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Thought exp. on time dilation

  1. Dec 29, 2011 #1
    It is a thought experiment and based on time dilation.
    It goes like..

    consider a cab moving with a speed close to light.Also the cab has been divide into two equal halves by a glass wall.
    there are two individuals in cab one in each part of the cab divided by the glass wall.One is very old man and the other is a normal guy which will serve as observer 'A'.
    And we have a ground observer 'B' (at rest).

    Now the portion in which i have the old man i put a clock and a cylinder of cyanide and made certain arrangements that if the clock slows down from its normal rate then a electronic system will start say a counter which will open the cyanide cylinder and the old man will die.
    *see the arrangements can be mechanical also using gears and hammers.

    since for the observer 'B' the cab is moving with a speed close to light.He sees the clock in cab to be dilated i.e. for him the cyanide cylinder will burst and the man will die but for the observer A,for him the clock is in rest thus no time dilation and hence no death of the old man.

    my problem is that... Life and Death are absolute truth(what i believe) so these shouldn't change from frame to frame that i am alive in respect with one frame and dead in another.
     
  2. jcsd
  3. Dec 29, 2011 #2

    Doc Al

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    That won't work. Realize that nothing within the cab will be able to detect any change in their clock rate. The cab clocks run slow only as seen by an outside observer, such as your ground observer.
     
  4. Dec 29, 2011 #3
    yes it is...
    my question is not related what is being observed by a single observer individually but what they both will observe simultaneously.
    clock will appear to slow down only for ground observer not for observer in cab.
    so does the ground observer will see the cylinder bursting and old man dying AND if so then that means that the person dies for grnd observer and live for the observer in the cab .
     
  5. Dec 29, 2011 #4

    Doc Al

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    Please explain how your mechanism, which is presumably within the moving cab, will detect a change in clock rate observed by the ground observer.

    (As you suspect: If the person dies in one frame, he dies in all frames.)
     
  6. Dec 29, 2011 #5
    give me two minutes..
     
  7. Dec 29, 2011 #6
    Even Enstein didn't describe the actual "mechanism" that why and how clock will dilate if we forget that hypothetical photon clock.what forces acts in slowing down that clock.
    (*If my knowledge is not in complete.)

    okay,for the time being i will use Einstein's clock.

    consider two light clocks and that cyanide cylinder.
    the cyanide cylinder has two censor plates.
    both the clocks are perfectly synchronised and in addtion to this synchronisation the clocks have lasers attach to one of the mirrors of both these clocks.
    such that each time when a photon hits the mirror of the clock it acts as a signal to laser and it emits a photon.

    Now place the two clocks vertical to each other that is
    one in such a way that light beam travel horizontally betwn the mirrors(say x-axis)(clock1) and other in which light beam travel vertical(y-axis)(clock2).

    (sorry i tried to draw and upload image for this but can't)

    these two clocks are at a distance 'r' from the two censors of the cyanide cylinder.
    now the cyanide cylinder will remain close if the photons from the lasers of the two mirrors reach those censors simultaneously.
    if due to any reasons they don't.... then the cylinder will open and the man will die.

    as we know when the cab moves,the clock2 will suffer time dilation(for ground observer) not the clock1.
    that is the laser of clock 2 will lag behind (as now the light beam of clock 2 take more time to reach the mirror) the laser of clock 1 hence the cylinder open and the man will die.
     
  8. Dec 29, 2011 #7

    Janus

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    Untrue, How a light clock is oriented will have no effect on any time dilation that it shows according to the ground observer. Both clocks will undergo the same time dilation.
     
  9. Dec 29, 2011 #8

    Doc Al

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    You have two light clocks inside the moving cab, one oriented along the direction of motion (horizontal) and the other perpendicular to the direction of motion (vertical)? I will assume that's what you mean.
    No, that's incorrect. The ground observer will measure both clocks to exhibit identical time dilation. (And within the cab, both light clocks work identically.) And since the mechanism of the light clocks and cyanide pills is within the cab, any time dilation observed by the ground observer is irrelevant to its operation.
     
  10. Dec 29, 2011 #9
    oh!sorry i made a mistake in calculation but... i am not getting that equal to equal to the dilation of clock2. "??????"

    and also i didn't get what you actually want to say by your last lines.
    are they to signify me as a fool?? if so then thank you very much because for me "No one is too intelligent to judge his/her intelligence by himself,regard himself a genius and consider other as fools.."
     
  11. Dec 29, 2011 #10

    Doc Al

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    Analyzing a light clock oriented along the horizontal is more complicated than analyzing one oriented vertically. For example: Did you take length contraction into account?

