Why does Jim think he'll die before reaching Homestead II?

Question

In the movie Passengers, the writers got a lot of details about how an interstellar starhip would work, from the heat shield to artificial gravity. But there was one detail that they only glanced upon in the movie that could change everything: the ship's speed.

In the movie, the awoken crew member Gus explained that the Avalon is traveling at 50 percent the speed of light.

As an object speeds closer and closer to the speed of light, relativistic effects (such as time dilation) will become significant on it.

When Aurora played back that video of her friend on Earth, her friend referenced the journey as a 120 year voyage; meaning that the travel time of 90 years is relative to the Earth's perspective.

Considering their speed and journey time, Homestead II could be placed at roughly 60 light years from Earth. If you calculated the level of time dilation and factored that in, the Avalon's entire flight time would be only 51.96 years. With 30 years of local travel time already cleared, the ship's remaining travel time would only be a mere 21 years.

If time dilation was factored in, wouldn't Aurora and Jim have made it to Homestead II alive and well even without sleeping most of the way?

Answer 1

No. The relative dilation experienced at half light speed would be around 14%. Even if we assume the ship is referring to their remaining journey time in Earth Standard Time (which, for the record it isn't, but let's say it is anyway for fun) that means that their remaining 88 years would be reduced to, at most, 74 years. Given that Aurora is in good physical health and in her mid-20's it's not impossible that she could still be alive and in her mid-90s. Jim appears to be in his mid-30s and would be well over a hundred on arrival.

For the record, if they

took turns using the autodoc to hibernate

They'd likely both make it to Homestead II in their late 60s/70s

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So, let's get back to whether they were referring to EST? This is made explicitly clear when Jim speaks to Aurora. We know that he was told that his remaining journey time was

Computer Voice: ... 90 years, 3 weeks and 1 day.

He then spends 1 year awake

Aurora: How long have you been awake?

Jim: 1 year and 3 weeks.

Which tallies very nicely with the amount of time remaining when Aurora asks the same question.

Computer Voice: We will arrive in approximately 89 years.

This gives us proof-positive that the ship is counting local time, not EST.