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Relative speed of light paradox

  1. Mar 28, 2010 #1
    I'm no physicist, but I read that the speed of light is constant from all observers (regardless of relative speed) and in doing a thought experiment I encountered a problem. Here is the situation:

    John shoots a laser at you. You turn and run away at near the speed of light, but you look back to see that the laser is still approaching you at the speed of light, unaffected by your speed. In order for that to happen it would seem that the beam has sped up to keep up with you. However, John does not see that the laser has sped up, but instead both you and the laser are traveling the almost the same speed. Now then, back into your point of view, you get hit by the laser and feel a burn. You immediately stop running because of the agony. In John's point of view, this laser has not yet hit you but you are already reacting to it.

    How can this be? Can somebody explain it to me?

    Furthermore, when John sees the laser hit you, will you feel it? It would then be as though you were hit by 2 lasers. Is this right or am I missing something?
    Last edited: Mar 28, 2010
  2. jcsd
  3. Mar 28, 2010 #2

    Doc Al

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    The thing is, it can't be.

    (1) You can't run at the speed of light with respect to John or anything else. No material thing can. Your speed with respect to John will always be some fraction of light speed.

    (2) If you ran away at 0.99c, then you'd see the light approaching you at its usual speed of light with respect to you. John, of course, will see the light move at its usual speed with respect to him and he'll see you moving at 0.99c with respect to him.

    (3) You and John will disagree on how long it takes for the light to reach you and on how far the light traveled. But strange things happen to moving clocks and measuring rods in relativity, at least according to those who see the clocks and rods moving.
  4. Mar 28, 2010 #3
    I don't know that much about lasers, but I do understand that the frequency of light decreases as you increase your speed relative to it. So if you were traveling very close to the speed of light, my guess would be that the frequency of the laser relative to you would have diminished enough that it would no longer burn you at all, or at least less than it would if you were standing still relative to its source or moving toward its source. In that case the beam's frequency would increase causing it to do more damage that it would if you were moving away or standing still relative to its source.
  5. Mar 28, 2010 #4
    I'm aware of this. For my purposes in the example, it isn't really relevant.

    These answers don't quite answer my question. The problem lies in that after being hit by the laser, you stopped running. When you suddenly stopped you entered the same point of view as John, so you will see the same laser approaching you that John still sees. How was this laser revived, and will you now be hit by a duplicate laser?
  6. Mar 28, 2010 #5
    All the so-called paradox in GR can be explain by clearly posing the problem and, most importantly, define simultaneity.
    All the paradox I know try to compare two observers which are not simultaneous…
  7. Mar 28, 2010 #6


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    There is no duplicate laser. The events that happen are the same for everyone. The only difference between different inertial observers is how they coordinate those events.
  8. Mar 28, 2010 #7
    Doc, I'm curious. Has frame variance(if I'm using correct terminology) been demonstrated in such a way that I can do it here in my home?
    Or is this "proof" relegated to sophisticated aerospace experiments?
  9. Mar 28, 2010 #8


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    You need very accurate measuring devices such as atomic clocks or a laser interferometer to be able to detect the variance. There aren't a lot of individuals who have such things, but any good college physics department will be equipped to test relativity.
  10. Mar 28, 2010 #9
    How can relativity be tested using any clocks or lasers in a situation of fixed gravity and velocity?
  11. Mar 28, 2010 #10
    With all due respect...
    Does frame variance not exist on a macroscopic level?
    I think this should be cleared-up, one way or the other.
  12. Mar 28, 2010 #11

    Doc Al

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    Sorry if I didn't address your question directly. Every frame agrees that the laser pulse hits you, they just disagree on how long it took for the pulse to reach you.

