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How long does it take to go 10LY?

  1. Aug 2, 2010 #1
    so, a bit of confusion here - suppose i have a spaceship that can acheive 0.99999C, and i decide to go to a star that is 10LY away.

    as i travel, the people on earth who ihave left behind determine that, by the clocks on earth, it takes me around 11 years to reach the star. however, due to time dilation, the clock on my ship tells me that it has only taken me about 2 years to travel the 10LY distance.

    so, did i get that correct? ie, that the ship clock will have only measured the passage of about 2 years during my 10LY travel distance while the clocks on earth have indicated 11 years?

    and, if i did indeed manage to go 10LY in only 2 years according to my clock, what does that tell me about the "real" distance between the earth and the star i traveled to? what am i missing here? thanks.
     
  2. jcsd
  3. Aug 2, 2010 #2

    Doc Al

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    Some corrections: Since you're practically traveling at the speed of light, earth observers will say it takes you about 10 years (not 11 years) to travel 10 LY. The Lorentz factor for a speed of 0.99999 c is about 224. So your ship clock would record 10/224 of a year--about 16 days (not 2 years).

    From the ship's perspective, that 10 LY distance measures only 10/224 LY. (Distance, like time, is frame dependent.)
     
  4. Aug 2, 2010 #3

    bcrowell

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    Your actual numbers are wrong for the velocity of 0.99999c, but other than that, you're correct.

    In your frame, the distance is Lorentz-contracted and appears shorter than in the earth's frame. There is no "real" distance. Different observers disagree on distances.
     
  5. Aug 2, 2010 #4
    so, based on that, if i could get to 0.9999999999999999999999999999C, it would take me essentially no time at all time to traverse 10LY, or any distance at all, correct?

    so, why then does it appear to take light 10 years to travel 10LY? surely for the photon, no time passes at all - is it only because of our reference frame on earth that light "appears" to take time to travel any given distance, and that in reality, it is an illusion to think that light has some fixed speed?
     
  6. Aug 2, 2010 #5
    Well, in your previous example, although it only takes you 16 days everyone else sees it take you about 10 years. So when you think about light in the same way you'll realise that the light travels everywhere in no time at all, but we see it take distance/C time. The same as everyone else saw you take 10 years to travel (10LY/C = 10 years).
     
  7. Aug 2, 2010 #6
    And... light DOES have a fixed speed. Its just that when you move that fast the rest of the universe shrinks to a very thin slice in the direction you're travelling (imaging a beach ball being flattened like a pancake). Therefore it doesn't take you long to go the distance because the distance has shrunk. But for everyone else watching the distance didn't shrink and they see it take you a long time.
     
  8. Aug 2, 2010 #7

    Doc Al

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    Sure. A very short time according to your clocks. Of course, earth observers still measure that it takes you 10 years to cover that 10 LY distance.

    What do you mean "appear"?

    The fixed speed of light is no illusion. While you can speculate on what a photon might experience, no real reference frame moves at light speed. (If it did it would violate relativity!) Even for you traveling in your super fast ship, light would still travel at its usual speed.
     
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