Four-force

In the special theory of relativity, four-force is a four-vector that replaces the classical force. In the special theory of relativity, four-force is a four-vector that replaces the classical force. The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper time: For a particle of constant invariant mass m > 0 {displaystyle m>0} , P = m U {displaystyle mathbf {P} =mmathbf {U} } where U = γ ( c , u ) {displaystyle mathbf {U} =gamma (c,mathbf {u} )} is the four-velocity, so we can relate the four-force with the four-acceleration A {displaystyle mathbf {A} } as in Newton's second law: