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Questions about the speed of light.

  1. Mar 30, 2007 #1
    1st Q~
    if a man in a spaceship travelling at say 0.5 c measures two beams of light outside the spaceship that are in opposite direction. (the two beams are from sources outside the ship) he would measure both light's speed as c as the einstein says. however, the distances for the two beams he measured would not be same.(or would they be?)
    if that's the case, he would have two sets of time. can he choose which one he'd like to use?

    2nd Q~
    if c is indeed constant as the relativity says, would say 0.5c also be constant? from what i learnt in math, i know if c is constant,0.5c should be, too. but it doesnt seem to be a math matter.

    If it is not constant, then people in relative motions would measure it differently. if a spaceship travelling at 0.6c measures another ship travelling at 0.5c(measured by 3rd person) but in opposite direction, what speed of the 2nd ship would be measured in the 1st ship? again from basic math,i reckon it'd be 1.1c,which is faster than c. is that right?

    If it is constant. then i could derive many interesting conclusions from it. if 0.5c is constant(i mean the velocity of an object which is 0.5c), there's no reason why 0.05c is not constant.(or is there?)
    if i walk with a speed of 1m/s, that is (3.33 * 10^-9) c. if that is constant, then people around me standing or running would agree on the speed of me,but not the distance i travelled. they would have different sets of time.
    and then back to the 1st question, they would have tons of sets of time. how do they choose?
    u tell me.
     
    Last edited: Mar 30, 2007
  2. jcsd
  3. Mar 30, 2007 #2

    JesseM

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    It's important to note that "travelling at 0.5c" can only be meaningful relative to a particular reference frame--there is no such thing as absolute speed in relativity. In some reference frame, the Earth is traveling at 0.5c right now.
    If they were both emitted from his own location at the same time, then the distance between himself and each beam would be the same.
    No, it isn't constant. If something is traveling at c in one frame, it is traveling at c in all other inertial frames, but that's not true of something traveling at 0.5c. In relativity, you can use the velocity addition formula to figure out how an object's speed changes in different frames. If an object is traveling at speed v in your frame, and you are traveling at speed u in the same direction in my frame, then the formula says I'll measure the object to be moving at speed (u + v)/(1 + uv/c^2) in my frame. So for example, if a rocket is moving at 0.5c to the right relative to you, and you're moving at 0.8c to the right relative to me, then the rocket is moving at (0.8c + 0.5c)/(1 + 0.8*0.5) = 1.3c/1.4 = 0.93c relative to me. On the other hand, if a light beam is moving at 1c relative to you, and you're moving at 0.8c relative to me, then the light beam is moving at (0.8c + 1c)/(1 + 0.8*1) = 1.8c/1.8 = 1c relative to me.
    Your question is confusing--if the ship measured the other ship to be moving at 0.5c, then by definition the speed of the second ship as measured by the first ship is 0.5c. Perhaps what you meant is that if a third observer, like one on Earth, measures one ship moving at 0.5c in one direction and another ship moving at 0.6c in the opposite direction, then what speed does each ship measure the other to be moving at in their own rest frame? In this case the answer is (0.5c + 0.6c)/(1 + 0.5*0.6) = 1.1c/1.3 = 0.85c.
     
  4. Mar 30, 2007 #3
    wow~thx. but for the 1st question, the two beams are from sources outside the ship and are in opposite directions would the distances he measures still be the same?
     
  5. Mar 30, 2007 #4

    JesseM

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    It's not outside or inside that matters, it's just the original distance between the beams and the observer at the moment of emission. If both beams are emitted from a source that 1 light year to the left of the observer, then after 3 years, the right beam will only be 2 light years away from the observer, while the left beam will be 4 light years away (each beam having traveled 3 light years from the source). Likewise, even if the source was a small distance away like 5 meters to the left of the observer, this means that once the right beam has passed him, the right beam will always be 10 meters closer to him than the left beam.

    As long as the source is a negligible distance from the observer when the beams are emitted, though, then both beams will be the same distance from the observer at all later times in the observer's rest frame, assuming the observer does not accelerate.
     
    Last edited: Mar 30, 2007
  6. Mar 30, 2007 #5
    do you imply that if the observer accelerates the distances would be different?
     
  7. Mar 30, 2007 #6

    JesseM

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    Well, if the observer accelerates then after the acceleration he'll have a different inertial rest frame, and in this new frame his current location may not be the same as the location that the emitter was at the moment it sent out the two beams, in which case his distance from the two beams wouldn't be the same.
     
  8. Mar 30, 2007 #7
    Then he would have two sets of time?
     
  9. Mar 30, 2007 #8

    JesseM

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    What do you mean by "two sets of time"? Each reference frame has a different way of assigning time-coordinates to events, if that's what you mean.
     
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