Geometrical Interpretation of Space Contraction in Two-dimensional Lorentz Transformation

Abstract

This paper points out that the transformation equations for the spatial and temporal coordinates between two frames of reference in the existing generally accepted version of the Lorentz transformation are deficient, since transformation equations are based on one dimensional motion between inertial frames. Therefore, all possible space-time coordinate transformation equations between moving and stationary frames by prolonging Lorentz transformation in a two-dimensional plane are thoroughly proposed in this article. If denotes the relative velocity between stationary frame (x, y) and moving frame (x', y'), then the transformation equations along X and Y-axis under two-dimensional Lorentz are given, respectively, by the formulas (see full text) . In this work we conclude that length and breadth of a rectangle appears to be shortened to the observer when there is the relative velocity between the rectangle and observer along both X and Y-axis. In particular, we present a concise and carefully reasoned account of a new aspect of Lorentz transformation which decently allows for the determination of space-time coordinates transformation equations in two dimensions of space.

Keywords

• Frame of reference
• Lorentz transformation
• Space contraction,
• Special relativity