Define what is meant by an inertial frame of reference.
An experimental beamline at a particle accelerator is designed to study the decay of unstable J-mesons. Two high-precision particle detectors are positioned along the path of the collimated meson beam at a distance of 288 m288\text{ m}288 m apart, as measured in the laboratory's frame of reference. The mesons travel at a constant speed of 0.96c0.96c0.96c.
Due to the decay of the J-mesons in flight, the beam intensity recorded at the second detector is exactly 25.0%25.0\%25.0% of the intensity recorded at the first detector.
Calculate the half-life of these J-mesons in their own rest frame.
In relativistic physics, distinguishing between proper time and dilated time is crucial. Identify the proper time in the calculation in Part 2, stating its value.
