Muon Experiment

The measurement of the flux of muons at the Earth's surface produced an early dilemma because many more are detected than would be expected, based on their short half-life of 1.56 microseconds. This is a good example of the application of relativistic time dilation to explain the increased particle range for high-speed particles.

Non-Relativistic

Non-relativisticRelativistic, Earth observerRelativistic, muon observer
ComparisonComments on comparisonVary parameters

Numerical example from laboratory setting
What is a muon?
Some history
A brief overview of time.
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Muon Experiment

Relativistic, Earth-Frame Observer

Non-relativisticRelativistic, Earth observerRelativistic, muon observer
ComparisonComments on comparisonVary parameters
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Muon Experiment

Relativistic, Muon-Frame Observer

Non-relativisticRelativistic, Earth observerRelativistic, muon observer

ComparisonComments on comparisonVary parameters
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Muon Experiment

Comparison of
Non-relativisticRelativistic, Earth observerRelativistic, muon observer

ComparisonComments on comparisonVary parameters

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Muon Experiment

Comparison of

In the muon experiment, the relativistic approach yields agreement with experiment and is greatly different from the non-relativistic result. Note that the muon and ground frames do not agree on the distance and time, but they agree on the final result. One observer sees time dilation, the other sees length contraction, but neither sees both.

These calculated results are consistent with historical experiments.

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ComparisonComments on comparisonVary parameters

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Muon Experiment

Vary Parameters

The calculation will be considered from the Earth frame of

Length L0 = x 10^ meters.

If the muon speed is v = c

then the relativity factor is γ =

The time-dilated halflife is x 10^ seconds.

The time to reach the Earth is t = L0/v = x 10^ seconds.

This is halflives,

leaving a population of out of a million.

Non-relativisticRelativistic, Earth observerRelativistic, muon observer

ComparisonComments on comparisonVary parameters
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