    That's just his signature, which attaches automatically to every post. Nothing about you personally! :smile: (Wise words though!)
     
  12. Dec 29, 2011 #11
    It just depends on frame of reference, in the cab's frame of reference their time is not dilated. In the "ground observer" frame of reference the time of the cab is dilated. So it's just going to depend on how you set it up.
     
  13. Dec 29, 2011 #12
    yes forget to include length contraction while calculating...now it is okay.(you guys save the life of that old man :-p).

    but if i again have some doubts or a new arrangement,i will pots that here again.


    And one more thing....
    i have a book named Introduction to classical mechanics by David Morin..
    here in time dilation portion he wrote while explaining that vertical component of light will not be c it will be √c2-v2 and horizontal comp. will be equal to v,the speed by which the arrangement is moving but if it is said that light always travel with c for every observer in any inertial frame then why it is written so..isn't this a violation.
     
  14. Dec 29, 2011 #13

    Doc Al

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    Good!

    Excellent book.
    The light does travel at the same speed c in every frame. From the 'stationary' frame that sees the light clock moving, the light takes a diagonal path. The velocity is c oriented along that diagonal. The vertical and horizontal components will be less than c, but the total speed must equal c.
     
  15. Dec 29, 2011 #14
    thanks a lot.. :)
     
  16. Dec 30, 2011 #15
    ok i found something more in this.

    one more problem...there are two elements in my arrangement.
    the two clocks and and those two lasers attach to those clocks.
    it is right that the clocks will be dilated by same amount that means the two lasers will shoot photon at same time but as i calculated the two photons will start their journey to censors together but will not reach together...

    for the photon starting from clock1
    will take
    T(clock1) =r'/(c-v)
    where r' is the contracted length and is equal to r'=r√1-(v2/c2)
    putting the value or r' and solving we get
    T(clock1)=(r/c)√(c+v)/(c-v)

    and for the photon starting from clock 2
    T(clock2)=r/√c2-v2 .

    so the two photon will not reach the two censors simultaneously.
    question is again the same..
     
  17. Dec 30, 2011 #16
    let me rephrase your thoughts in simpler sentences

    Definition,D=2 events A and B should occur simultaneously(striking of photons)else a third event C(death of the man)happens.

    You should note that the word simultaneous is not absolute meaning 2 events simultaneous in 1 frame(lets call the frame S) can no longer be simultaneous from any other frame which is moving wrt S. Now coming to your definition D you can see its incomplete you should have stated the frame in which it applies. You should attach a frame to that when you do it automatically adjusts itself appropriately to all other frames
     
  18. Dec 30, 2011 #17
    that i know.."Loss of simultaneity"

    there are two observer A and observer B.
    so two frames,one with observerA in the cab and 2nd with the observerB on
    ground.
     
  19. Dec 30, 2011 #18
    then can you state your question once again?
     
  20. Dec 30, 2011 #19

    Janus

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    It is not quite clear how you are arranging your clocks and sensors here, so I'll try to cover all the bases.

    First, I'll assume that the clocks are located at the same spot and firing at sensors located some distance away in different directions and equal distances (as measured in the ship frame). In this case it will be true that according to the ground observer, the lasers will hit the sensors at different times. However, the sensors must then transfer this information to the device that kills the man.
    If we place the device halfway between the sensors, we know that in the ship frame the signals from the sensors will arrive at the same time. In the ground frame, these signals, no matter how they are carried (wire etc.) will undergo the same effects as the laser pulses did, one signal taking longer to reach the device than the other. The result of this will be to completely cancel out the time difference in the laser arrivals. In other words, the signals will arrive at the device at the same time according to the ground frame also.

    Second, we'll assume that the clocks are separated by some distance and the lasers are aimed at censors located at the same spot as the triggering device, which is halfway between the lasers. According to the ship frame, the lasers fire at the same time and the reach the sensors at the same time, but we don't have to worry about transmission time from sensors to device.

    Now what happens according to the ground frame? The lasers take different times to reach the censors, however they still reach the censors at the same time. This is because even though the two clocks are undergoing the same time dilation, they are not synchronized according to the ground frame. They run at the same speed, but one clock will be ahead of the other, and by the same amount as difference in time that it takes for the lasers to travel to the sensors. This is due to the Relativity of Simultaneity. So the upshot is that in the ground frame, the lasers still reach the sensors at the same time, but they are not fired at the same time.

    There is no way to arrange things so that a contradiction occurs between the frames.
     
  21. Dec 31, 2011 #20
    here is the arrangement...
     

    Attached Files:

    Last edited: Dec 31, 2011
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