A charged pion is created at the origin of a laboratory and decays further along the axis

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Special relativity: spacetime and kinematics

Particle Physics, Ch Scales, units and the four-momentum

Problem

A charged pion is created at the origin of a laboratory and decays further along the

x

axis. Measured with clocks and rulers at rest in the laboratory, the decay happens at

x = 10.0\,\mathrm{m}

and

ct = 10.5\,\mathrm{m}

after the creation. ((a)) Compute

c^2t^2 - x^2

for the two events in the laboratory frame. ((b)) In the pion's own frame both events happen at the same place,

x' = 0

. Find

ct'

there, and the time

t'

the pion's own clock records between creation and decay. ((c)) Find the pion's

\beta

from

x = \beta ct

and its

\gamma

from

t = \gamma t'

, and check that the two satisfy

\gamma = (1-\beta^2)^{-1/2}

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