Rest mass

Author: Leandro Alegsa Creation date: November 13, 2022

Rest mass (physics), the mass of a body as measured when the body is at rest, but it is relative to an observer who is moving or not, an inherent property of the body. All matter, such as any object, has some rest mass. Energy, such as light or kinetic energy (the energy of a moving object) has no rest mass because it causes no change in spacetime in a frozen time frame. However, energy affects mass while time passes; therefore, it affects spacetime, so it has mass.

Formula

When using natural units in particle physics, energy and mass have the same unit. The center-of-mass energy is then generally the square root of the total quadrature momentum:

$\sqrt{s} = \sqrt{ \left( \sum_{i=1}^n{P_i} \right) ^2}$ ,

where by the square is meant the scalar product of the Minkowskimetric:

$\sqrt{s} = \sqrt{ \left( \sum_{i=1}^n{P_{\mu, i}} \right) \cdot \left( \sum_{i=1}^n{P_i^\mu} \right) }$ .

Here is

is the number of particles
$P_{i}$ their quad pulses.

Properties

The center-of-mass energy is invariant under Lorentz transformations; hence the name invariant mass. This follows from the fact that the sum of four-vectors is a four-vector and the square of a four-vector is a Lorentz scalar, i.e. a scalar which remains invariant under Lorentz transformations. Correspondingly, the root of a Lorentz scalar is also a scalar.
The center-of-mass energy of all particles before a collision is equal to their center-of-mass energy after the collision (conservation quantity).