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\section*{Doppler effect and Particle decay}
We start this week by going back to the 'twin paradox' program from week 41, called twins.py:
\begin{equation*}
 \text{\texttt{\scriptsize{http://www.nbi.dk/$\sim$bearden/BeardWeb/Teaching/Fys1L2007/Uge41/twins.py}}}
\end{equation*}
First, when you were asked last time to calculate the energy, some of you did this classically. At what energy (roughly) does the relativistic energy begin to be significantly different from the energy calculated classically? Plot (on paper, or using your favo(u)rite program) the kinetic energy as a function of veloctiy for both the classical and relatvistic formulation of kinetic energy. Does this make aliens visiting trailer parks in Mississippi seem more or less plausible?
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Next, run the simulation and measure the frequency of the signal sent from the moving twin as seen by the SAHT. Do this for the case when the travelling twin is moving away from earth and moving toward earth. Are the frequencies measured what you would expect for a source moving with the velocity of the spaceship? I once saw a license plate (nummerplade) with BLUSHFT on it (nb: this was a state that only required a license plate on the back of the car. If the person who bought this plate was trying to impress people with the speed of their car, did they have a good understanding of relativity?

Next, let us explore particle decay using physlets. Look at the following page:
\begin{equation*}
 \text{\texttt{\scriptsize{http://cwx.prenhall.com/bookbind/pubbooks/walker2/chapter32/custom1/deluxe-content.html}}}
\end{equation*}
Scroll down to section 32-2 Radioactive decay, and run the physlet. In addition to the question asked there, from what reference frame are we viewing the decay? The center of mass frame or the laboratory frame?
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Now, let us look into particledecay:
\begin{align*}
 & \text{\texttt{\scriptsize{http://webphysics.davidson.edu/applets/pqp$\_$preview/contents/}}} \\
 & \qquad \qquad \qquad \qquad \qquad \text{\texttt{\scriptsize{pqp$\_$errata/cd$\_$errata$\_$fixes/section3$\_$4.html}}}
\end{align*}
One of the decay channels of the K meson is into two pions. Using the physlet, look at this decay (assuming the K has a mass of 439Mev/c2, and the pions have a mass of 150 MeV/c2) for several K velocities. From what reference frame are you viewing the decay? How would the decay look if you were in the Kaons reference frame? In the simulation, the two decay products are always emitted parallel to the direction of the mother partcile's motion. Is this realistic? Roughly 2/3 of the time Lambda (a baryon made of uds quarks) decays to a proton and a pion. The lambda mass is 1115.7MeV/c2, and a mean lifetime of 0.26ps. Does the physlet take into account time dialation? (Hint: how would the measured lifetime change with the velocity of the lambda? In which reference frame would this change occur?)
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Ian Bearden 


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