in the special theory of relativity four-force is a four-vector that replaces the classical force; the four-force is the four-vector defined as the change in four-momentum over the particle's own time: :\mathbf{f} = {d\mathbf{p} \over d\tau}. for a particle of constant invariant mass m > 0, \mathbf{p} = m\mathbf{u} \, where \mathbf{u}=\gamma(c,\mathbf{u}) \, is the four-velocity, so we can relate the four-force with the four-acceleration as in newton's second law: :\mathbf{f} = m\mathbf{a} = \left(\gamma {\mathbf{f}\cdot\mathbf{u} \over c},\gamma{\mathbf f}\right). here :{\mathbf f}={d \over dt} \left(\gamma m {\mathbf u} \right)={d\mathbf{p} \over dt} and :{\mathbf{f}\cdot\mathbf{u}}={d \over dt} \left(\gamma mc^2 \right)={de \over dt}. where \mathbf{u}, \mathbf{p} and \mathbf{f} are 3-vectors describing the velocity and the momentum of the particle and the force acting on it respectively. in general relativity the relation between four-force, and four-acceleration remains the same, but the elements of the four-force are related to the elements of the four-momentum through a covariant derivative with respect to proper time. :f^\lambda := \frac{dp^\lambda }{d\tau} = \frac{dp^\lambda }{d\tau } + \gamma^\lambda {}_{\mu \nu}u^\mu p^\nu ==examples== in special relativity, lorentz 4-force (4-force acting to charged particle situated in electromagnetic field) can be expressed as: :f_\mu = qe_{\mu\nu}u^\nu, where e_{\mu\nu} - electromagnetic tensor, u^\nu - 4-velocity, q - electric charge. == see also == * four-vector * four-velocity * four-acceleration * four-momentum == references == * 
Force Minkowski_spacetime Theory_of_relativity