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It is commonly said that sun produces energy in the fusion process by converting mass into energy.
If we disregard the concept of relativistic mass, how do we know whether the rest mass of the sun decreases, or it is the kinetic energy (in relativistic mass concept it would be decrease in relativistic mass) of the particles?
Relativistic mass is a concept that is no longer used in studying particle physics because it is not an invariant quantity to Lorenz transformations, it changes values going from one inertial frame to another. It is not a conserved quantity.
What is an invariant quantity under Lorenz transformations is the invariant mass of a particle or a system of particles. The invariant mass is the length of the four vector describing the kinematics of a particle or a system of particles. With a system of particles one has vector addition, and the "length" of the total vector sum will be the invariant mass of the system. Invariant mass is a conserved quantity, but is not a summed quantity. The sum of the invariant masses of a system of particles gives the lowest value of the invariant mass of the summed system.
The system of nuclei and electrons summing up to the mass of the sun will have a single four vector whose "length" uniquely describes the instantaneous mass of the sun. Instantaneous because it is composed of an enormous sum of individual particle and radiation vectors.
The sun radiates away photons and also, to a smaller extent, plasma composed of electrons and nucleons, the four vectors of these have to be subtracted from the total four vector of the sun, at each instant. This means that the total four vector continually diminishes and thus the sun in losing rest mass .
If one considers the sun in motion in the galaxy, it has a relativistic mass which is the inertial mass to be taken to account if it hits with velocities close to the velocity of light another star, in order for the newtonian kinematics of scattering to make sense. This has nothing to do with the internal fusion processes taking place inside the sun.
