Lorentz Transformations

The Lorentz Transformation is a transformation that allows one to shift between different coordinate systems. Namely, it allows one to transform the cartesian coordinate system of a stationary reference frame to another cartesian coordinate system of a reference frame that is moving with constant velocity [math]\displaystyle{ v }[/math] with respect to the stationary reference frame. The Lorentz Transformation was first derived not by Lorentz, but rather by Woldemar Voigt in a paper he published in 1897 (insert link). In this paper, Voigt took an alternative approach to the already derived Doppler Effect in which he postulated that the wave equation should take on the same form in both the stationary and moving reference frames (a postulate for which he gave no reason). This postulate is equivalent to stating that the propagation velocity of the wave must be invariant under transformations between reference frames that are moving with constant velocity relative to one another.

For reasons not known, Hendrik Antoon Lorentz appeared to be inspired by this transformation. He rederived it in his 1904 paper (insert link) in which he investigated the electrodynamics of moving bodies. The transformation was eventually named after Lorentz in 1906 by Jules Henri Poincaré.

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