How does modern relativity modify the law of conservation of momentum?

The special theory of relativity, sometimes known as special relativity, is a physical theory that describes how space and time interact. Theoretically, this is known as STR theory.

The equation \({\rm{p = mv}}\) is the classical momentum formula. Instead of the velocity of the frame \({\rm{v}}\) used in classical physics, contemporary relativity modified the momentum to \({\rm{p = \gamma mu}}\).

Here, \({\rm{\gamma = }}\frac{{\rm{1}}}{{\sqrt {{\rm{1 - }}\frac{{{{\rm{v}}^{\rm{2}}}}}{{{{\rm{c}}^{\rm{2}}}}}} }}\) and \({\rm{u}}\) is the velocity of the moving object relative to an observer.

Therefore, Classical momentum is multiplied by the relativistic factor\({\rm{ y}}\) to get relativistic momentum \({\rm{p}}\).