Vesselin Petkov, 05.12.2016
Minkowski Institute, Montreal, Canada
The issue of relativistic mass (recently being questioned by an increasing!? number of physicists) is one more example of the kind of questions that are being analyzed at the Minkowski Institute.
Here is my personal position on the issue with which I enter the discussions at the Minkowski Institute. Once the position of the Minkowski Institute has been determined (after a rigorous examination of the existing theoretical and experimental evidence), it will be announced.
The fact  of the relativistic increase of mass is one of the deepest open questions in spacetime physics. Research on it is physics at its best.
Trying to deny the fact that mass increases with velocity or to declare it a matter of taste or fashion is, I think, physics at its worst, because a potentially groundbreaking research direction is excluded from the very beginning.
It is true that physics at its best also includes the ability to identify and rule out research directions based on misconceptions, but for reasons summarized below (and explained in detail in a book near completion: Introduction to Spacetime Physics) I do not think the relativistic increase of mass is a misconception.
On the contrary, the recent fashion to claim that mass does not increase with velocity is, I think, an unfortunate and embarrassing misconception.
When two facts are taken explicitly into account:
- the very definition of mass (that mass is defined as the measure of the resistance a particle offers to its acceleration)
- that in relativity acceleration is different in different reference frames
it becomes immediately clear that the mass of a particle cannot be the same in all frames in relative motion.
Proper or rest mass (which is an invariant) and relativistic mass (which is frame-dependent) are exactly like proper time (which is an invariant) and relativistic / coordinate time (which is frame-dependent) [and, to some extent, like proper and relativistic length].
9 September 2018: For a more detailed account see the Appendix (by the Editor): On Relativistic Mass included in a volume with(see the link at the bottom of the page).
 The fact is that an increasing force should be applied to a particle to accelerate it to speeds close to the speed of light. As Newton first realized it, to accelerate a particle, a force is needed to overcome the particle’s resistance to its acceleration (i.e. its resistance to a change in its velocity). And as the mass of a particle is defined as the measure of the resistance the particle offers to its acceleration, it is indeed a fact that the mass of a particle increases with velocity – to accelerate a particle to speeds approaching the speed of light an increasing force is needed because the particle offers an increasing resistance (as its speed increases), which must be overcome by the applied force; that is, an increasing force is needed to accelerate a particle whose mass (the measure of the particle resistance to its acceleration) is increasing.