The Cosmic Ray Observatory Paradox · AI Generator #GEN-7EAB6B62
Physics
Problem
A high-energy cosmic ray muon is detected by two identical particle detectors placed along its flight path. The muon travels at v=0.98c relative to Earth. Detector A is positioned at the top of a mountain, and Detector B is positioned L=6.0km directly below at sea level. The muon passes through both detectors.
In the Earth's reference frame, the muon is created at an altitude of 12.0km and travels downward. However, due to the high speed involved, relativistic effects become important for analyzing the detection events.
(a) What is the proper distance between the two detectors as measured in the muon's rest frame?
(b) If Detector A records the muon passage at time tA=0 in Earth's frame, at what time tB does Detector B record the passage?
(c) In the muon's rest frame, what is the time interval between the two detection events?