Four-acceleration
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In special relativity, four-acceleration is a four-vector and is defined as the change in four-velocity over the particle's proper time:
- <math>A^a:=\frac{dU^a}{d\tau}=\left(\gamma\dot\gamma c,\gamma\mathbf a\right)<math>
where
- <math>\mathbf a=\dot\gamma\mathbf u+\gamma\mathbf\dot u<math>.
The scalar product of a four-velocity and the corresponding four-acceleration is always 0.
Just like classical mechanics in low speed, the four-force and four acceleration can be related like Newton's second law:
- <math>F^a = m_0A^a<math>
where m0 is the rest mass of a particle.
See also: four-vector, four-velocity, four-momentum, four-force.