This is probably a “beaten to death” subject, but... as a student I was
first exposed to special relativity with the formula E=m c^2 with m as
the “relativist mass”. m increases with speed. m0 is the “rest mass”...
I later worked on particle physics experiments with highly relativist
particles that collide and decay. No one ever uses the “relativist mass”
concept: All you need to know is that 4-momentum is conserved, apply
Lorentz transforms to go between lab frames and different particle
frames and know that the norm of the 4-momentum of a particle is its
rest mass. Working with these on a daily basis I was soon convinced that
special relativity really works (we are not talking of abstract small
corrections). One more fun thing: broadening of rest mass measurements
is directly related to the life times in the particle rest frame...
Heisenberg was right.
So during my particle physics years, I decided that the teaching of the
“relativist mass” concept was (at best) confusing and unhelpful.
But now, many years later, I am not sure about this. Let's say I wanted
to compute the gravitational pull of a car (coasting by my lab) on a
very sensitive pendulum (the pendulum does not swing: I apply a small
force on it to keep it steady). The rest mass of the car is know.
I am tempted to use the car “relativistic mass” in my computation (This
is very natural: I believe that most non GR versed people would do the
same).
Is this a good idea? Is this a bad idea? Is it referential dependent?