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\section*{Relativity!}
For years now, students have been clamoring for relativity to be included in the lab exercises. This has proven difficult; as much as we would like to blame our mass increase on relativistic effects, it is probably more likely due to more mundane causes. Now, though, we have a group of students who are sophisticated users of computers, indeed, many are rather adept programmers. This allows us to include simulations of relativistic effects in the lab course. Now, as a student, you need to be aware that these are not 'proofs' that special relativity is a reasonable description of nature; on the contrary, these demonstrations include (correctly) the predictions of special relativity and allow us to visualize them. I think that this is generally true of simulations. They allow us to 'see' how a system behaves under a given set of rules, and we can compare this behaviour with our observations of the world and make a judgement about whether or not the simulation is reasonable. This is probably enough philosophy, but it is important to understand that what we are doing isn't an experiment that can confirm or refute a theory, it is a calculation based on the theory.

We will start today with a VPython program and a physlet demonstrating the synchronization of clocks. (Note, a physlet is a physics applet, a java application used to illustrate a physics concept:)
\begin{equation*}
 \text{\texttt{\small{http://webphysics.davidson.edu/Applets/Applets.html}}}
\end{equation*}
The VPython simulation can be run in the usual way:
\begin{equation*}
 \text{\texttt{\scriptsize{http://www.nbi.dk/$\sim$bearden/BeardWeb/Teaching/Fys1L2007/Uge40/SynchronizeClocks.py}}}
\end{equation*}
Note that by clicking in the animation window, you can make the simulation stop and start. First, try method 1. Is this a correct way to synchronize clocks? How does this compare to the way we do things in 'everyday' life? Now try method 2 and answer the same questions. For each method, what would an observer at the origin (the place from which the synchronization signal is sent) see as the time at the other clocks? Next, try this physlet:
\begin{equation*}
 \text{\texttt{\scriptsize{http://webphysics.davidson.edu/physlet$\_$resources/special$\_$relativity/illustration1.html}}}
\end{equation*}
Answer the questions above for procedures A and B, and think about where you must be located relative to the clocks shown to see what you see. To help you find out, investigate how observers at different locations would view these clocks:
\begin{equation*}
 \text{\texttt{\scriptsize{http://webphysics.davidson.edu/physlet$\_$resources/special$\_$relativity/illustration2.html}}}
\end{equation*}
Now that we see how clocks in a given reference frame can be synchronized, let us investigate how things appear from different reference frames, that is, we will try to understand what is meant by simultaneity (samtidighed, section 2.2.1 in your text). We start with an illustrative example that is similar to that illustrated in Figur 2.1 (page 19) of the text.
\begin{equation*}
 \text{\texttt{\scriptsize{http://webphysics.davidson.edu/physlet$\_$resources/special$\_$relativity/illustration3.html}}}
\end{equation*}
This same concept is illustrated, though in a different and more user-controlable way, in this VPython program:
\begin{equation*}
 \text{\texttt{\scriptsize{http://www.nbi.dk/$\sim$bearden/BeardWeb/Teaching/Fys1L2007/Uge40/RelativisticRockets.py}}}
\end{equation*}
Finally, we look a little into spacetime diagrams (sektion 2.9 i bogen):
\begin{equation*}
 \text{\texttt{\scriptsize{http://webphysics.davidson.edu/physlet$\_$resources/special$\_$relativity/illustration5.html}}}
\end{equation*}
Note that the physlets we've played with today, as well as some others, can be found here:
\begin{equation*}
 \text{\texttt{\scriptsize{http://webphysics.davidson.edu/physlet$\_$resources/special$\_$relativity/default.html}}}
\end{equation*}
\\
Ian Bearden 


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