Alyssa is a passenger on a train moving at a constant velocity relative to the g

Question

Alyssa is a passenger on a train moving at a constant velocity relative to the ground. Alyssa synchronizes her watch with the station clock as she passes through the Banning town station, and then she compares her watch with the station clock as she passes through the Centerville town station farther down the line.

a.) Is the time that she measures between the events of passing through these towns a proper time? Is it a coordinate time? Is it the spacetime interval between the events?

b.) If one subtracts the Centerville station clock reading from the Banning station clock reading, what kind of time interval between the events does one obtain? Defend your answers carefully. (Treat the ground as an inertial frame, and assume that the Banning and Centerville clocks are synchronized.)

Explanation / Answer

a) clocks that are stationary with respect to ground will continue measuring the same time . this is the proper time in the frame of reference of ground.

when alyssa measures her time, from her frame of referrence, depending upon her travelling speed, time dilation will take place

hence she will measure lesser time as compared to the time measured by the clocks in ground referrence.

so time measured by her is the dilated time although if her speed is no where near speed of light, it will be indeed very very small to be noticed.

part b:

if one subtracts the centerville station clock read from banning station clock reading, he/she will get the exact time it takes for the train to travel from one station to other in ground frame of referrence.

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