Ordered addition of two Lorentz boosts through spatial and space-time rotations

Chandru Iyer; G. M. Prabhu

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arXiv · 0704.2023

Ordered addition of two Lorentz boosts through spatial and space-time rotations

Chandru Iyer·G. M. Prabhu

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Abstract

The ordered addition of two Lorentz boosts is normally shown to result in a boost by utilizing concepts from group theory and non-Euclidian geometry. We present a method for achieving this addition by performing a sequence of spatial rotations and uni-dimensional Lorentz transformations. The method is first developed for two-dimensional space and it is then extended to three-dimensional space by utilizing the commutative property of the rotation of the y-z plane and a boost along the x-axis. The method employs only matrix multiplication and certain invariant quantities that are natural consequences of spatial rotations and Lorentz transformations. The combining of two boosts in different directions into a single boost cannot be expected a priori because we show that the converse of this statement is not true. That is, two rotations interspersed with a boost cannot always be reduced to a single rotation preceded and followed by boosts.

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Chandru Iyer, G. M. Prabhu. 2007-05-08. Ordered addition of two Lorentz boosts through spatial and space-time rotations. https://arxiv.org/abs/0704.2023

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