I'd like to add some thoughts from the realm of high school physics.
Interestingly enough, the very same discussion on the relativistic mass took place in Finland some years ago. A physics professor (who uses relativity in his research) noticed that popular books as well as high school physics books on relativity tend to introduce the concept of relativistic mass. He wrote a nice piece which discussed a bit of the relevant history and the contemporary situation: experts do not use relativistic mass anymore (the essay is available in Finnish for those who can read it :-): http://www.tsv.fi/ttapaht/022/maalampi022.htm>). In this piece he makes use of Adler's (1987) paper in AJP on the topic.
Not everyone agreed with him but it seemed to me that those who did not agree did not do any research using relativity.
John Denker has made an excellent point on spacetime approach to special relativity. Some of my students (well, very good students) read his papers (e.g. <http://www.av8n.com/physics/odometer.pdf>) and they seemed to grasp them quite well.
Usually relativistic mass is introduced in HS books as a way to explain why an object with rest mass cannot be accelerated to speed of light. Of course, it is not the only way to explain this (e.g. John Denker's papers give an elegant explanation in terms of space-time diagrams). I believe that we do disservice to our students by teaching them something which they'll have to get rid of later on if they decide to study physics at a university.
Finally, the International Baccalaureate physics syllabus just got rid of relativistic mass so I don't have to teach it anymore (even though I do mention that this concept exists).
Regards,
Antti
Reference:
"Does mass really depend on velocity, dad?" , Carl E Adler, American Journal of Physics 55 (1987) 739.
Antti Savinainen, Ph.D., B.Ed.
Senior Lecturer in Physics and Mathematics
Kuopio Lyseo High School
Finland
E-mail: <antti.savinainen@kuopio.fi>
Website: <http://kotisivu.dnainternet.net/savant/>
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