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Investigating Relativistic Lifetimes: Simulated Data |
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This activity is similar to the experiment section of this Website. You can work on this one more immediately and get results. Here we have simulated a range of data for cosmic ray counts taken at varying altitudes. Analysis of cosmic ray counts as a function of altitude should tell you something about how relativity affects muon lifetimes in a fairly rigorous mathematical way.
In this simulated experiment, experimenters climb in an aircraft from sea level to 3000 m. A cosmic ray muon count is taken every 100 m as the altitude h increases. The cosmic ray counts N(h) are based on an index where the count at 9000 m altitude would be 100. In the data table, the first column marked h (in meters) represents altitude and the second column marked N(h) represents the muon count.
To predict the lifetime of the muon from this simulation, it will help to know the mean speed of cosmic ray muons. Go to the Excel spreadsheet muonspeed to do the calculation using data from the SUNY-Albany QuarkNet Center. If the Excel sheet or that data is unavailable, you can use the generally accepted muon speed of 0.998 c.
The simulated experimental data is on the Excel spreadsheet muondata or the html document muonhtml.A quick link for those new to Excel.
Questions to Consider:
- If you graph the data, what will the graph indicate?
- How would you best use the simulated data to do a classical calculation of the muon lifetime?
- If you get a "classical" answer for the muon lifetime, how can you use relativity to adjust it?
- What is the relativistic lifetime of a cosmic ray muon?