Re: A paradox?

[Ken Caviness <caviness@southern.edu>]

Je 03:11 PM 24.02.98 -0800, Leigh Palmer skribis:

> > Sorry, I never learned about the Lenz-Thirring effect, or about the=
 Terrell
> > effect. I just recall that object cotract relativistically in the=
 direction
> > of motion by the factor of sqrt(1-v/c). Thus a rapidly moving sphere will
> > become a flat ellipsoid of revolution in my stationary frame of reference.
>
> That will be true of the instantaneous locus of points on the surface
> of the moving sphere when referred to the stationary frame. However,
> because of the limit of lightspeed, the appearance of the sphere will
> not be the same as its instantaneous shape in that frame. Light coming
> to the observer from a greater distance (the parts of the object more
> distant from the observer) will seem to come from a place the object
> occupies later than that light which comes to the observer from a
> lesser distance (the nearer part of the object). The overall effect
> for a sphere is that it will appear to be spherical, but rotated on an
> axis perpendicular to the observer's line of sight and the sphere's
> direction of motion. This is called "Terrell Rotation".
>
> Leigh
>
> Terrell, J., "Invisibility of the Lorentz Contraction",
> Phys. Rev. vol 116 no. 4 pp. 1041-1045 (1959)

Yes.  To amplify slightly, the sphere is somewhat flattened by Lorentz=20
contraction, but in addition we see it as skewed because of time-of-
flight differences between light rays originating at different points=20
on the sphere.  The fun part is that a projection of the skewed=20
flattened ellipsoid is (for a distant observer) indistinguishable from=20
a projection of the original sphere!

Similarly a cube travelling at relativistic speed would be appear skewed=20
just enough so that one would see the same projection as if it had been=20
rotated.  The side facing us is foreshortened, we see the trailing side=20
due to skewing/time-of-flight-delays, and the two effects combine to yield=
=20
a visual effect similar to a rotation.  For a distant observer.

If anyone is interested, I can dig out other references which followed
Terrell's original article.  There are some very interesting results.

Ken

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