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Four-acceleration




: A^a:= rac{dU^a}{d au}=\left(\gamma\dot\gamma c,\gamma\mathbf a ight)

where

: \mathbf a=\dot\gamma\mathbf u+\gamma\mathbf{\dot u}

and \gamma is the Lorentz Factor . It should be noted that a dot above a variable indicates a derivative with respect to the time in a given reference frame, not the proper time au.

The Scalar Product of a Four-velocity and the corresponding four-acceleration is always 0.

As in Classical Mechanics (at low velocity) the four acceleration is related to the Four-force by Newton's Second Law such that

: F^a = m_0A^a

where ''m''0 is the Rest Mass of a particle.

See also: Four-vector , Four-velocity , Four-momentum , Four-force .


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