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B Length contraction vs Space time

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  1. Apr 13, 2016 #1
    Does length contraction means the contraction of space time?
     
  2. jcsd
  3. Apr 13, 2016 #2

    Ibix

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    No. Length contraction can be seen as a result of viewing a 4d object at a different angle. It's closely analogous to the fact that you can slice a sausage perpendicular to its length and get a circular face, or at an angle and get an elliptical face. The sausage hasn't changed (and certainly spacetime hasn't), but the part of it you are looking at has.
     
  4. Apr 13, 2016 #3

    Nugatory

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    No. It cannot be that, because we all occupy the same spacetime yet we don't all observe the same length contraction.

    Length contraction is a natural result of the relativity of simultaneity. The length of an object is the distance between where its ends are at the same time, so when things that are at the same time for one observer are not at the same time for another observer, they will find different lengths.
     
  5. Apr 13, 2016 #4
    Looking at the twin paradox, the effect of the twin in acceleration is there that the twin on the spaceship does experience a time dilation. Right, I'll take some time to review this
     
  6. Apr 13, 2016 #5

    phinds

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    No, NOBODY ever "experiences" time dilation, It is something you see in objects that are moving relative to you but they see YOU as time dilated at the same time you see them as time dilated.

    You, right now as you read this, are MASSIVELY time dilated according to a particle in the CERN accelerator. Has your watch slowed down?
     
  7. Apr 13, 2016 #6

    Nugatory

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    The twin paradox is an example of differential ageing, a different phenomenon than length contraction and time dilation. One way of seeing that it is different from time dilation is to consider teh time dilation that is present in the twin paradix: at every point in the journey, the travelling twin is at rest relative to himself while the stay-at-home twin is moving; therefore the stay-at-home clock is the time-dilated one as far as the traveller is concerned. However, traveller is still able to correctly calculate that he will age less than stay-at-home - even though stay-at-home's clock is dilated throughout the journey.
     
  8. Apr 13, 2016 #7
    Hmm, the result of the twin paradox is that the person moving away from earth experience a slower time when traveling close to the speed of light. Therefore when the twin on earth ages 10 years, the twin traveling on the spaceship only ages 6 years by traveling toward a fraction of the speed of light. The same thing happens with gravitation time dilation as the person closer to earth experiences a slower time passing by then the one away from earth by a few nanosecond.
     
  9. Apr 13, 2016 #8

    phinds

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    No, the person on the spaceship does NOT experience slower time. He/she experiences time passing at one second per second just as does the stay-at-home. What happens is that the person on the spaceship takes a different path through space-time and therefore experiences fewer ticks of his one-second-per-second clock than does the stay-at-home.

    EDIT: and by the way, this is one of the most confusing things when you first start to look into special relativity so you're in good company not getting it right away.
     
  10. Apr 13, 2016 #9
    Well yes neither of the twins would experience a slower time, it feels shorter for one 6 years, and longer for the other one 10 years. I am thinking that speed causes space time to contract through length contraction matches the fact that the person on earth with a more compact space time has a time dilation. If gravity increases with a more compact space time the result would be more prominent
     
  11. Apr 14, 2016 #10

    Ibix

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    As we have said several times, nothing happens to spacetime in the scenarios we are discussing.

    Both length contraction and time dilation are effects that an observer observes happening to objects that are in motion relative to them. This is a symmetric effect - two observers in relative motion measure the same thing happening to the other. So it cannot be due to "spacetime contracting". Both observers would have to claim that spacetime was contracted for the other.

    The twin paradox is showcasing a different, but related, phenomenon. There is still no spacetime contraction involved. It turns out that the elapsed time showing on your wristwatch is a measure of "distance" travelled through spacetime (it's actually called the "interval"). In other words, your wristwatch measures "distance" through spacetime in a way analogous to the way the odometer in a car measures distance through space. The different ages of the twins comes from the fact that they took different routes through spacetime. This does not involve any kind of change to spacetime. It's essentially no different from the fact that the straight line distance between two points is different from the distance between them travelling via a third - one side of a triangle is not the same length as the other two put together.
     
