When a clock travels close to the speed of light as observed by us, it should tick slower.
Does this mean that, when using this clock to measure a second - it could travel much more than 300 000 km during a second? In fact, this clock could travel infinitely fast when viewed only from its own perspective?
Does this imply that if I traveled on a space ship, at the speed of 99 % of light, I would age 4 years, but could reach a destination perhaps 400 light years away?
My friends and family on earth would have perished, but the people I saw on the destination planet as I started my journey will have aged only 4 years as well.
If the last assumption is correct; it means that we could watch a launching space ship at alpha centauri, it could arrive here in just 3-4 days - appearing to travel much faster than the speed of light, without breaking the laws of relativity. We would just say that it was relativistic blue shift that made it seem to travel faster than the speed of light.