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:A) The one photon headed to the front arrives first according to the person on train.B) the one photon headed to the back arrives first according to the person on train.C) they both arrive at the same time according to the person on train.And on the ground do we see the photons hit at the same time? A) yes B) no

Answer 1

(a). As the decay of pion into two phtotons takes place in the train.

The two photons are having equal and opposite momentum in the train.

As one is heading to the front of train and other is heading back.

According to the person on the train, the events seems normal.

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

Hence, third option (they both arrives at the same time) is the correct answer.

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

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

As the photon traveling towards the right (front of car) is seems to be traveling faster and the photon which is moving towards the back of the car is seems to be traveling slower.

Hence, no is the correct answer.