Concisely, the mass of a system in special relativity is the norm of its energy-momentum four vector.

Note that mass is computed as the length of the energy-momentum four vector, which can be thought of as the energy and momentum of the system “at infinity”.

Note that in General Relativity, gravity is caused not by mass, but by the stress-energy tensor. Thus, saying that a moving particle has “more gravity” does not imply that the particle has “more mass”. It only implies that the moving particle has “more energy”.

Because General Relativity is a diffeomorphism invariant theory, it has an infinite continuous group of symmetries rather than a finite-parameter group of symmetries, and hence has the wrong group structure to guarantee a conserved energy.

Noether’s theorem has been extremely influential in inspiring and unifying various ideas of mass, system energy, and system momentum in General Relativity.

— Wikipedia on Mass in general relativity

2012.06.16 Saturday ACHK