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 Originally Posted by OngBonga
Let's put our science man to the test, since I absolutely can't argue with his response on the shape of the universe, even though I don't think humans are anywhere near knowing for sure...
How'd I do?
Originally Posted by OngBonga
If I'm traveling at half the speed of light, how much time does it take me to travel a light year?
ASSUMPTIONS:
1) you travel at a constant velocity throughout
2) you travel in a straight line
3) the path of travel is 1 ly (light year) in length to a stationary observer
The first thing we need is the relativistic gamma factor.
gamma = 1/SQRT(1-beta^2)
where beta is the fraction of the speed of light of the traveler (here 1/2)
gamma = 1/SQRT(1-(1/2)^2) = 1/SQRT(1-1/4) = 1/SQRT(3/4) = 2/SQRT(3)
gamma ~= 1.154
Now, we need to answer this in 2 meaningful reference frames: the traveler (you) and a stationary observer from the point of your journey's origin (me). We each have a reference sphere, just 'cause we're clever like that.
In your reference frame, your clock ticks normal and my clock ticks slow. Your sphere looks normal, but my sphere looks slightly pancaked. In my reference frame the exact opposite is true. My clock and sphere are normal, and yours are the ones that are distorted. Specifically, we see each others clocks are ticking 1.154 times too slow, and that each others spheres are 1.154 times shorter across the diameter parallel to the direction of your ship's travel.
In your reference frame, the distance you are traveling is LESS THAN 1 light year, since it's not just my sphere that's pancaked, it's the entire universe outside of your ship that's pancaked.
Your perceived distance to travel is 1 ly/1.154 = 0.866 ly.
Your perceived travel time is 0.866 ly/(1/2 ly/years) = 1.73 years
I see your pancaked ship travel a distance of 1 ly and it takes you 2 years to get there.
During your journey, you aged ~1 year and 9 months, while I aged 2 years. Does this count as time travel?
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