Well you know how it's said that things can't travel at or past the speed of light? However, can't they move at speeds greater than the speed of light relative to another object?

For example: What if two rocket ships that are travelling at 60% the speed of light fly past each other? Won't people on both ships perceive the other ship as travelling at a speed greater than the speed of light? If yes, does this have any significance?


marked as duplicate by John Rennie, Robin Ekman, Kyle Kanos, Alfred Centauri, DavePhD Jun 13 '14 at 12:14

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    $\begingroup$ I've suggested one duplicate of your question but there are many others. Search this site (or Google) for relativistic velocity addition. $\endgroup$ – John Rennie Jun 13 '14 at 9:32
  • $\begingroup$ Very sorry for that. $\endgroup$ – Gummy bears Jun 13 '14 at 17:32

This is not a dumb question. Note that when you say "two rocket ships that are traveling at 60% the speed of light fly past each other", their respective velocities are measured by somebody standing still and observing both of them: He sees that ship A travel at $0.6c$ from his left and ship B travel at $0.6c$ from his right, and they are about to fly past each other.

However, the situation is different if he, now on ship A, measures the velocity of oncoming ship B. By classical addition of velocity, he will measure the velocity of ship B relative to his ship be $0.6c+0.6c=1.2c$, which is greater than the speed of light. This is probably what you are thinking about. However, if you read about Lorentz velocity transformation:


(Or you can google it yourself). The velocity of ship B, relative to ship A is $\frac{v_{A}+v_{B}}{1+\frac{v_{A}v_{B}}{c^2}}\approx0.882c$.

  • $\begingroup$ Oh, I see. So it's impossible to attain the speed of light even in relative motion. So for normal motion this slight error during adding velocities is ignored? $\endgroup$ – Gummy bears Jun 13 '14 at 17:06
  • $\begingroup$ yes, unless you need a very high degree of accuracy in your calculations $\endgroup$ – DavePhD Jun 13 '14 at 17:43
  • $\begingroup$ One can exceed the speed of light in relative motion. However, due to clocks slowing down, lengths contracting, clocks at opposite ends of the rockets no longer being synchronized, any attempt to measure the actual relative motion between the two ships while onboard either of the rockets will result in a speed which is less than the speed of light. $\endgroup$ – Sean Jun 15 '14 at 19:31

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