If two spaceships travel in opposite direction at .6c (the speed of light) from earth, then why aren’t they exceeding the speed of light relative to each other?

Question

I understand that if I am standing on earth and a space ship takes off and travels at .6c, then I perceive the space traveler receding at .6c relative to me, and the space traveler perceive me as receding at .6c relative to him. If another traveler takes off in the 180-degree opposite direction, then likewise I perceive the other space traveler receding at .6c relative to me, and the other space traveler perceive me as receding at .6c relative to him.

So why don’t they perceive each other as traveling faster than c, the speed of light?

In: 29

Answer 1

This question touches on some of the ways relativistic motion is so strange.

Normally you would expect speeds to add together like those we interact with on a daily basis. For example if there is a car going 40 mph one direction and another is approaching it at 40 mph then their closing speed is 80 mph. Easy, simple, intuitive. But that isn’t how things work at speeds approaching the speed of light.

Instead moving near the speed of light results in some changes in the frame of reference of the traveler. Two major factors are time dilation and length contraction. Time dilation gets a lot of press, where less time passes for the traveler than in an “at rest” reference frame. As a result the travelers won’t agree on how much time has passed and therefore can disagree about their relative speeds.

Another significant factor is length contraction, where the shape of the surrounding universe changes according to the traveler. Things in the direction of their travel are compressed and shortened which means they don’t agree with other observers about how quickly they are traveling.

To illustrate imagine you have a traveler who is going to a destination 1 light year away at a speed close enough to the speed of light that it will seem to take only 10% of a year. Now the traveler is only going to experience 10% of a year in time so they can’t perceive themselves as having covered 1 light year or they will view themselves as having exceeded the speed of light! So not only is their time frame slowed to 10% they also view the distance to that destination as being somewhat less than 10% of a light year away!

This works not just for their destination but the universe as a whole, so the traveler watching the other ship flying away would view it as covering less distance just like it does itself.