Observer O is located in an infinite space and is bombarded by particles (shown in blue) coming from infinity and moving along straight lines in random directions. This "rain" of particles is isotropic in its directions. At large distance from the observer there is a region of scatterers S shown in red. The region contains many scatterers of the blue particles. The scatterers are not isotropic. However, their orientation is random. Can the observer O detect the presence of the region S in the space by simply observing the distribution of particles arriving at O from different directions?
Note: You may assume that the scatterers are "dilute", i.e. a particle is not scattered more than once.
(10/04) A solution to the problem has been submitted (7/7/04) by John G. Florakis, from University of Athens, Greece (e-mail sniper_700@hotmail.com). You can see the solution in the PDF file. However, we feel that a simpler solution, less specific, and relying on basic principles of mechanics should be possible.
The answer: The region should be undetectable.
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