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Travelling at the speed of light would have taken 0 seconds for you, the traveller, but 5-20 minutes for your observer.

However, the Lorentz factor at 20% of the speed of light is ~1.02. This means the distance you travel is only about 2% shorter, so relativistic effects aren't the reason for the discrepancy.



Plus, if it was large enough to have an effect on perceived time, it would affect the apparent distance as well, thus negating the point of the demo!




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