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What is the real meaning of lengh contraction of SR

  1. Mar 16, 2012 #1
    Assume a spherically symmetric transparent objects relative to the observer high-speed motion, what the observer will see?

    1, a discus (one dimension of contraction)
    2, a olive football (two- dimensional of contraction )
    3, a narrowing of the sphere (three-dimensional at the same time contraction)
     
  2. jcsd
  3. Mar 16, 2012 #2
    The observer will measure the sphere to be length contracted in one dimension parallel to its motion. The observer will see the sphere as a sphere (e.g. if he takes a photograph). This is a peculiarity of spheres due to their symmetry and the optical illusion caused by light travel times, but if we had another 3D object that does not have rotational symmetry such as a rectangular box, the observer will both measure and see the object to be length contracted along its axis parallel to its direction of travel.

    In a bit more detail, a relativistically moving object appears visually to be rotated. For a rectangular object the rotation is obvious. For a sphere, the sphere is length contracted and physically has the shape of an M&M or more technically is an oblate spheroid. When the spheroid is optically rotated its silhouette becomes a circle and gives the impression of still being a sphere, if you do not look too closely at the surface details which give the game away. Some people falsely claimed that this was proof that length contraction did not really occur.
     
  4. Mar 16, 2012 #3

    ghwellsjr

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    Excellent answer, yuiop, but you will note it is not one of the options that timeanalyser gave in his multiple choice question. He should have provided option 4, none of the above. I'll bet your answer was a complete surprise to him.
     
  5. Mar 16, 2012 #4
    1, this is a transparent sphere ,so it will not be seen as a sphere(but real oblate spheroid).
    you can easily distinguish the difference.
    2, Imagine a laser beam along the running track,what will happen? if it turn to a real oblate spheroid, the light will refraction, but it is inconceivable, because if there are 2 observers standing on both side at same time , will the light appear two lines?

    so i don't believe that it will turn to a oblate spheroid, i think it is a shrinked ball.
     
    Last edited: Mar 16, 2012
  6. Mar 16, 2012 #5
    No observation can be proved that existence of the oblate spheroid stars, but if you tell me that moving object appears visually to be rotated, you should explain #4-2 first.
     
    Last edited: Mar 16, 2012
  7. Mar 16, 2012 #6
    You can measure that the moving sphere object is an oblate spheroid by having two laser gates across the path of the sphere, that are closer together than the diameter of the sphere. When the sphere is moving at relativistic speeds relative to the gates, it is possible that there will be an instant when the oblate spheroid is between the two gates without breaking either of the beams proving that the length contracted sphere was occupying a space that is less than its diameter.

    As for #4-2 you will clarify the scenario you have in mind a bit better perhaps with a sketch. Bear in mind that you will have to deal with relativistic effects on lens shape, refraction index and aberration. While not totally intractable if you simplify the scenario, you should be aware it is not completely trivial at this level.

    As for a moving object appearing visually rotated, this is a well known and accepted result. Look up Penrose-Terrell rotation for references and explanations.

    Also, just in case you are not aware, relativistic objects do not actually physically rotate due to Penrose-Terrell rotation, it is just how things appear visually.
     
  8. Mar 16, 2012 #7
    I think that taking a photograph means to measure something.

    Instead of "measure" I would rather say 'deduce by taking into account the speed of light'.
     
  9. Mar 16, 2012 #8
    1, No, i don't think so. two laser gates across the path of the sphere just prove that lengh contraction is correct but not one-dimension lengh contraction is ture. if the physics reality is 2 or 3-dimensions lengh contractions , how the 2 laser gates can prove?

    2,you can image that the spheres come from afar, the material is total reflection, it is easy to konw that if the sphere turn to oblate spheroid and look like turns angles, the laser will turn to observer's side just bucause he stand on this side. so if there are 2 observers standing on both side, Is it will appear 2 laser reflection lines?
     
  10. Mar 16, 2012 #9
    I was trying to make a distinction between:

    i) Local measurements made simultaneously, using clocks and rulers which do not involve light travel times

    and

    ii) Remote measurements that are assembly of events that did not happen simultaneously in the observers rest frame. A photograph is such a measurement.

    I am also trying to make a distinction between an optical effect and a physical effect. If I look at an object through a magnifying glass it appears optically to be larger but the magnifying glass does not make the object physically larger. Of course I concede that than an optical effect is a part of physics and therefore could be called a physical effect but I think we could go around forever with these semantics. I can only hope that you guess the gist of my meaning from the context.

    When I said measure I meant "deduce by comparing the coordinates of events that happened simultaneously" and if we have local observers located at each event with synchronised clocks we do not need to take the speed of light into account. Of course we have to make certain assumptions about the speed of light in order to to synchronise the clocks in the first place but that is a different matter.
     
  11. Mar 16, 2012 #10
    OK we can send the sphere down a long tube which has the same diameter as the sphere and sensors all the way along its length that detect whether or not the sphere is touching the tube at its cross section. SR predicts that the cross section of the sphere will remain in contact with the side of the tube and will not shrink in the axes orthogonal to the direction of motion. More simply we could try to pass the the sphere through a hole that has a smaller cross section than the sphere. Relativity predicts that the sphere will not pass through the hole without damaging it for any relativistic speed.

    If you have relativistic length contraction in the orthogonal directions a paradox appears. Imagine two rings of equal diameter when at rest wrt each other. When they are travelling towards each other with their axes of rotation aligned with each other ring A might consider ring B to have its diameter length contracted and ring B might consider ring A to have its diameter length contracted. Which ring passes inside the other? Obviously they cant simultaneously be smaller than each other and so physical orthogonal relativistic length (width?) contraction is logically impossible.

    Still not clear what you are getting at here. Are you saying that the laser beam is aimed off centre of the advancing spheroid so that it is reflected off to one side differently to how it would reflect if the sphere physically remained a sphere? Not sure why you conclude that there will be two reflection lines either. Are you saying that there are as many reflection lines as there observers. If so that is partly true. The paths of light rays are different in different rest frames and therefore observer dependent. Also, purely visual observations are observer dependent. An observer standing far away from you sees you as smaller than an observer standing nearer you, but your proper height has a physical meaning that is observer independent.
     
  12. Mar 16, 2012 #11
    1. in fact ,I used to think the length of the contraction of the SR is just direction of movement. but now i think the length of contraction is about total moving coordinate system.

    2,I am sure that the relative motion is the movement of the two universes(time-space system). so there are not any paradox appears.

    3,if the sphere looks like a oblate spheroid and turns angles, then according to the law of reflection, the light will be reflect to the observer side. because this kind of rotation just bucause the observation of the observer,so if we have more obervers there,each one will see the different scene. then the paradox is everyone will see the different angles of the reflected light at the sane time.
     
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