Slow Motion

Consider a material particle P of rest mass $m$ and momentum $p$. These numbers are combined to specify yet another number

$\begin{align} \gamma \equiv \frac{ 1 }{ \sqrt{ \; 1 - \left( p/mc \right)^{2} \; \vphantom{{\left( p/mc \right)^{2}}^{2}} } } \end{align}$

where $c$ is a constant. Definition: $\gamma$ is called the**Lorentz factor**after the Dutch physicist Hendrik Lorentz. His original work

^{1}expressed $\gamma$ differently. But later, after discussing velocity, we will see that the forgoing definition is similar. The Lorentz factor is used to classify particles. If $\gamma$ is much greater than one, then we say that a particle is

**relativistic**. Or, if

$p \ll mc$

then $\gamma \simeq 1$ and we say that P is in **slow motion**. An ethereal particle cannot move slowly because $m = 0$ so the condition for slow motion cannot be satisfied by any value of the momentum.

$\begin{align} \gamma \simeq 1 + \frac{p^{2} }{2m^{2} c^{2}} \end{align}$