Lorentz Transformation Latex
Tags: #physics #relativity #lorentz #transformationEquation
$$(\vec{x}^{'}, t^{'}) = (\vec{x}^{'}(\vec{x},t), t^{'}(\vec{x},t)) \\ \vec{x}^{'} = \vec{x} +\frac{(\gamma-1)(\vec{x}\vec{v}) \vec{v}}{|v|^{2}} - \gamma \vec{v}t \\ t^{'} = \frac{\gamma(t-\vec{x}\vec{v})}{c^{2}} \\ \gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}} \\ \frac{\partial^{2}}{\partial{x^{2}}} + \frac{\partial^{2}}{\partial{y^{2}}} + \frac{\partial^{2}}{\partial{z^{2}}} - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial{t^{2}}} = \frac{\partial^{2}}{\partial{{x^{'}}^{2}}} + \frac{\partial^{2}}{\partial{{y^{'}}^{2}}} + \frac{\partial^{2}}{\partial{{z^{'}}^{2}}} - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial{{t^{'}}^{2}}}$$Latex Code
(\vec{x}^{'}, t^{'}) = (\vec{x}^{'}(\vec{x},t), t^{'}(\vec{x},t)) \\
\vec{x}^{'} = \vec{x} +\frac{(\gamma-1)(\vec{x}\vec{v}) \vec{v}}{|v|^{2}} - \gamma \vec{v}t \\
t^{'} = \frac{\gamma(t-\vec{x}\vec{v})}{c^{2}} \\
\gamma = \frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}} \\
\frac{\partial^{2}}{\partial{x^{2}}} + \frac{\partial^{2}}{\partial{y^{2}}} + \frac{\partial^{2}}{\partial{z^{2}}} - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial{t^{2}}} = \frac{\partial^{2}}{\partial{{x^{'}}^{2}}} + \frac{\partial^{2}}{\partial{{y^{'}}^{2}}} + \frac{\partial^{2}}{\partial{{z^{'}}^{2}}} - \frac{1}{c^{2}} \frac{\partial^{2}}{\partial{{t^{'}}^{2}}}
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Introduction
Explanation
Latex code for the lorentz transformation Equations. I will briefly introduce the notations in this formulation.
The Lorentz transformation leaves the wave equation invariant if c is invariant.
The general form of the Lorentz transformation is given by
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