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About confusion of lenght contraction, and possiblity of length expansion

  1. Sep 20, 2011 #1
    hello people.......

    i have a doubt regarding Lorentz length contraction................
    according to what he described, the length of a body measured in a moving frame appears shorter as compared to the one taken by an observer at rest........if a train moving with uniform relativistic velocity , is thought of and its length is measured by the observer outside the train at rest with rest to the ground and the moving one, and compared in cases considering the direction of train or light............
    the measurement by the observer in train is taken with the help of a torch in his hand and a mirror placed in the side facing him..... that is, same as the direction of motion of the train......... in this case light will have to move larger distance as compared to when train was not moving, to get reflected back..... but the distance it will have to travel backward would be smaller because the train would have covered some distance in the time it used to complete the first half of the motion and then that during its motion.......

    so in the two different directions, the length of the train would be different as distance is velocity * time.............(here i didn't consider the effect of time dilation..... because there again i think it should not just slow down but also speed up.......)
    so along with contraction , expansion of length is also possible...............
    if it were not to be possible both the ways then an observer moving in an inertial frame taking measurements of length of , say , a rod with very small diameter, and somehow communicates with someone at rest with respect to ground to compare the values of length........ he will be clearly able to note that because his measurements of length are small....... then due to length contraction he must be probably moving in the direction of the length element of the rod..............
    but this sounds against the principle of relativity........... that a moving body is aware that it is moving...... with the help of exchange of information about length contraction.............
    so please tell me, what i have been thinking, does that make sense and is it that length appears to expand too for a moving observer...........
    and if yes , is it applicable to time as well...........
    thanks in advance........
  2. jcsd
  3. Sep 20, 2011 #2


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    You are correct, no observer is aware of any length contraction or time dilation, they are only aware of it for observers moving with respect to them, and, because it is a reciprocal relationship, those other observers would be aware of length contraction and time dilation in the first observer. But it is always length contraction, never length expansion and always time dilation, never time compression. Also, each observer who is not accelerating will measure the round-trip speed of light to be the same value c using a light source, a mirror some measured distance away and a timing device to measure how long it takes for the light to go from the source to the mirror and back to the source.
  4. Sep 20, 2011 #3


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    Let me add something to what I said earlier:

    Actually, Lorentz believed that a body moving with respect to a supposed ether rest state would be contracted along the direction of motion. He also believed that light traveled at c in any direction (one-way) only with respect to this ether. He used length contraction and time dilation to explain why a moving observer would measure the round-trip speed of light to be c, even though, he thought, it really wasn't. He also realized that it was impossible to measure the one-way speed of light because that would identify the ether rest state which, of course, scientists of the time were coming to realize that even if it existed, it was impossible to identify this absolute rest state.

    When Einstein came along, he postulated that any observer, as long as he was not accelerating, could assume that the one way speed of light was identical to the two way speed of light. This means that he would be just like an observer at rest with respect to Lorentz's absolute ether rest state. This also means that he could assume that he was not being length contracted or time dilated, but rather all other moving observers would be.

    So what Einstein did was turn around the concept of what it means to be at rest so that any inertial (non-accelerating) observer could consider himself to be "normal" and all others, moving with respect to himself were the ones that were affected by length contraction and time dilation.
  5. Sep 22, 2011 #4
    i am really confused...........
    can you just mention in a sentence what you were saying.........please........
    then i guess i would try and allow this stuff enter my head........
    actually, you have said it is only length contraction............ but what i believe is that if length measured by a moving observer appears to contracts, then comparing the result of measurements by the two observer with continuation of further readings, would make them grasp who is moving and in which direction................is this what you agree to?..........
    if yes, the variation in their readings would suggest that either of them is moving, if they have any idea about length contraction.............and clearly the one who observed a shorter length must be moving along the direction of length........

    so to ensure that the principle that a moving body should never be able to guess if it is moving or the one with respect to it, is moving.......... i thought may be something like expansion should be the case...............

    so does it make sense?.......
  6. Sep 22, 2011 #5


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    No. If I am standing next to the tracks watching the train go by at 0.866c, I will see the train as length contracted by 1/2. In other words, if someone on the train measures the train to be 1 mile long, I will measure it to be 1/2 mile long. Conversely, according to someone on the train, it is the tracks and 1 that are length contracted. A length of track that I measure to be 1 mile long, he will measure to be 1/2 mile long.

