The idea of increasing mass as you get faster relates to kinetic energy that you gain.

Who gains the mass when there are two observers involved in an experiment?

The one who had his engine running.

Physicists are made very aware of relativistic mass increase when they try to accelerate electrons to moderately high velocities. If you use a simple cyclotron, then they just reach a limit to their top speed. You need to modify the magnetic field or driving frequency to get higher speeds to make the increased masses go in a circle of appropriate diameter. It's called a betatron.

I'm not sure how that relates to your foregoing statements, lightarrow. Of course, the electrons aren't in an inertial frame when they're in the betatron.

And I'm not sure if you want to say that relativistic mass is a useful concept or not or whatever.

Anyway, considering a fast moving charged particle's trajectory, it's true that you can ascribe the effect to a greater mass, but the problem is that this would be a "transverse mass" which dependence on the particle's velocity v is different from that of the "longitudinal mass" and this makes the concept of relativistic mass too complicated.

If you call

**F** the force on the particle, m,

**v** and

**a** its (rest) mass, velocity and acceleration (in bold to mean they are vectors), you have:

**F** = m

**a**/Sqrt[1 - (v/c)

^{2}] + m(

**v**•

**a**)

**v**/c

^{2}[Sqrt[1 - (v/c)

^{2}]]

^{3}where "•" means scalar product.

So, when the particle's speed

**v** is transverse to its acceleration

**a**,

**F** = m

**a**/Sqrt[1 - (v/c)

^{2}] and you can say that

**F**/

**a**, that is, the "mass", is m/Sqrt[1 - (v/c)

^{2}] = relativistic mass.

But when the acceleration is not transverse to the velocity, you see well that the result is different.