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Web-Based Special RelativityWhile Einstein's theory of Special Relativity does explain the null results of the Michelson-Morley experiment, implications like length contraction and time dilation seem to make the theory ripe for rejection by people raised in a classical Galliean world. However, experiments such as muon decay provide evidence that supports Einstein over Galileo and Newton. Muons are unstable sub-atomic particles, and in simplest terms can be thought as being identical to electrons except that they have 206.7 times as much mass. They have a half-life of 1.56 μs (not to be confused with their mean lifetime of 2.2 μs). The fact that they decay in such a predictable manner makes them a prime instrument for distinguishing between Einstein and Galileo. Muons are indirectly created by cosmic rays high in the Earth's atmosphere. Their velocity is pointed towards the ground, but even with very high velocities their short lifetime predicts that almost none survive to be detected at sea level. However, many muons do make it to sea level, and in fact very sensitive physics experiments often need to be carried out deep underground to account for this effect. How can the muons reach the ground? Time dilation! While their half-life might only be 1.56 μs in their own frame, that time is measured to be longer by observers on the Earth (moving clocks run slowly).
A muon telescope compares the number of muons detected at one height to the number detected at a lower height. While someday we might build a muon telescope at Foothill, for now we don't have the facilities for a true muon experiment. In any case, muon telescope experiments usually don't finish in three hours. What we will do this week is a web-based lab. We've written an applet that simulates relativistic muon decay. In the applet we assume that we have two balloons, each carrying a muon detector. The top detector does not move, it is anchored 1000m above the surface of the Earth. You can adjust the altitude of the lower detector. You are also allowed to choose the speed of the muons. The final user-adjustable parameter is how long in time to measure. Since the program introduces a random signal into the data, the longer you collect the data the smaller the uncertainty. The applet is at the bottom of this screen. Click here for student art illustrating the experimental setup. Using Excel or some other program, you should plot the ratio of muons found in detector 2 to the muons observed by detector 1 as a function of altitude. Do this for different velocities, finding a half-life for each. Then plot these half-lives as a function of velocity. Verify that Einstein's ideas are correct rather than Galileo's. Make sure you discuss measurement error. Be sure to review the formal lab report rubrics on the 4D lab pages when you write your report. Simulated Muon Experiment 2The altitude of the first detector is fixed at 1km.Choose the altitude of the 2nd detector, the duration of data collection, and the speed of the muons. Be sure to hit the RESET button in between each run to clear all of the output fields! |
