Question

Han and Greedo are at the rear and front of a relativistic train travelling at speed

u (with equivalent Lorentz factor gamma). As the train passes through a station (without

slowing), Han and Greedo are observed by the ticket collector on the platform to re

their laser blasters simultaneously. She also measures the length of the train to be LS.

Let the station and ticket collector be at rest in inertial frame S of the \standard

con guration", while the train, Han and Greedo are at rest in S0. De ne the origin

x0 = 0 of S0 to be Han's location at the rear of the train, and the origin x = 0 of S

to be the position of the rear of the train at the moment t = 0 in frame S when the

lasers are red.

i. Write down the (t; x) coordinates of the events corresponding to the ring of the

lasers in frame S, and transform them into S0 coordinates.

ii. Calculate the times in S0 when Han and Greedo each see the other fifi re their blaster.

iii. Comparing your results for parts (i) and (ii), could either Han or Greedo have red

their blaster in response to seeing the other shoot first?

Answer 1

The coordinates of the laser firing events in different reference frames are determined by Lorentz transformation, and time delays caused by light travel time are considered to ascertain the simultaneity of events in the reference frame of a relativistically moving train.

Step-by-step explanation:

This question deals with events observed from different inertial frames applying the principles of special relativity. When Han and Greedo fire their blasters simultaneously in frame S, the coordinates of these events in S are (t, 0) for Han and (t, LS) for Greedo. To find the coordinates in frame S', you would use the Lorentz transformation.

For part ii, we need to account for the time it takes for light to travel from one end of the train to the other in frame S'. This would involve calculating the difference in times when Han and Greedo would see the other's blaster fire using the speed of light and the length of the train in S'.

Part iii requires comparing the times from part i and ii. If one's perception of the other's action is delayed due to the time it takes light to travel, it calls into question whether either could have fired in response to the other. Relativistic speeds and the limit of the speed of light can cause differences in the sequence of observed events between frames.