The electric and magnetic fields are dependent on the velocity of an observer, so the relativistic form of the Lorentz force law can best be exhibited starting from a coordinate-independent expression for the electromagnetic and magnetic fields F , and an arbitrary time-direction, γ γ 0 . This can be settled through Space-Time Algebra (or the geometric algebra of space-time), a type of Clifford algebra defined on a pseudo-Euclidean space, as E = ( F ⋅ ⋅ γ γ 0 ) γ γ 0 and i B = ( F ∧ ∧ γ γ 0 ) γ γ 0 F is a space-time bivector (an oriented plane segment, just like a vector is an oriented line segment), which has six degrees of freedom corresponding to boosts (rotations in space-time planes) and rotations (rotations in space-space planes). The dot product with the vector γ γ 0 pulls a vector (in the space algebra) from the translational part, while the wedge-product creates a trivector (in the space algebra) who is dual to a vector which is the usual magnetic field vector. The relativistic velocity is given by the (time-like) changes in a time-position vector v = x ˙ ˙ , where v 2 = 1 , (which shows our choice for the metric) and the velocity is v = c v ∧ ∧ γ γ 0 / ( v ⋅ ⋅ γ γ 0 ) .