  12. Apr 14, 2016 #11
    Well what Wikipedia says on time dilation is that "The laws of nature are such that time itself (i.e. spacetime) will bend due to differences in either gravity or velocity – each of which affects time in different ways." I'm still skeptical about how velocity bend time, I'm not sure if it's mass related
     
  13. Apr 14, 2016 #12

    Ibix

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    That kind of thing is why you should be wary of Wikipedia as a source. Velocity does nothing to spacetime or mass (old textbooks will disagree about mass, but so-called relativistic mass has been a deprecated term since the 1970s, pop sci presentations notwithstanding).

    Assuming you are after a non-mathematical look at relativity, Ben Crowell's book Relativity for Poets is a good source. It's freely available from www.lightandmatter.com
     
  14. Apr 14, 2016 #13
    This sentence makes it seem as though one person can travel closer to the speed of light than another. Instead there is relative motion between two people. Either one could claim that the other is the one moving closer to the speed of light, or just the opposite. Either one could claim that he is the one moving closer to the speed of light. It's a meaningless assertion either way because as you chase after a light beam you find you make no more progress in catching it than does the other person.

    When the travelling twin moves away from the staying twin, the staying twin moves away from the traveling twin. The situation is symmetrical and each will observe the other's clock as running slow. The same is true when their relative motion causes them to get closer to each other. The only time the situation is not symmetrical is when the traveling twin changes direction, and it is this part that's responsible for the difference in proper times experienced by the twins.

    It is one thing to say that each twin's proper time differs from the other's dilated time. This always involves elapses of time between events that are spatially separated in at least one their rest frames. It is quite another to say that their proper times differ from each other. This always involves elapses of time between events that are not spatially separated in either rest frame. The former has nothing to do with the difference in their ages whereas the latter has everything to do with it.
     
  15. Apr 14, 2016 #14

    PeroK

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    In terms of velocity and gravity:

    If two observers are travelling with respect to each other, what does spacetime care about that? Spacetime remains flat and unchanged, but the two observers have different perspectives on it.

    If a large mass is occuping space, on the other hand, spacetime itself curves and this curvature can be detected by any observer.
     
  16. Apr 14, 2016 #15

    Nugatory

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    The sentence is just plain flat-out wrong.

    This might be a good time to remind everybody that wikipedia is not an acceptable source at Physics Forums, and stuff like this is the reason why.
     
  17. Apr 14, 2016 #16

    russ_watters

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    I thought it was both RoS and time dilation? What do you call it when you travel to Alpha Centuari at 90% of the speed of light and measure the distance traveled to be 2 LY (if I did that math right...).
     
  18. Apr 14, 2016 #17

    Nugatory

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    It's hard to separate the two - but I can say that the distance between earth and Alpha Centauri is pretty much by definition the distance between where the earth is right now and where Alpha Centauri is right now. That definition works whether I'm at rest relative to them or not, and yields the appropriately contracted length if I am not.

    Travel time only comes into it when we consider how long an object (not necessarily at rest relative to me) would take to traverse that distance.
     
  19. Apr 14, 2016 #18

    Ibix

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    My usual example is how do you measure the length of a beetle? You just stand it on a ruler and read off the position of its head and the position of its tail. If the beetle is walking, though, that procedure will not get you its length if you don't make the measurements at the same time. In that example, failing to measure simultaneously could just be sloppy experimentalism. But the relativity of simultaneity means that there is genuine, unresolvable, disagreement over what constitutes "at the same time" in different frames (and the beetle is moving in at least one of them), and that's where length contraction comes from. Observers at rest in the two frames use the same procedure to measure length, but because they disagree about simultaneity they get different lengths.

    Time dilation isn't directly relevant to this, although you can't build a symmetric picture of the world without invoking ot as well - you end up with an absolute rest frame.
     
  20. Apr 14, 2016 #19
    Isn't "an absolute rest frame" by definition the measurement of "proper length" with no distortion of observation via movement relative to the object (or distance) measured? So then the distance to Alpha Centauri or the length of a beetle is not changed by "how you look at" either in relative motion. How is the above wrong?
     
  21. Apr 14, 2016 #20

    phinds

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    "absolute rest frame" is an ambiguous term. Do you simply mean a frame of reference in which is an object is at rest? If so, then leave out the "absolute" since it adds nothing but confusion. If on the other hand, you mean an absolute frame of reference against which anything's motion can be measured, then that is an incorrect concept as there is no such thing.
     
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