Misplaced Pages

Revision as of 19:40, 16 May 2006

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 deterined 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:

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

Where:

${\displaystyle W}$ is the invariant mass of the system of particles

${\displaystyle \Sigma E}$ is the sum of the energies of the particles

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

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

${\displaystyle p_{i}^{\mu }=\left(E_{i},\mathbf {p} _{i}\right)}$

${\displaystyle P^{\mu }=\left(\Sigma E_{i},\Sigma \mathbf {p} _{i}\right)}$

${\displaystyle P^{\mu }P_{\mu }=\eta _{\mu \nu }P^{\mu }P^{\nu }=(\Sigma E_{i})^{2}-(\Sigma \mathbf {p} _{i})^{2}=W^{2}}$, since the norm of any four-vector is invariant.

See also

• Relativistic mass
• Invariant (physics)

• Relativity
• Mass