If a muon is moving at 90.0 % of the speed of light, how does its measured lifetime compare to i

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If a muon is moving at 90.0 % of the speed of light, how...

Key Concepts

Special Relativity

Special relativity is a fundamental theory in physics introduced by Einstein that describes the behavior of objects moving at constant speeds near the speed of light. It alters the classical ideas of space and time by introducing effects such as time dilation and length contraction, which become significant when objects move at relativistic speeds.

Time Dilation

Time dilation is a relativistic phenomenon in which the elapsed time between two events is longer for an observer in relative motion compared to an observer at rest with respect to the events. This effect means that a moving clock – such as a particle's lifetime in motion – appears to run slower when observed from a different inertial frame, explaining why moving muons have a longer measured lifetime in the laboratory frame.

Lorentz Factor

The Lorentz factor, denoted by gamma (?), quantifies the amount of time dilation (and length contraction) experienced by an object in relative motion. It is defined as ? = 1 / ?(1 - v²/c²), where v is the object's velocity and c is the speed of light. For an object moving at 90% of the speed of light, the Lorentz factor determines how much longer the observed lifetime is compared to the proper lifetime.

Proper Time

Proper time is the time interval measured in the rest frame of an object, meaning it is the time experienced by the object itself. In the context of the muon, the proper lifetime is the period measured when the muon is at rest, and it serves as the baseline to calculate the dilated lifetime observed in another inertial frame using the Lorentz factor.

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