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Abstract - During much of the 20th century it was widely believed that one of the significant insights of special relativity was “relativistic mass.” Today there are two schools on that issue: the traditional view that embraces speed-dependent “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it's speed-independent. This paper explores the history of “relativistic mass,” emphasizing Einstein's public role and private thoughts. We show how the concept of speed-dependent mass mistakenly evolved out of a tangle of ideas despite Einstein's prescient reluctance. Along the way there will be previously unrevealed surprises (e.g., Einstein never derived the expression for “relativistic mass,” and privately disapproved of it).
Today there are two schools of on that issue: the traditional view that embraces speed-dependant “relativistic mass,” and the more modern position that rejects it, maintaining that there is only one mass and it’s speed-independent.
Letter from Albert Einstein to Lincoln Barnett, 19 june 1948. ‘’ it is not good to introduce the concept of the mass M =m/( gamma)^0.5 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.’’
Is that saying not to use relativistic mass?
Here's Matt Strassler's take on the subject.http://profmattstrassler.com/2013/07/11/mass-ive-source-of-confusion/