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‎_my_stuff/papers/bib/physics.bib

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@article{lorentz1904electromagnetic,
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title = {Electromagnetic phenomena in a system moving with any velocity less than that of light},
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author = {Lorentz, Hendrik A.},
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journal = {Proceedings of the Royal Netherlands Academy of Arts and Sciences},
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volume = {6},
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pages = {809--831},
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year = {1904}
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}
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@article{einstein1905,
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author = {Einstein, Albert},
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title = {Zur Elektrodynamik bewegter K{\"o}rper},

‎_my_stuff/papers/physics/special_relativity/special_relativity.aux

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\citation{wikipedia:proper_time}
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\citation{wikipedia:proper_time}
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\citation{einstein1905}
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\citation{lorentz1904electromagnetic}
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‎_my_stuff/papers/physics/special_relativity/special_relativity.bbl

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\newblock Zur elektrodynamik bewegter k{\"o}rper.
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\newblock {\em Annalen der Physik}, 322(10):891--921, 1905.
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\bibitem{lorentz1904electromagnetic}
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Hendrik~A. Lorentz.
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\newblock Electromagnetic phenomena in a system moving with any velocity less
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than that of light.
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\newblock {\em Proceedings of the Royal Netherlands Academy of Arts and
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Sciences}, 6:809--831, 1904.
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\bibitem{physics:spacetime_hughes}
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{Scott Hughes}.
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\newblock {Spacetime: Introduction to Special Relativity}.

‎_my_stuff/papers/physics/special_relativity/special_relativity.blg

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‎_my_stuff/papers/physics/special_relativity/special_relativity.pdf

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‎_my_stuff/papers/physics/special_relativity/special_relativity.synctex.gz

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‎_my_stuff/papers/physics/special_relativity/special_relativity.tex

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the detector) in this case is $c t^{\prime}$ (the hypotenuse of
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the triangle shown in Figure \ref{figure:observer_motion}).
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\bigskip
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\medskip
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\noindent
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In general, the coordinates in the "stationary" frame of
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reference are denoted $(t,x,y,z)$, while the coordinates
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in the "moving" frame of reference are denoted $(t^{\prime},
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x^{\prime},y^{\prime},z^{\prime})$ (of course, stationary
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and moving are relative terms...) \cite{einstein1905}.
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\remark{Note that in general, the coordinates in the "stationary"
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frame of reference (call it $S$) are referred to as $(t,x,y,z)$,
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while the corresponding coordinates in the "moving" frame of
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reference (call it $S^{\prime}$) are denoted $(t^{\prime},x^{\prime},
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y^{\prime},z^{\prime})$. Coordinates in $S^{\prime}$ are related to
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coordinates in $S$ by the Lorentz transformations
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\cite{einstein1905,lorentz1904electromagnetic}.
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\label{remark:frames_of_reference}}
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\bigskip
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\noindent
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The $h$, $x^{\prime}$, $c t^{\prime}$ triangle is abstracted in
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Figure \ref{figure:triangle}.
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To compute $t^{\prime}$, consider the $h$, $x^{\prime}$, $c t^{\prime}$
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triangle shown in Figure \ref{figure:observer_motion}, which is abstracted
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\centering
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So for observer $O$ the passage of time on the moving train slows
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down by a factor of $\gamma = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}$.
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\section{The Lorentz Transformation}
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\label{section:the_lorentz_transformation}
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\section{The Lorentz Transformations}
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\label{section:the_lorentz_transformations}
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%
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\section{The Andromeda Paradox}
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\label{section:the_andromeda_paradox}
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\section{Spacetime Invariance}
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\label{section:spacetime_invariance}
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‎physics/special_relativity.pdf

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