The Force 4-Vector

Since this is a course in mechanics, its hard to avoid Newton's definition of the force \bgroup\color{black}$ \vec{F}={\partial\vec{p}\over\partial t}$\egroup. We have the same problem with time differentiation and try the same solution, the proper time \bgroup\color{black}$ \tau$\egroup.

\bgroup\color{black}$\displaystyle F_\mu={\partial p_\mu\over\partial \tau} = \g...
...r c}{\partial E\over\partial t},{\partial\vec{p}\over\partial t}\right) $\egroup

Since \bgroup\color{black}$ \gamma$\egroup gets large as the velocity approaches \bgroup\color{black}$ c$\egroup, it takes an infinite amount of force to accelerate a particle to the speed of light.

Jim Branson 2012-10-21