Four-force
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In the special theory of relativity four-force is a four-vector that replaces the classical force; the four-force of the four-vector a is defined as the change in four-momentum over the particle's own time:
- <math>F^a:= {dP^a \over d\tau}<math>.
Since <math>P^a = m_0U^a<math> where m0 is the rest mass and Ua is the four-velocity, we can relate the four-force with the four-acceleration as like Newton's second law:
- <math>F^a = m_0A^a = \left(\gamma\dot mc,\gamma\mathbf f\right)<math>.
Here, <math>m = m_0\gamma<math> is the relativistic mass and <math>\mathbf f=m_0\left(\dot\gamma\mathbf u+\gamma\mathbf\dot u\right)<math>.
See also: four-vector, four-velocity, four-acceleration, four-momentum.