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Re: Special Relativity Question



At 1:55 PM -0700 2/4/00, Abul Kalam wrote:

(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 ?

There is no violation inherent here. A related effect does occur, and
it is not understood to be an anisotropy of space *per se*. The cosmic
microwave background radiation is anisotropic, consistent with the
picture that the solar system is moving relative to it. However there
is no way to tell that the CMBR is not moving with respect to us; the
phenomena are indistinguishable. There is a certain emotional
asymmetry, I'll grant you. This is an "Everybody's out of step but my
Johnny" cachet to the whole picture, but the laws of physics are still
Lorentz invariant.

The apparent rotation (Terrell rotation) suggested here to resolve
this question is not relevant.

(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 ?

If they move at, say, 0.9 c the velocity with which they will be
observed* to be separating will be SQRT(vA^2 + vB^2) which, I believe,
is what you mean by the Pythagorean theorem. There is nothing wrong
with this velocity being greater than c.

Leigh

* "Observed" in this case will involve some calculation because the
objects will only be seen by the observer with light-delay.