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Re: Relativity



The appearance of extended objects at relativistic speeds is a *very*
stick problem. You must not only consider the Lorentz contraction but
also the fact that light from different parts of the object has to
travel different distances. There is a brief discussion of some of
the issues involved (in the form of a problem) in Taylor and
Wheeler's Spacetime Physics (exercise 3-17). There is a more complete
treatment in Taylor's textbook Introductory Mechanics. There is also
a brief discussion at an elementary level in Jones & Childers' intro
physics text Contemporary College Physics. There are some interesting
pictures of the real appearance of a train at various speeds.

The classic work on this subject was that of Terrell in 1959 (in
American Journal of Physics if memory serves), followed up by Scott
and van Driel in the smae journal in 1970.

The short answer to the first question is probably no. Recall that
there is more to an ellipsoid than just the major and minor axes. The
dimensions in between would suffer Lorentz contractions of
continuously varying amounts from large for parts of the ellipse near
the major axis to small for parts near the minor axis. This bits are
rather like the problem of a ruler tilted at an angle travelling at
relativistic speeds -- it appears to change size *and* rotate a bit.
Your ellispod would then change shape and rotate so that the new
major axis is *not* along the relative velocity vector. Now you can
add complications from the above-mentioned time delay effect.
Yuckaroo.

As for the second problem, I really have no idea. My gut feeling is
that it would take on an asymmetric appearance, with the side
rotating toward you more heavily contracted than the side rotating
away (presuming, of course, that it is travelling toward us so that
we view it in the plane of the rotation). However, that is likely a
very complicated problem involving Lorentz transformation of
differential volume elements.


A student has asked two question that I cannot answer and would appreciate
some help on:

1. If an ellipse is travelling at relativistic speed in a direction parallel
to its major axis, could it appear to a staionary observer as a perfect
circle? It would seem that the major axis could contract to equal the minor
axis but if the distance between the foci is also shrunk proportionally is it
not still an ellipse because they are not coincident?

2. If a disk moves past me at relativistic speed while it rotates about its
center at a constant angular velocity, what shape will I see? Since the top of
the disk is moving at a different speed relative to me than the bottom of the
disk, hwo does the different amount of contraction distort the disk from my
point of view.

Thanks for any help on these.

David Abineri


Paul J. Camp "The Beauty of the Universe
Assistant Professor of Physics consists not only of unity
Coastal Carolina University in variety but also of
Conway, SC 29528 variety in unity.
pjcamp@coastal.edu --Umberto Eco
pjcamp@postoffice.worldnet.att.net The Name of the Rose
(803)349-2227
fax: (803)349-2926