MOCANU’S PARADOX AND QUATERNIONIC TRANSFORMATION AS THE ANSWER
2012jiq | Ahmad Mushfiq  // Rajshahi University, Rajshahi, Bangladesh, mushfiqahmad@gmail.com

When two non colinear velocities are added following Lorentz transformation, a Wigner rotation comes into play, and reciprocity requirement is not fulfilled without this rotation: the velocity of B from A is not the negative of the velocity of A from B. Both Mocanu and Ungar have attributed the paradox (failure of reciprocity principle) to both non-commutativity and non-associativity of Einstein' law of addition of velocities. To resolve this problem, Ungar has proposed a "Weak Associative Law" ( a set of corrections) to make Einstein' law of addition commutative and associative. We have shown that the paradox can be resolved without requiring commutativity. We are proposing a hypercomplex Pauli quaternion law of composition of relativistic velocities, which fulfills physical requirements. The proposed hypercomplex law compares well with Einstein's law of addition of velocities and fulfills all relativistic requirements.

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