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Question: A light-year is the distance light travels in one year and is equal to $9.46*10^{15}m$ Imagine you travelled at a constant velocity of $0.97c$ from earth to the next nearest group of stars, the Alpha Centauri group, which is at a distance of $4.26$ light-years. Calculate, in years:

a) the time it would appear to take from Earth for you to complete the trip. b) the time it takes to complete the trip from your point of view as you travel.

Now the problem I have is to see from the frame of reference that the question asks.

For a), the answer says that this time is the proper time. But from my interpretation, this would be the relativistic time. Since I am in motion relative to an observer in a stationary frame of reference, from a stationary observer's perspective, my time would be slower.

And same thing goes for b), the answer says this is the relativistic time. Wouldn't this be the proper time? This time is the Proper time from my point of view and I can consider myself as stationary while space is rushing pass me, can't I?

From my interpretation, everything seems correct and logical to me but apparently not. What am I missing?

EDIT (answer): enter image description here

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  • $\begingroup$ It looks like whatever book you're using has made a mistake. (b) is the proper time, (a) is the time as measured in the frame of the Earth. $\endgroup$
    – knzhou
    May 12, 2020 at 2:30
  • $\begingroup$ @knzhou Hey, I included the answer. Can you take a look again? Cheers. $\endgroup$
    – CountDOOKU
    May 12, 2020 at 2:56
  • $\begingroup$ Now that you've posted the answer, it seems like the book is correct but you quoted it incorrectly. $\endgroup$
    – knzhou
    May 12, 2020 at 3:52

1 Answer 1

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The screenshot you provided does not say proper time for a) and relative time for b). It says proper distance, and relative distance, respectively. Proper length is measured in the rest frame, so the book is correct. (And this is not in contradiction to your correct understanding of proper/relative times.)

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  • $\begingroup$ so I am and the answer provided by the book is correct? $\endgroup$
    – CountDOOKU
    May 12, 2020 at 3:46
  • $\begingroup$ @Nhoj_Gonk Yep. $\endgroup$
    – hiccups
    May 12, 2020 at 4:06

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