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Faster than light relative speeds (I know it's impossible!)

  1. May 10, 2012 #1
    We have particle accelerators on Earth that can speed up particles to near the speed of light. Earth itself is hurtling through space, as is the solar system and galaxy that its a part of.

    If an observer were to float outside of our galaxy and observe those speeding particles in the accelerator on Earth, how would the cumulative movement of the particles, Earth, the solar system, and the galaxy not add up to more than the speed of light (Aside from the fact that the velocities might not add up)?

    Time dilation?

    I know that FTL travel is impossible, so I'm not trying disprove it or anything futile like that. I just can't wrap my head around how this works, and I couldn't find a thread that addressed this question.

    Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?"

    Phewph! Thanks for your help.
  2. jcsd
  3. May 10, 2012 #2
    Simple. Speed doesn't add up like normal. If an observer sees a train moving at velocity [itex]\vec{v}_1[/itex] and you're walking on it at velocity [itex]\vec{v}_2[/itex] (relative to the train), your speed as observed from the observer is not [itex]\vec{v}_1+\vec{v}_2[/itex]. It's a bit different, and supported by time dilation.
  4. May 10, 2012 #3
    My time as an observer dilates as the train passes me? I thought it would be the train's time that would dilate...

    So close to understanding, and yet so far.
  5. May 10, 2012 #4


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    Good. Also, nothing with mass can even reach light speed.
    Impossible. The train cannot travel at the speed of light.

    Please look up the relativistic velocity addition rule, e.g.


    As Whovian said, you can't add velocities with v1 + v2.
  6. May 10, 2012 #5


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    Yes, it is basically the same, and the answer is:

    First, you can't ask any question about "a train moving at the speed of light", because, as you say, that's impossible so there is no such thing. But you can pose the same general problem by asking about a train that is moving at 99.99999999999999999% of the speed of light.

    If you are on that train and walking forward at speed v, your speed relative to the train will be v.

    However an observer watching the train pass at speed u, very close to the speed of light, will NOT measure your speed as u+v, but rather as (u+v)/(1+uv).

    Here I'm measuring distances in light-seconds and time in seconds, so the speed of light is equal to 1; if I used some other units there'd have to be a c^2 in there somewhere.
  7. May 10, 2012 #6
    From your reference frame, no, you count quite well as an inertial observer.

    From the person off the train's reference frame, yes, both you and the train are severely time-dilated.
  8. May 10, 2012 #7
    So in my galaxy, solar system, Earth, particle accelerator thought experiment, which is admittedly overly-complex, the same principal of the train applies, and the magical floating observer measuring the velocity of the particles in the accelerator from outside the galaxy would see them as moving slower than the speed of light because he would be time-dilated because of his movement relative to the galaxy etc... that he's observing?

    Is there a maximum time dilation? It seems to me (incorrectly?) that the more movement you add on top of other movement, the more time has to dilate to accommodate.
  9. May 10, 2012 #8


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    Actually, that's pretty much about right.... no maximum time dilation. The amount of time dilation is given by:

    [itex]1/ \sqrt{1-v^{2}}[/itex]

    and that becomes infinite as v approaches 1 (the speed of light in my seconds and light-seconds units). So the more velocity you add, the more time dilation and length contraction you get, and these effects become arbitrarily large as you get arbitrarily close to the speed of light.
    Last edited: May 10, 2012
  10. May 10, 2012 #9
    Yussss. I've heard and read people say things like, "70% time dilation." Is that relative to a reference frame? As in, you're time is dilated 70% relative to mine?
  11. May 10, 2012 #10
    Yes. The accelerator physicists sitting next to the accelerator measure their particles to have some velocity relative to the earth. They do this using some sort of generalized meter-sticks and stopwatches, recording how far the particles travel in some amount of time, and then calculating speed = distance / time.

