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Circular space contraction

  1. Jun 24, 2010 #1
    I have a curiosity. I do not have a degree in science (going to university later this year) so this should be very simple to follow. I'm looking for a refutation (preferably with words and not unnecessary equations), confirmation, maybe a link to this sort of stuff.

    I'm aware that as an object approaches C, stationary observers see it contract in the direction of motion. From the perspective of the object, space itself contracts in the direction of motion. The typical A-level physics question I would do would be a muon traveling at a percentage of the speed of light, and from that working out how long a 2km atmosphere would appear to the muon.

    Take something like this and have it be two-dimensional, circulating across a sphere. Or in a real example, something in orbit approaching the speed of light (and gravity to keep it there). It seems to me that since from space constantly being contracted in the direction of this thing's velocity (even if the velocity's direction is changing), the circumference of the sphere will likewise seem smaller. In other words, a satellite orbiting a sphere causes the radius of the sphere to shrink (relative to the satellite).
     
  2. jcsd
  3. Jun 24, 2010 #2
    There is no contraction in the direction perpendicular to the direction of motion, so, the radius will not appear contracted.
     
  4. Jun 24, 2010 #3
    Would you say it's at least oval-shaped?

    I'm looking for a better explanation for this.
     
  5. Jun 24, 2010 #4

    George Jones

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  6. Jun 24, 2010 #5
    Since the radius is not contracted what will the observer see?
     
  7. Jun 24, 2010 #6
    Yes, this is true for the radius pointing in the direction of the orbiting observer. But what about the radii which have coponents parallel to the instantaneous direction of motion of the orbiting observer.

    Of course the Penrose-Terrell rotation, a non relativistic effect, has to be taken into account if we wish to describe what we actually see.

    Matheinste.
     
  8. Jun 24, 2010 #7
    The Terrell-Penrose effect is a relativistic effect, it is a direct consequence of the Lorentz transforms.
    Spheres are invariant under the Terrell-Penrose effect , i.e, they appear as spheres. Spheres are exceptions in this respect. Here is an excellent source of information (in German)
     
    Last edited: Jun 24, 2010
  9. Jun 24, 2010 #8
    Let us for the present ignore PT rotation effect. Is it not the case that length contraction takes place on the radii which have components in the directions parallel to the instantaneous motion of the orbiting body.

    Matheinste.
     
  10. Jun 24, 2010 #9
    You brought it up, I explained to you that it is a non-factor for spheres.


    True. In the case of a ship orbiting a sphere different radii are seen under different angles. All the radii seen under an angle different from 0 or [tex]\pi[/tex] will exhibit some length contraction in the direction tangent to the orbit.
     
  11. Jun 24, 2010 #10
    That's all I wanted to confirm. Thanks.

    Matheinste.
     
  12. Jun 25, 2010 #11

    A.T.

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    Is it really a relativistic effect?

    The fact that you can http://www.spacetimetravel.org/bewegung/bewegung5.html" [Broken] is a consequence of the finite light speed, which was known long before Relativity.

    The only modification that Relativity adds to this optical illusion, is that the object doesn't appear stretched as well, because the Lorentz contraction cancels out the visual stretching due to signal delay.
     
    Last edited by a moderator: May 4, 2017
  13. Jun 25, 2010 #12
    The fact that something was know before a theory was developed is not an argument for excluding this as a phenomenon that can be explained by that theory.

    That is clearly a logical fallacy.
     
    Last edited by a moderator: May 4, 2017
  14. Jun 25, 2010 #13

    Ich

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    What you wrote is a fallacy, but you misrepresented A.T. He merely poited out that SR is not needed to explain the effect, he never said that SR can't explain it. I mean, SR includes that postulate, so it can definitely be applied.
     
  15. Jun 25, 2010 #14
    No he questioned if it is a relativistic effect with the argument that SR was not invented. (See the statement before the quote). Anyway is it not worth arguing over.
     
  16. Jun 25, 2010 #15

    Ich

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    Well, if relativity is not needed to explain it, you'd hardly call it a relativistic effect, would you?
     
  17. Jun 25, 2010 #16
    As I understand it the PT effect is caused by light form different parts of the observed moving object reaching different parts of the observing mechanism at different times. A purely classical geometric optical effect which does not require SR to explain it.

    If anyone could show me the SR explanation I would be interested.

    Matheinste.
     
  18. Jun 25, 2010 #17
    The website I cited has some papers attached to it. The papers invoke SR in the explanation. If you wish, I can write for you the explanation of the very funny looking spoked wheels on their website. The explanation definitely requires SR
     
    Last edited: Jun 25, 2010
  19. Jun 25, 2010 #18
    I'll take a look later. Thanks.

    Matheinste.
     
  20. Jun 25, 2010 #19

    A.T.

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    No, my argument was that the optical effect of apparent rotation can be explained classically.

    You need SR to predict the physical shape of the moving object (Lorentz contraction). But the optical distortion due to signal delay is a classical effect. The final visible shape is of course a result of both.

    The reason for my nitpicking: Actual relativistic effects are often wrongly assumed to be effects of signal delay. Therefore I think it is important to keep those apart.
     
    Last edited: Jun 25, 2010
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