Blog of Veikko M.O.T. Nyfors, Hybrid Quantum ICT consultant

Quantum Mechanics demystified, a try

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Time Dilation with \(\mu\)-mesons

In 1962 Frisch & Smith performed an experiment to demonstrate time dilation with muons (mu-mesons). Video is available in YouTube.

In order to better understand what was going on, I summarize experiment with layman’s understanding.

In short they measure number of muons decaying on top of a mountain at 2000m followed by the same measurement at sea level.
Number of decaying muons at sea level should decrease in relation to muon’s decay time, speed of muons and the distance traveled.

Half-life on \(\mu\)-mesons is 2.2*10^-6 s, which has been measured with laboratory experiments, e.g. with LHC. This is in muons own frame of reference.

Speed of muons analyzed is narrowed down to be 0.995c to 0.9954c by:

The compound in scintillator also reacts to muon decays by generating a pulse of light (photon) which can the be detected.

On top of the mountain they counted 568 decays in one hour.
147 of those were ones, that took more than 6 microseconds to decay in scintillator. In 6 microseconds our muons would had traveled the 2000 meters from top of the mountain to sea-level in the air. Expectation is, that when they repeat experiment at sea level, they should count about 147 decays there.

At sea level, they reduced the pile of iron a bit to compensate for the 2000m of air.

When they counted decays in one hour at sea level, they ended up at 412. Quite a bit more.

If we calculate how much time it would take muons, with 2.2*10^-6s half time, to drop down from 568 to 412, it would take 0.7 microseconds. Indicating that 0.7 microseconds had passed in the muon’s frame of reference.

This matches perfectly with Lorenz factor.