Muon Speed

Purpose

In this experiment we'll measure the speed of the cosmic ray muons. The muons have a range of speeds but you'll find that the average speed is close to the speed of light ( 3.0 * 109 meters per second). Even the lowest energy cosmic ray muons have speeds that are within a few percent of the speed of light.

Here is a paradox. We know that the muons originate from interactions of primary cosmic rays with the atmosphere about 10 km up. If they are traveling at the speed of light, how long does it take for them to reach the ground? You'll find that this time is much longer than the muon lifetime (a value that you can measure in another experiment). So then, the question is how can the muons live long enough to reach the ground. Once you've figured this out, you will have discovered one of the basic results of Einstein's theory of relativity.

Procedure

In this experiment we will measure the time that it takes cosmic ray muons to travel between two of the detector paddles. In order to have a large enough time difference for a precise measurement, the distance between the paddles should be large, ideally 3 meters or more. When you take the data you will make a log file that will contain part of the raw data stream. An example of this data stream is show below.


A value in Column 3 greater than 128, signals a new event. In this data row, the value of Column 3 minus 128 is the relative time, T1, of the hit in detector 1 in units of 1.25 ns. The value in Column 4 is the relative time, T2, of the hit in detector 2 in units of 1.25 ns. Taking the difference of the two, T1-T2, gives the time difference between the two paddles. Ignore data rows for whcih Column 3 is less than 128 or for which Column 4 is zero.

You can do this experiment by separating the detector paddles either vertically or horizontally. Separating the detectors vertically has the advantage of giving a much higher rate of incident muons but has the disadvantage of being more difficult to arrange mechanically.

Vertical arrangement

  1. First we need to measure the intrinsic time offset between the two detectors. To do this, stack the two detectors vertically directly on top of each other. Then the actual time difference of a cosmic ray muon traversing the two detectors is less than 1 ns.
  2. Run the "2fold" experiment.
  3. Set the following configuration.
    4. Delay Time: 0.1 μs
    Gate Width: 0.2 μs
    Channel Enable: 1, 2,
    Coincidence Level: 2
  4. In the RUCosmic window click on "File" and then on "Log". This will write the raw data as a log file as described above.
  5. Start counting and run for about 5 minutes.
  6. Analyze the log data file as described above to determine the intrinsic time difference between the two detectors
  7. Now separate the two detectors vertically by 3 meters or more. One way to do this is to place one detector on the bottom shelf of a tall bookcase and the other detector on the top of the bookcase.
  8. Measure the distance between the two detectors.
  9. Start counting and run for about 5 minutes or more.
  10. Analyze the log data file as described above to determine the time difference between the two detectors.
  11. Subtract the intrinsic time difference of the two detectors that you determined in step 3 above.
  12. Divide the distance between the two detectors by the time you measured in the step above. This gives the speed of the muon.

Horizontal arrangement

  1. Position the two detectors horizontally separated by 3 meters or more. The detectors should be oriented perpendicular to the horizontal.
  2. Run the "2fold" experiment.
  3. Set the following configuration.
    4. Delay Time: 0.1 μs
    Gate Width: 0.2 μs
    Channel Enable: 1, 2,
    Coincidence Level: 2
  4. In the RUCosmic window click on "File" and then on "Log". This will write the raw data as a log file as described above.
  5. Start counting and run for 12 to 24 hours.
  6. Analyze the log data file as described above to determine the time difference between the two detectors.
  7. The time differences should cluster around two values, one for which the muon passes through detector 1 first and then detector 2 and another where the muon passes through detector 2 first and then detector 1.
  8. Take the difference of these two values and divide by 2. This is the time it takes the muon to move from detector 1 to detector 2.
  9. Divide the distance between the two detectors by the time you measured in the step above. This gives the speed of the muon.

Note that with this arrangement we didn't have to first determine the intrinsic time difference of the two detectors. That subtracts out when we take the difference in step 8 above.

Questions

This page is maintained by Prof. Steve Schnetzer.