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Bienvenue au Geneve



Welcome to Geneva and to CERN, the European Laboratory for Nuclear Research. Pause, if you have time, to look around CERN.

Dr. Cosimo Curre will see you now...


"Welcome, welcome! Please sit down!"

"Right to business! As you know, some quantities increase arithmetically: you add one thing, then the next, and so on, like the score in a football game. Others increase geometically, due to repeated multiplication. Our understanding is that the cosmic ray muon count should increase exponentially as one goes higher in the atmosphere. Specifically, it should follow the formula

Count at Altitude H = (Count at Sea Level) x [eH/vT]

where H is altitude in kilometers, v is the speed of the muon in km/microsec, and T the muon lifetime in microseconds. The quantity e is the base of natural logarithms and is equal to about 2.718 .

I know, I know, we physicists talk too much in mathematics. Let me break it down for you.

First, what number did you obtain from your tests for the Muon Count at sea level? Good! Fill that in here:

Count at Altitude H = _______ x [eH/vT]

Now, our claculations here at CERN show that vT = 0.6 km. So,

Count at Altitude H = _______ x [eH/0.6]

Soon you will take your measurement equipment and your rented Opel Astra and drive to Chamonix, France. It is about a 2 hour drive. Chamonix is in the French Alps at a nice altitude of about 1 km above sea level. There you will measure the cosmic ray muon count. When you fill that in, you get

[________ at alt] = [_______ at sea level] x [eH/0.6]

With a bit of algebra, we can transform an exponential into a natural logarithm:

H = 0.6 x LN [ (_____ at alt) / (_____ at sea level) ]

So this is what you actually do:

  1. divide muon count at altitude by muon count at sea level: you get a number
  2. take the natural log of this number; you can use the table on the next web page to help you
  3. multiply that natural log by 0.6 and
  4. viola, you've calculated the altitude!

I know, you are saying, 'But we already know the altitude of Chamonix...it is 1 km.'

That is where our hypothesis comes in! The altitude of Chamonix is 1 km in our fixed frame of reference. According to Einstein's Special Theory of Relativity, however, because the muon is travelling very fast (close to the speed of light), space and time behave differently for it. It will 'see' the altitude of Chamonix as very much shorter. The faster the muon, the shorter it will see the distance to be.

So?

So, if you calculate H (the altitude) that the muon sees and compare it to H that we see, you can find out how fast the muon is going. If you get an answer between 0.28 and 0.30 km/microsec, you will get a speed that we expect the muon is moving at...and confirm that relativity is the reason for the strange readings we get!

Now off you go! Good luck!"


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