Two parties (A and B) are signing a treaty at opposite ends of a 40.0meter table. The two parties and very suspicious so it is important for the two to sign the documents at the same time. This is arranged when the light from a light bulb at the center of the table reaches them. However, an anxious party member from one side (say A) is watching over the proceedings and is travelling in a space ship parallel to the table from the direction of the other party (B) at a relative velocity v = 0.95c (c=3.00E8 m/s).
a. According to the party member in the space ship, which representative signs the treaty first? What is the time interval between signings by the two representatives in this frame?
b. Suppose now the space ship is traveling at the same speed, but opposite direction. In this case, which representative signs the treaty first?
Relativistic velocity addition formula?
u' = (u - v)/(1 - (uv/c2))
Or Postulates of Relativity
Speed of light c is invariant
The Attempt at a Solution
Well, my first attempt at the solution was to argue that the light reaches party B first because of the relative velocities, however according to the postulate of relativity for c, the speed of light is always c, regardless of relative velocity. So originally I had the light travelling faster than c but I don't think that is correct.
Is it possible for light to be Observed to travel faster than c if one is traveling in the opposite direction?
What I think the answer is: the light reaches the two representatives at the same time regardless of what frame is it observed in so they sign the documents at the time, is this a correct assumption?