Let's say an astronaut with a terminal illness that gives them one year to live on Earth travels to a star one lightyear away, travelling at almost the speed of light. Suppose they perceive that the trip takes them 55 days or so, due to time dilation. Will they still be alive when they reach their destination? What will their health look like to observers on Earth?
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@JonCuster Are you saying the journey still appears to take a year for the astronaut? That's not my understanding. – AndrWeisR Apr 08 '23 at 01:43
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3@AndrWeisR Then your understanding is incorrect. Time dilation is a relative effect, and so everyone experiences the passage of time at 1sec/sec in their own frame of reference. But an observer who is external to the astronaut, will see a clock in the astronaut's frame tick at a slower rate. – joseph h Apr 08 '23 at 01:53
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@josephh My understanding is that due to length contraction, as opposed to time dilation, the astronaut perceives that they have less distance to travel, and so the journey takes less time. – AndrWeisR Apr 08 '23 at 01:58
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Then your specific question is a duplicate of How long would it take me to travel to a distant star? – joseph h Apr 08 '23 at 02:36
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The astronaut will see the distance to the star as Lorentz contracted. The trip therefore takes $55$ days or so.
An observer on the star will see the distance as $1$ light year. He sees the astronaut's clock running slowly. He sees $55$ days pass on the astronaut's clock during the trip.
Both the astronaut and the observer agree that the astronaut survives the trip.
mmesser314
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"What will their health look like to observers on Earth" if he sends a message to earth that he is still living and has 10 more month to live, this message will reach earth one year later, when he is dead. So observers on earth have no information of his actual health. – trula Apr 08 '23 at 16:03