Relativistic energy-momentum relation derivation

Relativistic energy momentum relation:

From Einstein mass energy relation

E = mc2 (1)

Also from variation of mass with velocity relation

m = m0/(1 – v2/c2)1/2 (2)

Where m0 is the rest mass of the object

Put value of m in equation (1) and then square both sides, we get

E2=  m02c4/(1 – v2/c2)                (3)

As momentum is given by

p = mv

Put equation (2) and square

p2 = m02v2/(1 – v2/c2)

Multiply both sides by c2

p2c2 = m02v2 c2/(1 – v2/c2)         (4)

Subtract equation (4) from (3) and solve, we get

E2 – p2c2 = m02c4

Or E = (p2c2 + m02c4)

This is Relativistic energy momentum relation

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