Foundations of Physics, Vol. 19, No. 11, 1989 The Relativistic Velocity Composition Paradox and the Thomas Rotation Abraham A. Ungar 1 Received February 10, 1989," revised June 15, 1989 The relativistie velocity composition paradox of Moeanu and its resolution are presented. The paradox, which rests on the bizarre and counterintuitive non- commutativity of the relativistic velocity composition operation, when applied to noncollinear admissible velocities, led Mocanu to claim that there are "some difficulties within the framework of relativistic electrodynamics. "' The paradox is resolved in this article by means of the Thomas rotation, shedding light on the role played by composite velocities in special relativity, as opposed to the role they play in Galilean relativity. 1. INTRODUCTION Following Feynman, a "paradox is a situation which gives one answer when analyzed one way, and a different answer when analyzed another way, so that we are left in somewhat of a quandary as to actually what would happen. Of course, in physics there are never any real paradoxes because there is only one correct answer." In physics, thus, "a paradox is only a confusion in our understanding. ''(2) Special theory of relativity (STR) is a rich source of paradoxes in physics, several of which were listed by Sastry. (3) Attention to a paradox which arises from the noncommutativity of the relativistic composition of noncollinear velocities, not listed by Sastry, was recently drawn by Mocanu. (1) Having no known resolution, Mocanu regards the paradox as a source of several "difficulties within the framework of relativistic electrodynamics, ''(1) prompting him to elaborate "a new electrodynamics of moving bodies at relativistic velocities, different from that of Einstein and 1 Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105. 1385 0015-9018/89/I100-1385506.00/0 © 1989 Plenum Publishing Corporation