I recently studied SRT and came across a strange thing which I don't really understand (it's from a book, but without the example):
Let's consider two charged particles which repell each other such that momentum is conserved. In classical mechanics kinetic energy is not conserved (but the sum of kin. and potential energy).
Now, one could boost to a different reference frame and the principle of relativity then implies momentum conservation again. But, as total momentum transforms as $-\gamma v E$ it follows that E must be also a conserved quantity and therefore the particles masses must decrease accordingly.
I find this really strange since such a time dependent mass would have a huge impact on dynamics. More over, this effect seems to be only occuring when momentum is conserved . So, a particle in an extern field will not change its mass?
The book then makes a few examples where the mass-defect is stated. One of them is a mass which is put to a different height in a homogenous gravity field and therefore loses some of its mass, which seens is also strange to me..
It seems like I have a missunderstanding about some of the concepts in SRT. Maybe, someone knows how to resolve it?