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**1. The problem statement, all variables and given/known data**

Observer O at the origin of a coordinate system is at rest relative to two equidistant space stations located at x=+3.00×10^6km (station A) and x=−3.00×10^6km (station B) on the x axis. In reference frame O, station A sends out a light pulse at t = 0 (event 1) and station B also sends out a light pulse at t = 0 (event 2). Observer C moves relative to O with velocity 0.650 c0 in the positive x direction.

What is the displacement from event 1 to event 2 according to observer C?

**2. Relevant equations**

L = Lproper / gamma

**3. The attempt at a solution**

If event 1 and event 2 occur at two locations that are at rest relative to observer O, can I say that the measured distance from 1 to 2 in O's reference frame is the proper length? Because that's how I approached the problem.

Lproper = 2*(3.00*10^6 km)*(1000m/1km) = 6*10^9 m

gamma = 1/sqrt(1 - ((0.65c)^2/c^2)) = 1.316

L observer C = L observer O / gamma = (6*10^9 m)/(1.316) = 4.56*10^9 m

Is the assumption I made incorrect?