# Relativistic Momentum

As per equation (9), the momentum is not conserved in frame. We get different results with change in internal frame and it violates Einstein theory of relativity that laws of physics are invariant in different inertial frames. We have used Lorentz transformation for the transfer of velocity from *S *to frame. Lorentz theory is correct because it explains the cosntancy of velocity of light. So, the problem could be, the definition of linear momentum in relativistic dynamics. One has to take the appropriate definition of linear momentum such that it follows the fundamental laws physics like conservation of momentum in the absence of applied force. It should also reduce to the definition of classical physics, when the velocity of the body U<

The relativistic momentum can be defined as ,

. . . . . . . . . . . . . . . . . . . . . ( 10 )

where is the distance traveled by a particle of mass *m * and the time interval . Here is the proper time, that is the time measured with respect to the moving frame of velocity attached to the body.

As per the time dilaton relation, we know that,

** **** . . . . . . . . . . . . . . . . . . . . . ( 11 )
**We can rewrite equation (11) by taking mass m as m

_{0}, where m

_{0}represents rest mass or mass of the particles as per Newtonian non-relativistic mechanics.

**. . . . . . . . . . . . . . . . . ( 12 )**