Using Lorentz transformations, analyse the following sequence of events taking p

Question

Using Lorentz transformations, analyse the following sequence of events taking place in a spaceship piloted by O': A light pulse emitted from a horizontally positioned laser in the back of the spaceship travels towards a detector mounted on the front of the spaceship. O' measures the time delta t' needed for the laser light to travel this distance, and could use this information to verify the length of her spaceship (call this length L' and write down the formula O' will utilize). An outside observer O, who sees the spaceship move with velocity +V, also observes the events and, based on position and time measurements, calculates the length of the spaceship to be L (write down the formula used by O).

Explanation / Answer

time taken by the light pulse to cover the distance L' = dT'
speed of light in the fram e of space ship = c
so, c = L'/dT'
hence
L' = cdT'

for the outside observer
speed of spaceship = v
time noted by this observer = dT'*gamma
where gamma = sqroot(1 - v^2/c^2)
speed of light in this frame = c
so c = L/dT
but dT = dT'gamma
c = L/dT'*gamma
L = c*dT'*gamma = c*dT'sqroot(1 - v^2/c^2) = dT'sqroot(c^2 -v^2)

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