    Now, from the perspective of the distant observer the Earth has some large velocity through space. As a result, the observer perceives all the meter-sticks on Earth to be length-contracted along the Earth's direction of motion, and all the stopwatches on Earth to be slow. As a result the distant observer does not agree with the speed calculation performed by the accelerator physicists on Earth. If he does his own calculation of the speed of the particles relative to the Earth, using his own meter-sticks and his own stopwatches, he will get a smaller value than the accelerator physicists. Then when he adds in the velocity of the Earth, he will always get a value less than c, no matter how fast the accelerator physicists observe the particles to be traveling in their reference frame.
  12. May 10, 2012 #11


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    No, he would see them as moving slower than the speed of light because speeds do not combine just as "u+ v" (Whovian says "Speed doesn't add up like normal". I would say, rather, that "combining speeds do not add".) For any u and v less than c, (u+ v)/(1+ (uv/c^2))) is still less than c.

    People with respect to whom the observer is moving would see him "time dilated" with respect to them, he would see them "time dilated" with respect to him. There is no "maximum time dilation" (nor "minimum time rate") the closer the speed of an object, relative to me, is to c, the slower I would observe their timer rate. Since the speed of an object, relative to me, can be arbitrarily close to c, but not equal to c, the time rate I observe could be arbitrarily close to 0 but not equal to 0.
  13. May 10, 2012 #12
    In essence - yes. Maybe this mental image will help you. Photon (quanta of light) and proton (a baryon, nucleus of hydrogen) are racing across the galaxy. Let's say that proton has so much energy and it's so fast that after 100 years of racing, it's only 1nm behind photon. Let us also assume that one of the postulates of STR, velocity of light is the same in all inertial systems, is true. So, if light always has the same speed for all observers, how come photon managed to run away only 1nm in 100 years?

    TIME DILATATION. Having so much kinetic energy, while we spent entire lifetime, proton saw only 10^(-17) seconds of action. So, that's what happens and when you lay that on a paper, you get neat velocity addition formulas you can find on wiki or somewhere.
  14. May 10, 2012 #13
    Would it be totally off base to say that the farther you zoom out in the universe, the greater the level of time dilation since movement compounds on top of movement at the smaller levels relative your zoomed out reference frame?
  15. May 10, 2012 #14
    Time dilation doesn't depend on position or separation, only relative velocities. If you add up all the velocities at the smaller levels (using the non-classical velocity addition formula, of course), then you'll find a net relative velocity between you and what you're observing, and that is what time dilation will depend on.
  16. Aug 9, 2012 #15
    Didnt Einstein himself imagine himself speeding through space on a beam of light? if light can not travel less than the speed of light then he must have been travelling at the speed of light.
    Its people like you that tell others something cant be true, without any real evidence, that keep our civilisation static. Its good job Einstein was able to think like that without having to endure critisism because we might not have the theory in the first place.
  17. Aug 9, 2012 #16
    Funniest trolling I've seen in a long time, keep up the good work :)
  18. Aug 9, 2012 #17

    Doc Al

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    Note that it is Einstein's own theory--for which there is ample evidence--that prohibits trains and other massive objects from moving at light speed.
  19. Aug 9, 2012 #18
    the point is that he imagined himself on a beam of light, and came up with a theory that says it is impossiple to do what he imagined. People claim his theory explains how the universe works. (which i find amusing due to the fact that Einstein himself said that his theory was not complete and didnt explain everything)

    Here is a question that i hope i can get an answer to. Why is it not possible for GPS to give exact results when we use GR. it gives results to within a few metres but if GR is precise then using it would surly give precise results.
  20. Aug 9, 2012 #19

    Doc Al

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    Do you seriously think that the only thing affecting GPS accuracy is GR? Many other factors are involved. (The point for this forum is that SR and GR must be accounted for in GPS systems.)
  21. Aug 9, 2012 #20
    actually i dont think that at all - i think that there is a lot we dont know - for example light travels at the speed of light but only in a vacuum. so how is that revelent when the signals have to pass through an atmosphere?
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