Question

An elementary particle called a pion-zero decays into two identical particles called photons. Such a pion sits in the exact center of a train car traveling to the right relative to those of us in the laboratory frame. If the energies of each pion are identical, and if they both head in opposite directions - one to the front of the car and the other to the back, relative to the physicist on the train with the original pion:From the perspective of the person on the train: A: The one headed to the front arrives firstB: The one headed to the back arrives firstC: They both arrive at the same timeFrom the perspective of the lab Will we see the photons hit at the same time? A: yes B: no

Answer 1

(a)

As the decay of pion into two photons takes place in the train. The two photons have equal (same magnitude) and opposite (direction) momentum in the train.

As one is heading to the front while the other is heading back; according to the person in the train, the events seems normal (inertial frame).

Thus, both photons are traveling at the same speed and reach at the same time.

Therefore, option (C); they both arrive at the same time is the correct choice.

(b)

According to the person on the Lab frame (rest), the velocity (relative velocity) of the photons changes.

Thus, the time taken by the photons to reach is different.

As the photon traveling towards the right (front of the car) seems to travel faster than the photon which is moving towards the back of the car.

Therefore, option (B); no, is the correct choice.