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Since, all the laws of physics are the same in all inertial frames, linear momentum must be conserved in all frames. In order to obey this condition, we must modify the definition of linear momentum to satisfy following conditions: (i) linear momentum (P) must be conserved in all collisions and (ii) the relativistic value calculated for P must approach the classical value as u approaches zero. For any particle, the correct relativistic equation for linear momentum is:
Here, u is the velocity of the particle and m is the mass of the particle and γ is given as:
When u is much less than c, γ → 1 then P→ mu. Thus, the relativistic equation for momentum reduces to the classical expression when u is much smaller than c.
The relativistic kinetic energy is given by,
And, total energy is given by,
Total Energy = Kinetic Energy + Rest Energy
Or E = K + mc2
Or E = γmc2
This is called Einstein’s equation for mass-energy equivalence and is given by,
Common Sense of Special Relativity:The common sense of special relativity is that all of the laws in physics retain their mathematical forms in the inertial frames of reference. This referred as the common sense postulate in special theory of relativity.
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Relativity