Newtonian momenta, calculated as ⁠ p = m v ⁠, fail to behave properly under Lorentzian transformation. The linear transformation of velocities ⁠ v ′ = v − − u ⁠ is replaced by the highly nonlinear ⁠ v ′ ′ = ( v − − u ) / ( 1 − − v u / c 2 ) ⁠ so that a calculation demonstrating conservation of momentum in one frame will be invalid in other frames. Einstein was faced with either having to give up conservation of momentum, or to change the definition of momentum. This second option was what he chose.