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(1) My colleague, who is a mathematician by vocation but quite
knowlegeable about and interested in much of physics, is intrigued by a
Special Relativity question : A fast moving object in space (v ~ c )
would see celestial objects crowding in one direction over another, such
as a driver in a rain would see the rain come down at an angle.
According to Special Theory, laws of physics are the same in all
inertial frames, but in this case, the property of isotropy of free
space is changed for some inertial frames at higher velocities. Does
this apparent incongruity violates the first postulate of Special
Relativity ? I suggested that in Doppler Shift, a similar thing is
noticed when various frequencies are heard, but that, by no means,
violates the first postulate of special relativity. What do you suggest ?
(2) His second special relativity question : Two objects, A and B, move
near the speed of light along x and y-directions, as those speeds are
measured by an observer, C, at the origin of co-ordinates. Then,
according to observer C, the objects A and B are moving away from each
other with a relative velocity of 1.414c. Is Pythagorean theorem
applicable in this case ?
- Abby