QUESTION #215

# If two lasers 1 mile apart and facing each other emitted a pulse of light at the same time surely the relative velocity between these 2 pulses of light would be 2c (c=speed of light). I was under the impression that nothing could exceed the speed of light so what is the true relative velocity between the 2 pulses?

Asked by: Anthony Hanson

### Answer

You are correct in saying that the relative velocity between the two pulses is 2c. But, this does not contradict Einstein's theory of special relativity. A relative velocity is only a concept, nothing is actually travelling at twice the speed of light. Your impression is correct, nothing can actually travel faster than the speed of light. Let's see why your example doesn't go against special relativity:

To be a little more concrete, let's look at a modified version of your question... If we change one of your light pulses into a spaceship travelling at 0.9 times the speed of light, it is easier to analyze. This is because we can now ask what two different observers actually measure. The two observers are: the person (person A) in your question, who sees the light pulse and the spaceship racing towards each other, and the person (person B) in the spaceship racing towards both person A and the light pulse. If you ask person A what the relative speed is between the light pulse and person B, you come up with the answer of 1.9c in person A's reference frame. But, if you ask the same question to person B, the answer would be quite different. Person B would measure person A's speed as 0.9c (since person B is at rest in his own reference frame), but would say that the light pulse is racing towards himself at exactly c, not 1.9c.
Answered by: Andreas Birkedal-Hansen, M.A., Physics Grad Student, UC Berkeley