Time Dilation - An Experiment With Mu-Mesons


A classic experiment on the time dilation phenomenon was performed by
B.Rossi and D. Hall in 1941 .

Student Solutions To These Sums
Here, cosmic rays entering the earth's atmosphere from space were monitored - in particular
the production of particles termed ' Mu - Mesons '. The essential details of this experiment are given below:

1) A m meson is a charged particle that decays into an electron or positron , a neutrino and an antineutrino.

m+ ---> e+ + n1 + n2
m- ---> e- + n1+ n2

2) As produced by cosmic rays the mesons travel through the atmosphere at speeds very close to that of light.

3) With the help of a scintillation counter, the arrival of the mesons may be detected and at a measured time later, their decay into an energetic electron.

Observation of the second stage means that the meson has stopped in the detector so the decay of mesons AT REST is being recorded. Here is a schematic chart to show 568 counts that were obtained in one hour at the top of Mt Washington (6300ft above sea level.)

4) Since the mesons travel at nearly the speed of light, the time axis can be relabelled in thousands of feet and then we can see how many mesons should reach sea level if they decay in the same way in flight as they do at rest:

On this basis if the detecting equipment is taken to sea level, 27 counts should be recorded in one hour, as this diagram  shows.

This diagram indicates the number of mesons passing the 3600ft datum if they decayed in flight as they do at rest. Accepting the result of this stage means we can go on to predict what fraction of a group of mesons should be lost through decay in a trip of a given distance (d) and duration ~ (d /c) .

5) The scintillation counter is now taken down the mountain to sea level. At sea level a full hour's count is taken : Instead of 27 we have 412 mesons left at sea level. 412 counts corresponds to about 0.7msec on the decay clock. 0.7 divided by 6.3 equals 1/9. These mesons moving at near light speed keep time at 1/9 the rate they do when they are at rest with respect to us. To the observer on the ground, the mesons survive the journey in far greater numbers than one would predict from studying their decay at rest. The time-dilation factor of 9 corresponds obviously to a particular value of meson velocity v. (See problems.) In fact mesons from cosmic rays have a wide range of energies, so we need to examine the detection process in more detail.

Every time a mu meson passes through the plastic scintillator, a flash of light is emitted. These are detected by the photomultiplier which turns the flashes into electrical signals.

If a meson stops and decays in the scintillator a second flash occurs.The oscilloscope is arranged to show only these decay pulses as an energetic electron is produced. The selection of a particular value of v/c is achieved by making observations only on those mesons that stop within a relatively thin layer of material (the plastic scintillator) after having traversed a specified large thickness of matter (iron + atmosphere). Muons of less than the chosen speed get stopped before they reach the plastic; higher speed mesons pass right through and in both cases go unrecorded. To be accepted a muon must come to rest in the plastic scintillator and decay there.

The register counts the mu mesons that have entered the scintillator and decayed there. Where the decay pulses occur on the time scale is recorded by polaroid camera.

This experiment clearly shows that time dilation can be a
very significant effect
for clocks that are in high speed relative motion.