    You seem to think that this event (the laser pulse hitting you) somehow happens in one frame (yours) without also happening in other frames (namely John's). Not so. There's no 'duplicate laser' pulse. (Of course, John himself won't see the pulse hit you immediately. After all, he is possibly miles and miles away by the time you get hit.)
  13. Mar 28, 2010 #12


    Staff: Mentor

  14. Mar 28, 2010 #13
    But, at this point, it would then take the distance between you and jonh, divided by C, time for john to have seen you actually be shot. By this time you can both be certain about the fact that you were shot although you may disagree about exactly how long ago it happened.
  15. Mar 29, 2010 #14
    Thank you for all the help. I have a better understanding now, but it is clear that I've got a much longer path through the this field. I'll be spending much time at this forum.
  16. Mar 31, 2010 #15
    It would seem as if the laser has sped up to keep up with you because you will always measure the speed to be exactly the same. No matter how fast you run, according to you, you will make no progress running from the laser. If the speed of light were slow enough for you to see it (ignoring the fact that you can't see it until it reaches you), you would notice that it always comes toward you with the same velocity.

    John would see that you are moving faster and that you are making progress in running from the laser. But because time is moving more slowly for you as you increase speed, you will have the false impression that the laser is matching your speed. If time slows for you, you won't notice it in the slightest by only watching the laser. The laws of physics will not change for you even if time is crawling with respect to everyone else. You will intuitively know that you increased your speed and it will blow your mind that the laser is still moving at you. Sorry, but it just IS. And if you think about it, it really is simple.

    A key point. John will not see you react to the laser until he first sees it hit you. Information travel is limited by the speed of light. You will both disagree on when A, the firing of the laser occurred, and B, when you got hit. Yet in no one's frame of reference will B ever occur before A. This is because there is no situation in the universe which can allow an event to precede a cause. The firing will always occur first, but you both will disagree on the time elapsed between all events.

    You must consider time dilation when thinking about this. Time is the key to understanding your perceived paradox. The only reason that you see the laser chasing you at constant speed is because your perception (and your actual state) of time and distance are altered as you approach the speed of light. Light speed is constant, so time and distance changes to accommodate it.

    John sees everything in perfect clarity because he is not undergoing time dilation. You, on the other hand, will notice that no matter how fast you go, you are not gaining on the laser, but instead the distance you are trying to cover to get away from the laser is being squashed smaller and smaller as you run faster. You don't feel so fast, but when you look at the world around you, you are moving through a squashed version of it and thus covering huge distances. Everything is slowing down as you zoom by once distant objects that are not so distant anymore... Everything is slowing down... except for that damned laser beam.

    When you come to and your buddy finally catches up with you, he will say that you were flying to get away from that laser.
    Last edited: Mar 31, 2010
  17. Apr 1, 2010 #16
    Thanks for the explanation kamikaze.

    I actually figured it out a yesterday. My problem was in defining simultaneity. I failed to consider lorentz contraction for one.
  18. May 19, 2010 #17
    I'm a little baffled by this but let me try and put my own take on it.

    1. As you move faster time slows relative to distance?
    2. As you move faster large distances seem short due to time slowing?
    3. So when you run from the laser it would appear to keep up with you due to the distance you are covering appearing smaller than it actually is?

    Number 3 assumes the impossibility of you moving at a speed matching or faster than the laser.
  19. May 20, 2010 #18
    1) As you move faster you move through time slower when compared to someone observing you who is not moving as fast. They will mirror this and move through time more slowly compared to you.

    2) When you move faster you don't notice time slowing at all. Only other people observing (stationary or slower thanyou) will notice anything. Distances may shrink though due to length contraction. This is an actual physics phenomena. Not an optical effect. So distances ARE shorter. Not SEEMINGLY shorter.

    3) The laser DOES keep up with you because you always measure the speed of light relative to you to be the same. You'll see the man with the gun zooming away from you really fast. At some point the laser beam will be shot from that gun and will approach you at the speed of light, as expected. You'll see the laser beam comin at you at C, and the man moving away from you at nearly C (0.99c i think we decided on).
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