This might be the easiest "particle physics without a particle accelerator" experiments you can do. This is your accelerator:<p><a href="https://en.wikipedia.org/wiki/Air_shower_(physics)" rel="nofollow">https://en.wikipedia.org/wiki/Air_shower_(physics)</a><p>And the muons produce two pulses in your detector, one when they are scattered to a stop and another when they decay. By measuring the time between the pulses you can fit the probability distribution and determine the half life of the mupn which is about 2.2 microseconds [1] And of course you can take measurements over time, at different altitudes and in different positions. If it wasn't for relativistic time dilation, muons would mostly decay high up in the atmosphere and not reach the ground.<p>This was one of the most popular experiments in the Physics 510 lab, which was the only class you had to take to get a Physics PhD at Cornell because it was so easy. It's also popular for high school physics for the same reason.<p>[1] <a href="https://en.wikipedia.org/wiki/Muon" rel="nofollow">https://en.wikipedia.org/wiki/Muon</a>