juanrga
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Phrak said:I find it cleaner and more obvious to avoid square roots where possible and use the vector equations that are good in Minkowski coordinates for adding masses.
define\mu for a particle.
\mu = (E/c^2, \textbf{p}/c)
The bases vectors are dropped for convenience.
For a two particle system.
\mu_1 = (E_1/c^2, \textbf{p}_1/c)
\mu_2 = (E_2/c^2, \textbf{p}_2/c)
Vector addition.
\mu_1+\mu_2 = ([E_1 + E_2 ]/c^2, [\textbf{p}_1 + \textbf{p}_2 ]/c)
The particle masses.
m_1 = |\mu_1|
m_2 = |\mu_2|
The combined mass.
m_\Sigma = |\mu_1 + \mu_2 |
Beautiful, only to remark that if the particles are not free, neither m_1 nor m_2 represent the masses of the particles.