equivalent......



The kinetic energy gained adds to the "mass" of the object, thus it takes more energy to accelerate it further...

I have not heard that the concept is "falling out of favor"



First off, my advisor is a theoretical relativist who designed his own space borne gravitational wave mission to compete with LISA but due to the politics, was cheerfully absorbed into the LISA project. About this he ain't wrong.

Second, I never took a GR course and/or suffered through the pages of MTW and I can't find my copy of Wheeler's "Spacetime Physics" to back me up here, but I did find this blurb to make me feel more certain that this wasn't a halucination.

From: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html#c5

Problems with variable mass
Even though circumstances like that described at the Cambridge accelerator are conveniently described by assuming an increasing mass, that is not the only way to describe these experiments, and there are problems with the concept of variable relativistic mass. Einstein's point of view is described in the following quote:



"It is not good to introduce the concept of the mass of a moving body

for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion."

Upon being introduced to special relativity for the first time, it is easier to contemplate concepts like the speed of light as the speed limit of the universe by envisioning the mass as increasing to infinity at velocity c. However, when one has become familiar with the concepts of relativistic momentum and relativistic energy, there is no real need for the variable mass concept.