If/when humans send a mission to Alpha Centauri, will the subjective time experienced by the craft be more than 20 years?
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Alpha Centauri is about 4 light years away. Time dilation means that if the craft accellerates fast enough, the time it experiences can be arbitrarily low; possibly even less than 4 years.

See here for various theoretical methods and how long they would take.

Close date updated to 2200-01-01 12:00 am

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For reference, 9.81m/s^2 * 1 year = 305900km/s (102% of the speed of light). The time the mission experiences can only be arbitrarily low if the acceleration is arbitrarily high. But generally there is a tradeoff between acceleration rate and specific impulse. To reach high speeds you need a very high specific impulse which probably entails low acceleration. All current ion drives have a thrust to weight ratio of less than 0.8m/s^2

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