Savchenko Problem 1.1.4
Physics · mechanics · electromagnetism
Problem
Counters A and B, which register the moment of the arrival of a -quantum, are located at a distance of 2 m from each other. At a point between them a meson decayed into two -quanta. Find the position of this point if counter 0 A detected the -quantum 10−9 s later than counter B. The speed of light is 3108 m/s.Intuitive explanation
The key is recognizing that light travels at a finite speed, so the time difference between detections reveals which counter is closer to the decay point. Since counter A detected its photon later, it must be farther away—the photon had to travel a greater distance. Use the time delay and the speed of light to set up equations for the distances from each counter to the decay point, then solve for the position along the line between them.
Intuitive explanation
The key is recognizing that light travels at a finite speed, so the time difference between detections reveals which counter is closer to the decay point. Since counter A detected its photon later, it must be farther away—the photon had to travel a greater distance. Use the time delay and the speed of light to set up equations for the distances from each counter to the decay point, then solve for the position along the line between them.