Velocity Transformation Rules
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Recall
the Lorentz transformation
The
differential version of Eq. (1) is
From the
definition of velocity
Eqs. (3)
to (5) are the transformation laws for velocity. The inverse transformation is
obtained from Eqs. (3) to (4) by interchanging primes and the sign of v
to give
To
obtain the transformation law for g
‘ we simplify Eqs. (3) to (5) by dividing by c to give
where ak
º uk/c.
We wish to find
Substituting
the relations in Eq. (5) into Eq. (6) results in
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