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Question about length contraction

  1. Nov 12, 2008 #1
    In most special relativity primer book, length contraction section, the length is always defined or measured by the time of a light flashing at one end of a rod, traveling to the other end, reaching a mirror and reflecting back to the first end.

    Please read this example if I did not make myself clear. http://www.berkeleyscience.com/relativity.htm

    My question is, why cannot we define or meature the length by a one-way trip of the light flash, either from left end to right end, or from right to left? And if we define this way, the result will be different than L=L'/γ. The length seems to be more contracted towards the moving direction of O' frame L=L'/γ * (c / (c+v)). The length also seems to be less contracted opposite the moving direction L=L'/γ * (c / (c-v))

    So, could anyone explain to me:

    1. Why is length defined this way?
    2. How to explain to results of one-way light trip definition?
     
  2. jcsd
  3. Nov 12, 2008 #2
    Think about the difficulties in measuring the one-way trip of light, that should give you an indication as to why that would not make any sense.
     
  4. Nov 12, 2008 #3
    Thanks Jennifer for the quick reply.

    According to the experiment mentioned in http://www.berkeleyscience.com/relativity.htm , it is not difficult to measure the one-way trip of light.

    Two way: left end of the rod, light source, clock; right end, mirror.
    One way: left end of the rod, light source; right end, clock.
     
  5. Nov 12, 2008 #4
    Really? Where does it state that?
     
  6. Nov 12, 2008 #5
    Could you open the link http://www.berkeleyscience.com/relativity.htm , then locate "Length Contraction" section (starting with "Note: in the clock above...")? You can find a very detailed mathematic deduction over there.

    Thanks a lot!
     
  7. Nov 12, 2008 #6

    Jonathan Scott

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    Gold Member

    So how do you set the clock? The standard method is to send a light speed signal to the other end and back and to assume that the time difference is half the time it took for the signal to return. However, that relies on the assumption that the speed of light is the same in both directions, and that in turn depends on the frame of reference.
     
  8. Nov 12, 2008 #7
    I read that but that does not deal with an experiment that demonstrates the one-way speed of light.

    Anyway you had a question I tried to help you understand that measuring the one way speed of light does not make any sense, and I suppose that is all I can do for you.
     
  9. Nov 12, 2008 #8
    The web site (http://www.berkeleyscience.com/relativity.htm) reads

    Suppose that there was a O' frame clock attached to the left end of the rod, and that this clock reads T' when the light reaches the left end of the rod. Because of time dilation, we know that
    T = T'γ = 2L'/cγ
    so, L = L' / γ

    So the clock is simply attached to one end of the rod.

    My question is again, why the standard method is two way trip, not one way?

    And there can be other definition, such as flashing a light at both ends, then measuring the time difference when they reach the origin. This definition will yield similar results as one way definition.
     
  10. Nov 12, 2008 #9

    Jonathan Scott

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    Gold Member

    For ANY measurement of speed, you need a clock at each end, and you need the clocks to be synchronized. The standard synchronization procedure (equivalent to carrying a clock not too rapidly from one end to the other) relies on the assumption that light travels at the same speed in both directions, and this is the method conventionally used to define time in a particular frame of reference.

    From the point of view of a relatively moving frame, this procedure is flawed, because from their point of view the light has a shorter distance to travel one way than the other, so according to the convention for synchronizing clocks in that frame, the first clock is set incorrectly.

    In the first frame, we could actually consider the other point of view. What if light (and all similar signals) "really did" travel faster in one direction than the other? If so, we have no means of detecting it, because our only method of synchronizing is to use the assumption that it doesn't.

    Before relativity came along, the same mathematical results were discovered by Lorentz and Poincare, but were typically interpreted in terms of a static "ether", in which light travelled at c. From frames of reference which were moving relative to the ether, the Lorentz transformations described the distortions due to the fact that light travelled one way faster than the other, yet the transformations worked in such a way that it was difficult to see any way to actually measure the speed relative to the ether. It was Einstein who realized that the ether was unnecessary and that any inertial frame was as good as any other.
     
  11. Nov 12, 2008 #10
    The reason is failure of simultaneity. Note how that web site does the analysis:
    1. Calculate how long the two-way trip takes in the O frame. We do this by starting our stopwatch at t=0 and stopping it when the light flash gets back to the left end of the rod at t=T. The time for the trip in the O frame ("lab frame") is therefore T.

    2. Calculate how long the two-way trip takes in the O' frame. We do this by setting the clock on the left side of the rod to t=0 and reading it when the light flash gets back to the left end of the rod at t=T'. The total time in the O' frame (rod frame) is therefore T'.

    3. Notice that T is not equal to T', and therefore the rod has different lengths in the two frames.

    At this point in the web page, and in a typical relativity class, the concept of simultaneity failure is not yet introduced. But it is the reason why step 2 of the procedure above will not work for the one-way trip.

    In step 2, we read the same clock (glued to the left end of the rod) twice. That is fine. If you wanted to do this for the one-way trip, you would be reading two different clocks: one on the left end of the rod, and one on the right end. But because these clocks are glued to a moving rod, they are not synchronized in the lab frame. You cannot therefore simply take one measurement (on the right end of the rod) and subtract the other (on the left end) to obtain the time the trip took in the rod frame.

    If you wanted to read the clock on the left side when the light flash reaches the right side, again you have the problem of simultaneity failure. You will not be reading the correct time on that clock because the events "left clock reads time T'" and "light flash reaches the right side" are NOT SIMULTANEOUS in the rod frame, even though they are simultaneous in your frame, so you are NOT measuring the time it takes to make the one-way trip in the rod frame that way.

    You CAN do the analysis including failure of simultaneity, but in doing so you must include the fact that the clock on the right end of the rod is unsynchronized with the clock on the left end by an amount xv if you want to calculate the time taken in the rod frame for the trip.
     
    Last edited: Nov 12, 2008
  12. Nov 12, 2008 #11
    In trying to reintroduce myself to relativity over the past few years, I've come to the conclusion that most sources do not spend enough time on frames of reference as an introduction. I did not realize why some of my own perceptions were initially off base until I read that Einstein spent considerable time studying frames of reference in his own preparation for developing his relativity theories. Sure enough, when I focused on frames and their meaning I was able to clear up many of my own questions.
     
  13. Nov 12, 2008 #12
    Thank you so much guys. I started to gain some idea why one way trip does not work, and what needs to be taken into consideration if we want to make one way trip work. I will need some time to study and understand it.

    I really appreciate your help!
     
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