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

Because that’s simply not how velocities add, even though we’re all used to thinking it is. It’s just that at the sorts of speeds we’re used to, it might as well be. Your teachers didn’t exactly lie to you – but they didn’t tell you the whole truth, either.

The simple total is a rule of thumb that works *really* well at human speeds, basically – you’d need to be involved in something very specific and scientific for it not to be good enough. And it’s what we all get taught at school, because it’s “close enough”. But it isn’t actually correct.

This is all about how the universe *actually* works, and specifically General Relativity (tested many, many times). And at low velocities, it might as well not be. The difference between the number you get by just adding two values, and [the actual result](https://en.wikipedia.org/wiki/Velocity-addition_formula), is *incredibly* small. For most day-to-day purposes it’s undetectable and irrelevant (and a long, long way below the margin of error of anything you’re likely to have available to measure your speed).

But that difference *is* still there. And at high velocities – significant proportions of the speed of light such as this, say – it really starts to show up.

If you add, say, 100mph and 100mph, I make it that the actual result is about 20 *quadrillionths* of one mph less than the simple total of 200mph. You can probably be forgiven for not noticing. But 0.6c plus 0.6c? That adds up to, roughly, 0.88c. That, you’re going to find hard to miss.