Reflective Special Relativity Paradox.

A well known consequence of Einstein's Special Relativity theory is that objects contract in the direction of their motion by a factor of:
(1 - V2/ C2)  ½

Where V is the object's velocity and C is the speed of light.

Assume that an object is whizzing by us at the gigantic velocity of 934,660,377,934 KPH = 259,627,882.759 KPS = 0.866 C. Everything about this object looks weird to observers watching the object zoom by. Clocks on the object are running at half speed, the object seems twice as heavy as when it was at rest, and it is foreshortened by a factor of two in it's direction of motion. These oddities are well established experimentally.

From the point of view of an observer on the object, however, everything on the object appears and acts normal, but the time and space of the rest of the universe appears heavier, slower and foreshortened by a factor of 2.

If this is your first exposure to special relativity, you're probably in a state of disbelief. You'll have to go read the relativity FAQ cited below. See 'ya when you get back.

If you're already familiar with special relativity, you're thinking, so what? This has been established for years. I understand it.


Then you'll have no trouble explaining the following:

Assume that the object mentioned above is a reflecting telescope, and that the object is headed at Sirius, the brightest star in the sky. Before the telescope starts its journey, the observer traveling with the telescope carefully focuses it on Sirius. She and her telescope then accelerate to 87% of the speed of light, and all of the above relativistic effects occur. The telescope is foreshortened, so the tube is only half or it's original length. The mirror is also foreshortened, so it's focal length is twice its original length. An observer on the ground claim that the telescope can no longer be focused on Sirius. Our intrepid observer with the telescope claims that Sirius is still in focus.

Who is right? Why?

Newtonian diagram

(This should make for one complicated Lorentz diagram.)

There is an explanation. Once you've truly given up on this, or simply want to check your answer, Click here for a hint

1) For more about special relativity, and relativity in general, have a look at the UseNet Relativity faq