From what popular science tells us, if I travel at close to the speed of light, I'd age slower. So if I travel at 99% of SOL and travel the distance of one light year, for other people one year has passed. But for me, hardly any time has passed.

So - for me and my ship, we travelled one light year in very little time. If that is the case, then for me I travelled much faster than the speed of light!

How does that reconcile with the statement that nothing can exceed the speed of light?

  • $\begingroup$ It isn't the case. So no reconciliation needed. You travel at 99% like you said. $\endgroup$ – Rory Alsop Oct 12 '20 at 9:45

You have neglected length contraction in your analysis. You see the initial distance of the star contracted by the same factor that the elapsed time is shortened.

So, from the perspective of the Earth, you take 1.0101 years to travel a distance of 1 light year at a speed of $0.99c$.

From your perspective, the destination comes to you. It arrives after 0.1425 years, travelling a distance of 0.1411 light years, again at a speed of $0.99c$.

No faster-than-light travel is involved anywhere.

(In the above, I have rounded non-terminating decimals to 4 decimal places)


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