    This preserves the Principle of Relativity since each of us measures the other as length contracted. The trick is that you can't consider length contraction just by itself. You have to include time dilation and the Relativity of Simultaneity, to see why this is the case.
  7. Sep 22, 2011 #6


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    I thought my first sentence to you explains it all very well:
    No, I don't agree to that. Even when they compare each other's measurements, as long as they continue in their relative motion, they will not be able to grasp who is moving and who is not.
    It might make sense, but it is not true. Remember, even a "moving" body can consider himself to be at rest and everything else to be moving past him. When he measures the length of a ruler moving with respect to him, aligned along the direction of motion, it will be shorter than a ruler he is carrying with him. And someone traveling with that ruler will determine that the first person's ruler is shorter compared to the one he is carrying with him. I don't know how to make it any clearer.
  8. Sep 23, 2011 #7
    Something like expansion would make it possible to detect "who is moving" in just the same way as you proposed that it may be detected with contraction...

    The clue is in relativity of simultaneity and time dilation. If you only look at length contraction, then you mislead yourself about the total effect except for those special measurements in which time effects don't play a role. Only all those effects together make that the total effect is symmetrical. And because accounting of three effects is rather complex, you cannot expect to fully grasp it with just words - you will likely need to make drawings and do calculations to fully understand how it works. At least, that's how it went for me. :tongue2:
  9. Sep 24, 2011 #8
    you have said, someone at rest with rest to the ground observing a moving body will also find its length shortened and the one moving find the length contracted of the things otherwise stationary.......
    but wasn't Lorentz said that the length measured by moving body seems contracted, vL= L0, where v is gamma...the reduction factor in terms of V and C,and L0 is the length seen by observer at rest..........

    please tell me what i am going wrong with here.......?
  10. Sep 24, 2011 #9
    true, after pondering about this train situation, i understood it had effects of time dilation coupled.... and problem of trying to be simultaneous.........
    can you please provide me an example describing length contraction without the effect of time dilation and simultaneity involved.....

    thanks for letting me take a note of my mistake. .. . .. . . . . . . . . ..
  11. Sep 24, 2011 #10
    Not positive what you are asking, but length contraction cannot happen without time dilation...If you want to forget about time dilation, then just consider lengths of objects in relative motion.

    What IS difficult to comprehend is that it is the speed of light that is measured to be the same by all observers in constant relative motion.....neither time nor distance is fixed as would be expected from our everyday low speed experience. So to "think" in relativistic terms you need to leave behind a few everyday precepts...that length and time are fixed..... you would otherwise take for granted. The new paradigm: the speed of light is the only entity that is fixed for all observers. It's not that all this makes "common sense"...it's that it has been experimentally verified and so it is acepted as correct.
  12. Sep 24, 2011 #11


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    Lorentz did not say that a moving body would measure its own length to be contracted, he said that a body moving with respect to the absolute stationary ether would be contracted (along the direction of motion) but so would its measuring device so the two effects would cancel out making it impossible to notice the contraction.

    In terms of one observer measuring the contraction of a moving body, it is the normal length divided by gamma (not multiplied) because the Lorentz Factor, gamma, always has a value greater than 1.
  13. Sep 24, 2011 #12


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    Maybe you could benefit from someone else's recent question about https://www.physicsforums.com/showthread.php?t=530141". If you take a look a that thread and look at the animations that I reference there, you will be able to see how time dilation, length contraction and relativity of simultaneity all work together to make each observer have the same experience even though they are moving with respect to each other.
    Last edited by a moderator: Apr 26, 2017
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