If it is 4.2 light years to the Alpha Centauri system, does the trip there take less time the closer you get to the speed of light?

When considering time dilation, if we traveled at the speed of light would we age 4.2 years, would the trip be instantaneous, or somewhere in between?

Another way this question was asked is when a light particle leaves Alpha Centauri what age is it when it arrives on Earth?

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    $\begingroup$ Welcome Arphaxad! I think this question would be better suited to Physics since it is primarily concerned with the theory of special relativity. I suspect there are answers there that already address this question. $\endgroup$ – Jack Apr 25 '19 at 19:59
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    $\begingroup$ Light experiences no duration. That basically defined the paths that light follows. $\endgroup$ – Steve Linton Apr 25 '19 at 21:08

We can't talk about travel at the speed of light, because the length contraction goes to zero for the travelers and their time dilation goes to infinity. It would take infinite energy to go that fast.

Instead, let's assume our craft reaches 87% of the speed of light on the way to the Alpha Centauri system. From the perspective of the travelers, the trip is indeed shorter than you'd expect from nonrelativistic physics, because the travelers see that the distance between the sun and Alpha Centauri is length-contracted to $\sqrt{1 - v^2/c^2} = \sqrt{1 - (0.87)^2} \approx 50\%$ of the original distance ($\approx 2.1$ lightyears). From the perspective of people on Earth, the travelers will still travel $4.2$ lightyears, but they will age less, owing to time dilation. From the perspective of Earth, clocks on the spacecraft will run slower, $\approx 50\%$ of their rate on Earth. Isn't it neat how relativity is consistent like that?

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  • $\begingroup$ After 4.2 * (1+ (1-0.87)) actual years for both parties travelers reach destination, but this information needs time to reach different observers . Earth observers need extra time to get light info because travelers move away from them while travelers get light info at c + (c * 0.87) from their target. $\endgroup$ – Stefanos Zilellis Sep 24 '19 at 14:26

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