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I am trying to understand time dilation as a total newbie. This question is all about my trying to understand enough such that in a work of fiction an offhand comment (about FTL being a bit silly) makes sense.

If a ship were to travel for a period of say 25 years at a very modest speed such that time dilation is nominal (for this question, negligible too). Then, from the same destination, a ship was to travel at some speed a tiny fraction less than C (or even C, for simplicity) and catch up (in let's say a day) what would the experiences of the two crews be?

Obviously "ship B" would experience 25 years of waiting plus 1 day of travel before they meet. Would "ship A" experience 25 years plus 1 day, or much more time?

I found one answer which explained the complexities of the twin paradox well enough but that's not what I am looking for as I cannot use the answer to solve my own question.

Matthew Brown aka Lord Matt
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    Let $X$ be the event "Ship A leaves earth". Let $Y$ be the event "Ship B leaves earth". Let $Z$ be the event "Ship A meets Ship B". You say that $X$ and $Y$ are 25 years apart. According to whom? You say that $Y$ and $Z$ are 1 day apart. According to whom? You say that $A$ and $B$ occur at the "same destination", by which I think you mean the "same location". According to whom? Different observers measure different times and distances between a given pair of events. Until you tell us who's doing the measuring, it's impossible to figure out what you're asking. – WillO Aug 05 '17 at 14:41
  • Obviously "ship B" would experience 25 years of waiting plus 1 day of travel before they meet. Would "ship A" experience 25 years plus 1 day, or much more time? Imagine there is a race in space between say 10 spaceships. Each of the pilots, looking at their instruments (not outside for various reasons) will be happy that time is passing in absolutely normal way for them, but they will all think the other guys have problems with their clocks. So using the word experience implies an absolute time, but there is no absolute time, only relative time. –  Aug 05 '17 at 15:12
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    @Countto10 "Experience" is usually linked to the (Lorentz invariant) proper time. Further, given sufficiently accurate observation from their own POV, all participants in this exercise can agree on all the proper times. – dmckee --- ex-moderator kitten Aug 05 '17 at 15:47
  • One thing is clear. Like John Snow, I know nothing. – Matthew Brown aka Lord Matt Aug 06 '17 at 15:06

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Obviously "ship B" would experience 25 years of waiting plus 1 day of travel before they meet. Would "ship A" experience 25 years plus 1 day, or much more time?

Well that is quite simple:

A travels 25 years then waits N * 1 days, where N is how many times faster A's clock runs, according to A. (How many days A's clock proceeds when B's clock proceeds 1 day)

N is the time dilation factor, also known as Lorentz factor.

stuffu
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