RELATIVISTIC TIME DILATION

INTRODUCTION: This week we will study a famous experiment which conclusively disproves the classical theory of relativity by showing that moving muons -- subatomic particles with a mean lifetime of 2.2 microseconds -- have significantly longer lifetimes when they move at speeds close to the speed of light. We will watch a film demonstrating the experiment, and then we will measure the lifetime of these particles. BEFORE LAB: Skim David Frisch and James Smith, Am. J. Phys., 31, pp. 342-355 (1963).

THE MOVIE: This week you will be watching a film of the experiment (Frisch and Smith, above) designed to measure time dilation using muon decay. After the film, please answer questions 1-4 below in your lab notebooks, which you should turn in at the end of lab. After these preliminaries, we will start our experiment, which is described below.

PRELIMINARY QUESTIONS:
1. DESCRIBE THE EXPERIMENT: Briefly describe the procedure used in the experiment. Your description should answer all of the following:
• What do the two counts (blips) recorded on the oscilloscope represent?
• How do the researchers know that they are only counting muons?
• What is the purpose of the iron, and why is less used at sea level?
2. TIME DILATION FACTOR: The article mentioned above states (p. 351) that the muons measured in their experiment had velocities of v =0.9950c to 0.9954c for the measurements on top of Mt. Washington (6300ft), but 0.9881c to 0.9897c in Cambridge, MA. So, overall, we can say that v = 0.992c ± 0.003c.
• Calculate the time-dilation factor, γ (gamma), including uncertainty, for v = 0.992c ± 0.003c. (Make use of your lab text --- D. C. Baird's Experimentation --- if you don't already know how to calculate uncertainty.)
3. LAB FRAME: (Answer the following for an observer on the ground.)
• Convert Mt. Washington's height to meters (1m = 3.28 ft)
• How long does it take the muons to travel this distance?
• If the muons' mean lifetime is 2.20 μs in their own frame, what is it in the lab frame? (Include uncertainty.)
• How many lifetimes does it take the muons to reach sea level? (Include uncertainty)
4. MUONS' FRAME: (Answer the following from the muons' perspective.)
• To the muons, how high is Mt. Washington? (Include uncertainty.) How long does it take to travel this distance?
• What is the muons' mean lifetime in their own frame?
• How many lifetimes does it take the muons to reach sea level? (Include uncertainty)
THE EXPERIMENT:
• Turn on the computer first. Do not touch any of the electronics until after you have turned on the computer and logged in.
• Make sure that all dials on the muon experiment control box and on top of the detector are turned to zero. Then turn on the power to the control box (rear panel).
• Run "muon" application from the lab computer desktop. Click the configuration button. Choose:
• Select Port: COM04
• Decay time histogram scale: 6 microseconds
• Select bin number: 20 bins
• Now it is time to set up the experiment. The photomultiplier tube [PMT] requires about 900-1000V to amplify the signal that occurs when it detects a flash of light inside the scintillator. Connect a voltmeter to the "High Voltage monitor 1/100" on the top of the detector unit (It shows this voltage divided by 100.) and dial the "High Voltage Adjust" knob to around 8, or about -1000V. Record all these values (knobs and measured voltages) in your lab notebook. Make sure that the pulser is turned off.
• Connect the oscilloscope [GDS-820C Digital Storage Scope] to the output of the box. Your instructor will set it up so that When the high voltage is applied, you should see actual spikes like those in the film. Adjust the "[Threshold] Control" knob of the control unit until it also registers these spikes. Monitor this value ("[Threshold] Monitor") and record it in your notes (both the knob value and the monitored value). Sketch a typical spike, with its height and duration, in your notes. How does the width of this spike compare to the accepted mean lifetime of the muon? Why is this important?
• There are two types of events that will be registered by the computer. One is the number of spikes that exceed the threshold. This is the quantity in the "Monitor", "Rate Meter", and "Muons through detector" graphs on the screen. But not all such events are necessarily muon events. There is a specific "signature" to muon events, and these events are recorded in the "Muon Decay Time Histogram" graph on the top righthand side of the screen (and the "Total Events" inset to that graph), from which you will measure the mean lifetime of these particles.

DATA COLLECTION:
• Sign up in lab for a 20-hour time slot for collecting data. You will need to set your experiment up for collecting data, check that the software is collecting data, and "harvest" your data at the end of the run. If you have problems setting up the computer to take data, it is imperative that you contact the instructor for help right away. (Home phone number is in the "Larry" if you've got one of the weekend shifts.)
• At the end of your 20-hour shift, you need to do all the following:
• Make sure that the y-axis of the screen graph is logarithmic. Click the "Change Y Scale: Linear/Log" button. (What should the graph look like with this axis choice?) Grab a screen shot of your data. Move your cursor out of the way and press the "Print Screen" button. Open your favorite geraphics program (or even "Word", if you must) and "Paste" the screen into the document. Save this as a graphics file (*.gif or *.jpg, preferably) on this lab's T: drive account, with your name in its title. I will use these next week.
• Press the "View raw data" button and enter a large enough number under "Number of raw data records" to include all your data. Cut and paste these data into an Excel spreadsheet and store it on this lab's T: drive account (with your name in the title), where you can access it easily next week. Notice, not all these data are useful. The majority of them record a time of 40000 microseconds, which is bogus. We'll delete those points when we analyze the data.
Press the "Quit" button in the muon program. This will close down the program and provide a clear signal to the person following you that you have finished your shift and that they can start.
ANALYSIS:
We'll do this in class during week two of this lab. FYI: The mean lifetime, <τ>, and the 'half-life' , τ1/2, represent two different ways of quantifying the statistics of the range of lifetimes that a radioactive particle like a muon exhibits. They are related by τ1/2 = 0.693 <τ>. Calculate the halflife of the muon from the accepted mean lifetime. Verify from your graph that the count rate decreases by a factor of two after one halflife, by four after two halflifes, etc.