A measurement or calculation of the mass of an object that is the same for all frames of reference. Also known as rest mass because it is the mass that an observer in the same frame of reference as the object would measure. It can be determined from an object's energy and momentum.

Particle physics

In particle physics, the mathematical combination of a particle's energy and its momentum to give a value for the mass of the particle at rest. The invariant mass is the same for all frames of reference (see Special Relativity).

The invariant mass of a system of decay particles is related to the rest mass of the original particle by the following equation:

$\backslash mbox\{W\}^2\backslash mbox\{c\}^4=(\backslash Sigma\; \backslash mbox\{E\})^2-(\backslash Sigma\; \backslash mbox\{pc\})^2\; \backslash ,$

Where:

$W$ is the invariant mass of the system of particles

$\backslash Sigma\; E$ is the sum of the energies of the particles

$\backslash Sigma\; pc$ is the vector sum of the momenta of the particles (includes both magnitude and direction of the momenta) times the speed of light, $c$

A simple way of deriving this relation is by using the momentum four-vector (in natural units):

$p\_i^\backslash mu=\backslash left(E\_i,\backslash mathbf\{p\}\_i\backslash right)$

$P^\backslash mu=\backslash left(\backslash Sigma\; E\_i,\backslash Sigma\; \backslash mathbf\{p\}\_i\backslash right)$

$P^\backslash mu\; P\_\backslash mu=\backslash eta\_\{\backslash mu\backslash nu\}P^\backslash mu\; P^\backslash nu=(\backslash Sigma\; E\_i)^2-(\backslash Sigma\; \backslash mathbf\{p\}\_i)^2=W^2$, since the norm of any four-vector is invariant.

See also

• Relativistic mass
• Invariant (physics)

relativity | Mass

Invariáns tömeg | mirovna masa | Ruhemasse