Question

A train moves eastward at speed v with respect to the ground. Two evetns occur simultaneously, a distance L apart, in the train frame. What are the time and space separations in the ground frame?

Answer 1

The time separation in the ground frame can be found using the Lorentz transformation, while the space separation in the ground frame is the same as the distance between the two events in the train frame.

Step-by-step explanation:

In the ground frame, the time separation between the two events is different from the train frame due to the relative motion between the train and the ground. This is known as time dilation. The time separation in the ground frame can be found using the Lorentz transformation:

t' = γ(t - (vL/c^2))

where t' is the time separation in the ground frame, t is the time separation in the train frame, L is the distance between the two events in the train frame, v is the velocity of the train relative to the ground, c is the speed of light, and γ is the Lorentz factor given by γ = 1/√(1 - (v^2/c^2)).

The space separation in the ground frame is the same as the distance L between the two events in the train frame.