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%           SWIM 2023
%           July 11-12-13, 2023
%           Angers, FRANCE
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\newtheorem{prop}{Proposition}

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\newcommand\authors{Author One$^{1}$, Author Two $^{1}$ and Author Three$^{2}$}

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\newcommand\papertitle{Relativity}

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{\small
$^{1}$ Leibniz University Hannover, Institute of Geodesy\\
Schneiderberg~50, 30167 Hannover, Germany\\
\texttt{\{schoen,lohmann\}@ife.uni-hannover.de}\\
$^{2}$ Carl von Ossietzky Universität Oldenburg, Distributed Control in Interconnected Systems\\
26111 Oldenburg, Germany \\
\texttt{andreas.rauh@uol.de}
}

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% KEYWORDS - required
{\noindent\bf Keywords:} Science, Knowledge, Relativity

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\subsection*{Introduction}
In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

\subsection*{Basic properties}
Einstein discerned two fundamental propositions:  the constancy of the speed of light and the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system.

\begin{prop}
If a system of coordinates $\mathcal{K}$ is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates $\mathcal{K}'$ moving in uniform translation relatively to $\mathcal{K}$.
\end{prop}

Henri Poincaré provided the mathematical framework for relativity theory by proving that Lorentz transformations are a subset of his Poincaré group of symmetry transformations.

\subsection*{Main results}
Two events happening in two different locations that occur simultaneously in the reference frame of one inertial observer, may occur non-simultaneously in the reference frame of another inertial observer (lack of absolute simultaneity).

From the first equation of the Lorentz transformation in terms of coordinate differences

\begin{equation*}
\Delta t^* = \gamma \left(\Delta t - \frac{v\Delta x}{c^{2}} \right)
\end{equation*}

It is clear that two events that are simultaneous in frame $S$ (satisfying $\Delta t = 0$), are not necessarily simultaneous in another inertial frame $S^*$ (satisfying $\Delta t^* = 0$). 
% Only if these events are additionally co-local in frame $S$ (satisfying $\Delta x = 0$), will they be simultaneous in another frame $S′$.

\subsubsection*{Acknowledgement}
Thanks the National Institute of Relativity.


% REFERENCES
\subsection*{References}
\begin{description}

% Book
\item[{[1]}] {\sc D. Kleppner and D. Kolenkow},
		{\it An Introduction to Mechanics},
		Cambridge University Press, United Kingdom, 2010.

% Paper
\item[{[2]}] {\sc A. Einstein and J. Laub}, 
		On the Fundamental Electromagnetic Equations for Moving Bodies,
        {\it Annalen der Physik}  (ser.~4) 26, 532–540, 1908.
                
\end{description}

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