A Roller Coaster Ride through Relativity/Appendix E
Travelling 'faster than light'
If you travel for a distance x at a speed v, owing to length contraction, the proper time interval (ie the number of years you age during the journey) between setting out and arriving will be:
A light beam, on the other hand, will actually take:
If we put these two expression equal, we can find out at what speed it is necessary to travel in order to get the effect of travelling as fast as light.
ie 71% of the speed of light.
Let me just say again what this means. You are not actually travelling faster than light – but you will reach Alpha Centauri, 4 light years away, in only 4 of your years.