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Does space (distance) between two bodies contract according to SR?

  1. Oct 12, 2013 #1
    Suppose if travel towards the nearest star (alpha centauri) 4 light years away at 90% the speed of light does the distance between my spaceship and the star undergo length contraction?
    but i think in Wikipedia it its written as the distance undergo length contraction
    http://en.m.wikipedia.org/wiki/Twin_paradox
    read the "Specific example" topic in it
     
  2. jcsd
  3. Oct 12, 2013 #2
    Yes, distance length contracts. Lay down a set of rulers end to end in a line. Remove every other ruler. Now from the point of view of an observer moving along the line, the gaps between the rulers length contract to the same extent as the rulers themselves.
     
  4. Oct 12, 2013 #3
    if i haven't included the Wikipedia link u should have said "no" the distance won't shrink, only physical bodies undergo length contraction"
     
  5. Oct 12, 2013 #4
    Then if an object moving towards me at 90% speed of light light from a distance of 1hr light c. Without length contraction i calculate it to be arriving at 1hr and 6 minutes on my clock, so when i include length contraction will it arrive more early?
     
  6. Oct 12, 2013 #5
    No, not if you use a frame in which you are at rest. Then there is no length contraction.

    If you used the frame in which you are moving and the object is at rest, the distance would be length contracted, so the object would indeed arrive earlier than that (or rather you would arrive at the object earlier), but your clocks would also be running slow due to time dilation. The two effects cancel and so your clocks would read 1 hour and 6 minutes.
     
  7. Oct 12, 2013 #6
    You measure the distance to be 1 light hour and the time of travel to be ≈ 1 hour 6 minutes.

    They measure the distance to be ≈ 26 light minutes and the time of travel to be ≈ 29 minutes.

    You both calculate the velocity using your own measurements of distance and time to be 0.9c.
     
  8. Oct 12, 2013 #7
    Hey Trojan 666...the trick is this....time dilation and length contraction is due to relative motion....in special relativity, flat spacetime [no gravity].

    So anything traveling in your frame, with you, is 'stationary' relative to you: that means a clock you carry, for example, always ticks at it's same fixed rate [called proper time] and you do not contract in size along the direction of motion. But the other outside observer, in motion relative to you, sees your clock slow and your size diminish along the direction of motion.

    So when you move really fast on your way to Alpha Centauri, that distance is in another reference frame....right??....your local wrist watch time ticks along as usual but the distance you travel is reduced. From an observer on Alpha Centauri, the distance remains unchanged [since it is in the static frame of that observer] but she sees your clock ticking more slowly....when you meet up and compare elapsed times, voila they don't agree....she thinks your elapsed local time is less than her local time. YOU have aged less than she.

    You each 'disagree' on the elapsed time and distance traveled.....and you are both right.
    Different observers resolve these 'paradoxes' via Lorentz transforms which explain the differences.
     
  9. Oct 12, 2013 #8
    Trojan666:

    Can you now answer this correctly on your own??
     
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