suppose two rockets with a passenger are nearing speed of light velocities and are going opposite directions. Relative to eachother one rocket will seem stationary while the other rocket will look like it’s going almost twice the speed of light. What do both passengers see?

Question

I can’t wrap my head around it. But maybe it might be a very silly question with a simple answer.

In: Physics

Answer 1

There is a formula from relativity for adding speeds, that formula is:

(v_1 + v_2) / ( 1 + (v_1*v_2)/c^2 )

where v_1 and v_2 are the speeds. If either, or both, of the speeds are much smaller than the speed of light, c, then the denominator is close to 1 and we just add speeds like we do with standard Newtonian physics. If the two speeds are both close to c, what is commonly called ‘relativistic’ speeds, then the denominator gets close to 2 and instead of adding the two speeds, we average them.

For example, if both rockets are going 0.9c or 90% of the speed of light, we get:

(0.9 + 0.9)/(1+0.9×0.9/1^2) = (0.9 + 0.9) ∕ (1 + ((0.9 × 0.9) ∕ (1^2 ))) = 0.99447514c or 99.45% of the speed of light. That is the speed each passenger sees the other rocket approaching at.