For purchase of this item, please read the instructions.
Volume 12: Pages 527-530, 1999
Lost in Velocity Space: Problems with the Single‐Boost Lorentz Transformation
Michael H. Brill
David Sarnoff Research Center, Box CN 5300, Princeton, New Jersey 08543‐5300 U.S.A.
A Lorentz velocity boost preserves spatial coordinate values perpendicular to the boost direction. Composing a Lorentz x‐boost with a y‐boost does not preserve any spatial coordinates. Hence, the composition of an x‐boost with a y‐boost cannot be represented as a single boost. In (2 + 1) space, a corrective spatial rotation renders the double boost into a single‐boost form. This rotation can be expressed in terms of the total relative velocity between initial and final reference frames. However, the new formula still does not restore the x‐axis to the correct direction, and also does not admit an inverse transformation in the same set. These problems urgently call for a rethinking of the Lorentz transformations in more than one spatial dimension.
Keywords: special relativity, Lorentz transformation
Received: May 19, 1999; Published online: December 15, 2008