What is the true meaning of Einstein's energy formula for a particle?

[paweld]

I wonder what's the precise meaning of Einstein's formula for energy of a particle \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}. Is it total energy of particle (considering potential energy)? If it is then if we move (infinitesimally slowly) the particle from area of low potential to high its mass will increase. So the inertial mass is changing.

 

[ZapperZ]

I wonder what's the precise meaning of Einstein's formula for energy of a particle \frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}. Is it total energy of particle (considering potential energy)? If it is then if we move (infinitesimally slowly) the particle from area of low potential to high its mass will increase. So the inertial mass is changing.

You should start by first reading one of the entries in our FAQ thread. After that, if you can get access to it, read this paper: E. Hecht, Am. J. Phys. v.77, p.799 (2009).

Edit: I found an online copy of the paper here:

http://physics.princeton.edu/~mcdonald/examples/EM/hecht_ajp_77_804_09.pdf

Zz.